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Measuring public preferences in France for potential consequences stemming from re-allocation of healthcare resources
Journal Pre-proof Measuring public preferences in France for potential consequences stemming from re-allocation of healthcare resources Nicolas Krucien, Sebastian Heidenreich, Amiram Gafni, Nathalie Pelletier-Fleury PII:
S0277-9536(19)30770-1
DOI:
https://doi.org/10.1016/j.socscimed.2019.112775
Reference:
SSM 112775
To appear in:
Social Science & Medicine
Received Date: 17 May 2019 Revised Date:
16 December 2019
Accepted Date: 20 December 2019
Please cite this article as: Krucien, N., Heidenreich, S., Gafni, A., Pelletier-Fleury, N., Measuring public preferences in France for potential consequences stemming from re-allocation of healthcare resources, Social Science & Medicine (2020), doi: https://doi.org/10.1016/j.socscimed.2019.112775. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd.
Cover page Manuscript number SSM-D-19-01573R2 Title Measuring public preferences in France for potential consequences stemming from re-allocation of healthcare resources List of authors Nicolas KRUCIEN(1) Sebastian HEIDENREICH(1) Amiram GAFNI(2) Nathalie PELLETIER-FLEURY(3) (1)
Patient-Centered Research, Evidera Ltd, London, United Kingdom Centre for Health Economics and Policy Analysis, Department of Clinical Epidemiology and Biostatistics, McMaster University, Hamilton, Canada (3) Centre de Recherche en Epidemiologie et Santé des Populations, Université Paris-Sud, UVSQ, INSERM, Université Paris-Saclay, Villejuif, France (2)
Corresponding author Nicolas KRUCIEN Patient-Centered Research Evidera Ltd The Ark 201 Talgarth Road London W6 8BJ United Kingdom Tel: +44 20 8576 5000 Email: [email protected] Acknowledgments We thank all participants who took part in the study.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
Abstract When deciding which new programme to implement and where the additional resources, if needed, will come from, the decision makers need to accommodate the uncertainty of the potential changes in population health and medical expenditures that can occur. They also need to determine the value of these potential changes. The objective of this study is to identify a public valuation function measuring how the public values changes in population health and medical expenditures when healthcare resources are re-allocated. We report the results of a choice experiment conducted in March 2016 in a representative sample of the population living in France (N=1,008). The main results indicate that the public is more sensitive to changes in population health than changes in the level of medical expenditures. There is a non-linear valuation of these changes with evidence of asymmetric preferences and non-constant marginal sensitivity. The public gives 1.4 times more weight to decrease in population health than for the same-size increase. The public becomes less sensitive to marginal changes in population health as the level of changes increases. In a simulation study of 5,000 resource allocation decisions, we show that non-linearities in public valuation of population health and medical expenditures matters. The linear and non-linear public valuation functions were associated with respectively 50.1% and 28.1% of situations of acceptable outcome of the reallocation of resources. The level of agreement between these two functions was moderate with a Kappa coefficient of 0.56, and the probability of agreement was mainly driven by the distribution of net changes in population health. This study provides a method and an estimation of a public valuation function that describes the preferences (or values attributed) for every potential outcome stemming from the reallocation of healthcare resources. The results show the importance of measuring such function rather than assuming one. Keywords France; Stated preferences; Choice experiment; Choices modelling; Resources allocation; Economic evaluation
1
1
1: Introduction
2 3
If healthcare budgets were unlimited, the most effective treatments could be adopted. However,
4
resources allocated to healthcare are scarce, hence health policy decision-makers (hereafter decision
5
makers) need to decide how to best allocate them. Resources scarcity can occur in different contexts
6
(i.e., fixed budgets, shrinking budget with less resources allocated to healthcare, growing budget with
7
more resources allocated to healthcare) as long as the total amount of resources available is not
8
sufficient to support the implementation of all the most effective treatments. As a result of scarcity,
9
decision makers need to determine where the resources should come from to fund the implementation
10
of new treatments to replace or complement existing treatments. For example, in the case of a fixed
11
budget, decision makers may decide to cancel existing treatment(s) in order to free up resources to
12
implement the new treatment(s). In the case of a growing budget, because not all new treatments can
13
be implemented, decision makers would still need to decide which new treatment(s) to implement and
14
which ones not to implement.
15 16
The decisions to allocate healthcare resources (hereafter allocation decisions) are challenging because
17
they typically require to trade off potential health gains for patients who will benefit from the new
18
treatment against potential health losses for those who will see their current treatment being cancelled
19
or replaced (or potential new treatment not adopted). In this context, decision makers need to consider
20
the opportunity costs of their decisions. In a world where full information about all the potential
21
programs for cancellation is not available, a second best option is to “ensure that the value of what is
22
gained from an activity [e.g., implementing the new treatment] outweighs the value of what has to be
23
sacrificed [e.g., cancelling a different treatment]” (Williams, 1983; page 63).
24 25
Cost–effectiveness analysis (CEA) is widely advocated as a tool to inform this allocation decision in a
26
way that maximizes the health benefits produced to the population from the available resources. The
27
analytical tool of CEA is the incremental cost-effectiveness ratio (ICER), which is compared to a
28
threshold value (λ) to determine whether the new treatment should be implemented. Assuming that 2
1
healthcare resources were efficiently used, this λ should in principle correspond to the ICER of the
2
last treatment adopted (Weinstein & Zeckhauser, 1973) and would then correspond to the shadow
3
price of the budget constraint. However, this approach would lead to an optimal use of healthcare
4
resources only under strong assumptions of perfect divisibility and constant returns to scale of all
5
programs (Gafni & Birch, 2006; Birch & Gafni, 1992; Gafni & Birch, 1993). Birch & Gafni (B&G)
6
have suggested an alternative approach which relaxes these two assumptions. The differences are: (i)
7
it does not require to subscribe to the assumptions of perfect divisibility and constant returns to scale,
8
and (ii) it does not require the use of an ICER and cost-effectiveness threshold. This approach
9
requires the identification of the source of the additional resource requirements for the new program
10
and bases the recommendation regarding the adoption of the new program on a direct comparison of
11
the total additional benefits produced from the new program with the total benefits forgone. In doing
12
so it ensures, that if followed and under conditions of certainty, “the value of what is gained from an
13
activity outweighs the value of what has to be sacrificed” (Williams, 1983; page 63).
14 15
In the past two decades it has been recognized that both costs and effects of all programs are
16
stochastic. The B&G approach has been extended to account for the uncertainty in costs and effects
17
of re-allocating resources (Sendi et al, 2002). Visually, it takes the form of a decision-making plane
18
(DMP) allowing to describe all the possible potential outcomes stemming from resource reallocation
19
due to the uncertainty. In contrast, the cost-effectiveness plane (CEP) describes only the difference in
20
health outcomes (E) and costs (C) of a candidate treatment for implementation (A1) with a reference
21
one (A0) using measures of incremental effectiveness (∆E = E − E ) and increment costs
22
(∆C = C − C ). Those measures are used to compute the ICER and compare it to the ICER
23
threshold. The DMP “extends” the CEP by also comparing a candidate treatment for cancellation
24
(B1) with another reference treatment (B0) (i.e., the explicit consideration of the source of additional
25
resources), leading thus to another set of incremental effects (∆E = E − E ) and costs (∆C =
26
C − C ). The DMP can also be extended to the case where more than one existing treatment have
27
to be replaced in order to free up resources for the implement of the new treatment. All these
3
1
incremental measures are used to compute net changes in health outcomes (∆E = ∆E − ∆E ) and
2
costs (∆C = ∆C − ∆C ) which are then mapped into the DMP (Figure 1A). The DMP is divided into
3
four quadrants which will affect the allocation decision. Quadrant I (QI) describes situations where the
4
joint decision to replace A0 by A1 and B1 by B0 allows improving the population health (i.e., ∆E > 0)
5
and an overall lower level of medical expenditures (i.e., ∆C < 0). At the opposite, quadrant III (QIII)
6
describes situations where population health is decreased (i.e., ∆E < 0) and medical expenditures
7
increased (i.e., ∆C > 0). Quadrant II (QII) describes situations where both the population health and
8
level of medical expenditures are decreased (i.e., ∆E < 0; ∆C < 0). Quadrant IV (QIV) describes
9
situations where both the population health and level of medical expenditures are increased (i.e., ∆E >
10
0; ∆C > 0).
11 12
Assuming decision makers want to improve the health of the population from the available resources,
13
the decision to replace existing treatment(s) in order to free up resources for the implementation of a
14
new treatment should be made only if the final outcome {∆E; ∆C} will be located in QI. However,
15
this cannot be guaranteed because of the uncertainty in net changes which exposes decision makers to
16
the risk of dealing with a consequence that was not intended (i.e., the consequence of the reallocation
17
of the resources does not fall in QI). Visually this uncertainty takes the form of a joint distribution of
18
all potential outcomes in the DMP (Figure 1B). In order to assist the decision makers in dealing with
19
the uncertainty stemming from the allocation decision, Sendi et al (2002) suggested that decision
20
makers might use as a decision rule the following one: healthcare resources should be re-allocated if
21
more than 95% of the potential outcomes fall into QI.
22 23
Gafni et al (2013) noted that this decision rule may be too restrictive because it implicitly assumes
24
that all potential outcomes within the same quadrant are equally desirable (i.e., the rule ignores the
25
magnitude of the potential outcomes). It also assumes that all outcomes falling outside QI are equally
26
undesirable. The valuation of a potential outcome is likely to depend on both the specific quadrant
27
that it falls in (i.e., between-quadrant effect), and the exact location within the quadrant (i.e., within4
1
quadrant effect). In order to account for these between-quadrant and within-quadrant effects, and not
2
just the probability of where all potential outcome fall, one needs information about decision makers’
3
preferences for each potential outcome (i.e., net changes in ∆E and ∆C). This information can then be
4
used to help decision makers deal with the uncertainty of the final outcome by using a decision rules
5
which avoid the assumptions mentioned (e.g., proceed to re-allocation of resources only if expected
6
value of the allocation decision is positive). To the best of our knowledge such valuation function,
7
that describes the preferences (or value attributed) for every potential outcome in each quadrant of the
8
DMP, does not exist. The goal of this study is to illustrate how such function can be obtained.
9
Assuming that the decision maker is interested in public preferences for the potential outcomes of
10
resources reallocation, in this study we describe how such “public valuation function” (PVF) can be
11
measured.
12 13
In the present study we use a previously developed preferences-elicitation instrument (Krucien et al,
14
2018) to measure preferences for ∆E and ∆C of a representative sample of the French population.
15
When looking for the best PVF, we were also interested in investigating the likelihood of non-
16
linearities in public preferences, such as asymmetric preferences (i.e., higher sensitivity to negative
17
changes compared to same-size positive changes) and non-constant marginal sensitivity (i.e., marginal
18
sensitivity to changes increase/decrease with their magnitude). We used a non-linear specification of
19
the PVF and assessed its statistical performance in comparison with a linear specification. This
20
comparison showed that the non-linear PVF significantly outperformed its linear counterpart. In a
21
simulation study, we also compared the linear and non-linear PVFs in terms of the effect on the
22
decision regarding the decision to re-allocate of healthcare resources.
23 24
The remainder of this article is as follows: Section 2 explains the preference elicitation instrument and
25
how data was collected. Section 3 compares alternative functional forms of the PVF. Section 4
26
describes the simulation study. Section 5 discusses the findings and limitations of the study.
27
5
1
2: Experimental setup
2 3
2.1: Design
4
We conducted a choice experiment (CE) to measure how the public values net changes in health
5
outcomes (∆E) and costs (∆C). CEs are frequently used in health economics to investigate patients’,
6
public, and health professionals’ preferences for a wide range of topics (de Bekker-Grob et al, 2012;
7
Clark et al, 2014).
8 9
Following the concept of Healthy Years Equivalent (Gafni & Birch 1997; Mehrez & Gafni 1989), we
10
used changes in the “equivalent number of years in good health” to describe ∆E. ∆C was defined as
11
net changes in the level of medical expenditures (in euros). Based on our pre-test of the CE, attribute
12
levels were defined per person to make the values easier to understand by participants: ∆E = {-8; -4;
13
0; +4; +8}; ∆C = {-120,000; -60,000; 0; +60,000; +120,000}. These values represented the total net
14
change for the whole population affected divided by the number of people affected. Once multiplied
15
by the size of the population affected, positive values of ∆E and ∆C indicated an improvement in
16
population health and decrease (or no change) in the level of medical expenditures respectively. These
17
attributes’ levels were combined into scenarios describing potential outcomes stemming from the
18
decision to re-allocate resources. Every choice task included three choice options, with one option
19
describing a “neutral situation” (NS) with null net changes (i.e., ∆E = ∆C = 0), and the participants
20
were asked to choose their preferred option (Figure 2).
21 22
Twelve choice tasks were generated using a D-efficient design with Bayesian priors optimised for a
23
multinomial logit (MNL) model. The order of the twelve experimental tasks was randomised across
24
participants to mitigate the influence of order biases such as learning/fatigue (Savage & Waldman,
25
2008; Campbell et al, 2015). The order of the choice options within the tasks was also randomised to
26
mitigate the influence of decision biases associated with a left-to-right processing of the information
6
1
(Ryan et al, 2018). The participants were also asked questions about their socio-demographic
2
characteristics and understanding of the choice context.
3 4
2.2: Sampling
5
A commercially managed online access panel was used to recruit a sample of the population living in
6
France that is representative of the general population in terms of age, gender and geographical spread
7
(n=1,008). The survey was administered to the participants as an online questionnaire. The inclusion
8
criteria were to be older than 18 years and to be able to read the questionnaire. A descriptive analysis
9
of respondents’ personal characteristics can be found in Table 1.
10
The institutional review board (IRB00003888, IORG0003254, FWA00005831) of the French Institute
11
of Medical Research and Health has reviewed this project and attested that this kind of research did
12
not need an opinion of a research ethics committee according to the French law. Moreover, the project
13
was in accordance with the French Law concerning personal data protection at the time of data
14
collection.
15 16
2.3: Data quality
17
In addition to the 12 experimental tasks we included three non-experimental tasks to control the
18
quality of choice data: (i) one warm-up task (Task #1) to familiarise the participants with the task
19
format; (ii) one stability test (Task #14 as repetition of Task #1); (iii) one monotonicity test (Task
20
#15) with one option being superior to the others in terms of ∆E and ∆C. We also checked the quality
21
of the choice data by analysing variability in the choices. A respondent was identified as a “serial non-
22
participant” (SNP) if she always selected the neutral situation as most preferred option in all 12
23
experimental tasks. This absence of variability in the choices is an indication of low engagement in
24
the CE. Only 13 (1.3%) individuals were identified as SNPs, and it was decided to remove them from
25
the analyses as they don’t provide a meaningful information about underlying preferences for ∆E and
26
∆C (A sensitivity analysis of preferences including/excluding serial non-participants can be found in:
27
[INSERT LINK TO FILE [Online supplementary material]).
7
1 2
3: Modelling public preferences for ∆E and ∆C
3 4
3.1: Method
5
We estimate a public valuation function (PVF) from the CE data using a multinomial logit (MNL)
6
model (Train 2009). Given that net changes in population health (∆E) and medical expenditure (∆C)
7
differ in magnitude and direction, sensitivity to marginal changes is unlikely to be constant. Hence,
8
we suggest a function that can account for potential non-linearities in the valuation of ∆E and ∆C (Eq.
9
1).
10
∆ PVF = ρASC + β I ∆E
11
'
∆& β% δ% !1 − I ∆C #
∆ − δ !I − 1 ∆E # $ + '
∆& − −I ∆C $ + φ∆E ∆C + τ
(1)
12 13
∆ ∆& The I and I terms are two binary variables indicating whether the re-allocation of healthcare
14
∆ resources improves population health (i.e., I =1 when ∆Entj ≥ 0) and decreases medical expenditures
15
∆& (i.e., I =1 when ∆Cntj ≤ 0).
16 17
Regarding the model parameters, β1 and β2 capture the respondents’ preferences for a 1-unit change in
18
∆E and ∆C. To make the estimates more comparable, the ∆C attribute is rescaled by dividing its
19
values by 10,000, such that a 1-unit change in rescaled ∆C indicates an increase/decrease of medical
20
expenditures by 10,000 euros. We expected respondents to prefer a higher level of population health
21
(∆E > 0) and a lower level of medical expenditures (∆C < 0) (i.e., H1a: β1 > 0; H1b: β2 < 0). The α1 and
22
α2 parameters allow for non-constant marginal sensitivities. We expected respondents to become
23
marginally less sensitive to changes in both population health and medical expenditures (i.e., H2a: α1
24
< 1; H2b: α2 < 1). The δ1 and δ2 parameters allow for a change of preferences between positive and
25
negative changes in ∆E and ∆C. We expected individuals to give more weight to negative than same-
8
1
size positive changes (i.e., H3, : δ > 1; H31 : δ% > 1). The ρ parameter captures a systematic
2
preference for a situation of non-neutral changes. We expected individuals’ choices to be biased
3
towards the neutral situation (i.e., H4: ρ < 0). The φ parameters allows for an interaction between the
4
valuation of ∆E and ∆C. We expected preferences for ∆E and ∆C to be linked, and more specifically
5
we expect to observe a positive interaction effect (i.e., H5: φ > 0). As each respondent completed 12
6
choice tasks, we accounted for potential correlation in the data by specifying an additional error term
7
(τ ) which is normally distributed with null mean and standard deviation to be estimated (i.e.,
8
τ ~Normal<0, σ ?).
9 10
Starting from this general specification, it was possible to apply constraints to obtain more
11
parsimonious specifications. For instance, a linear and additive weighting of ∆E and ∆C (Eq. 2) could
12
be obtained with the following constraints: ρ = α = δ = φ = 0.
13 14
PVF = β ∆E + β% ∆C + τ
(2)
15 16
We determined whether allowing for non-linearities in the valuation of ∆E and ∆C improved the
17
modelling of the choices by comparing statistical performance of the PVFNOLIN and PVFLIN
18
specifications.
19 20
3.2: Results
21
Regarding the quality checks, 127 (12.6%) and 208 (20.6%) individuals failed the monotonicity and
22
stability tests respectively. As anticipated, the PVFNOLIN significantly outperformed its linear
23
counterpart (Log-likelihood ratio test: Deviance = 565.2; P < 0.001). The results are presented in
24
Table 2. Respondents positively value an improvement in population health and a reduction of
25
medical expenditures (i.e., cost saving). The estimate for ∆E appeared to be relatively large compared
26
to ∆C, indicating that individuals gave more weight to net changes in health than expenditures (i.e.,
27
0.525/0.055 ≈ 10). The estimate for the ρ parameter is negative and significant, indicating that
9
1
respondents did not want to re-allocate resources ceteris paribus. All four parameters allowing for
2
non-linearities in preferences reached significance. The results showed evidence of loss aversion in
3
valuation of ∆E with losses being 1.4 times more valued than equivalent gains. At the opposite,
4
individuals appeared to give less weight to losses in ∆C compared to gains. There is also evidence of
5
non-constant marginal sensitivity to changes in both ∆E and ∆C. Individuals exhibited diminishing
6
marginal sensitivity in their valuation of ∆E and increasing marginal sensitivity in their valuation of
7
∆C (Figure 3).
8 9
The non-linearities in the PVF resulted in a transformation of the valuation space. Panel A in Figure
10
4 is based on the results from the PVFLIN function and describes the valuation space once public
11
preferences for ∆E and ∆C are taken into account. The grey area describes potential outcomes that
12
would be positively valued by the public. This valuation frontier describes all {∆E; ∆C} outcomes
13
which would be associated with a null valuation and can be interpreted as an indifference curve.
14
Given that preferences were assumed to be linear, this curve takes the form of a straight line, and its
15
slope corresponds to the marginal rate of substitution between ∆E and ∆C (i.e., one needs to increase
16
∆C by 3.31 units to compensate the positive effect of increasing ∆E by 1 unit). Outcomes falling in QI
17
are positively valued by the public. Conversely, all potential outcomes belonging to QIII are negatively
18
valued. This result was anticipated by Sendi et al (2002) who suggested that healthcare resources
19
should be reallocated if more than 95% of the potential outcomes fall within QI. Our study results
20
suggest that this decision rule could be over-cautious because some outcomes in QII and QIV are also
21
positively valued. QIV has a larger share of positively valued outcomes than QII because public gives
22
more weight to ∆E than ∆C.
23 24
Panel B corresponds to a modified version of linear function allowing public preferences to be biased
25
towards the NS (PVFLIN+NS). As the valuation function remains additive in its arguments, we only
26
observe a horizontal translation of the grey area. This translation has two major implications. First, all
27
outcomes in QI are no longer unambiguously good. Second, the NS preference significantly decreases
10
1
the probability of finding improvements in the allocation of healthcare resources (i.e. positively
2
valued outcomes). In Panel A, the grey surface represented approximately 50.3% of the valuation
3
space. In Panel B, this proportion decreased to 35%. Regarding QI, the NS bias represents a 19.3%
4
loss of optimality. The optimality loss is represented by the white surface within QI. Panel C is
5
obtained with the non-linear valuation function (PVFNOLIN). Due to non-linearities in the preferences
6
for ∆E and ∆C, the marginal rate of substitution between these two quantities is no longer constant.
7
The results show that the non-linearities in preferences reduce the impact of the NS effect on the
8
valuation space, as the optimality loss decreases to 8.4%. Panel D is a contour plot of the valuation
9
space. Altogether these results show the importance of allowing for both between-quadrant and
10
within-quadrant effects when exploring public preferences for the allocation of healthcare resources.
11 12
4: Implications of non-linearities in preferences on the allocation decision
13 14
4.1 Method
15
Whilst the non-linearities in public preferences for ∆E and ∆C significantly improved the statistical
16
representation of respondents’ choices, there is a priori no guarantee that these would significantly
17
influence the allocation decision (i.e., whether the uncertainty is acceptable or not). In a simulation
18
study we compared the PVFLIN and PVFNOLIN using 5,000 allocation decisions. For each allocation
19
decision, we simulate a large number of potential outcomes and then apply the PVFLIN and PVFNOLIN
20
functions. The goal is to compare the effect on the decision to re-allocate healthcare resources or not.
21
As a benchmark decision rule we assumed that the decision makers would compute the expected
22
value of the potential outcomes and decide to re-allocate resources only if this expected value is
23
positive (Rule #1). However, to check the sensitivity of our finding to a change in the decision rule,
24
we also tested two additional rules: “Proceeding to re-allocation if at least 50% of the potential
25
outcomes are positive (i.e., median value > 0)” (Rule #2) and “Proceeding to re-allocation if at least
26
95% of the potential outcomes are positive” (Rule #3). We chose these two alternative rules for the
27
following reasons. A comparison based on the median value, instead of the mean (expected) value,
11
1
could be more appropriate in cases of large departures from normality in the distribution of the
2
potential outcomes as the median is less influenced by extreme values. The second rule (rule #3) was
3
chosen following the rule suggested by Sendi et al where the health decision maker will accept the
4
reallocation of resources when 95% or more of the outcomes fall into the Quadrant I of the DMP,
5
which is similar to the rule used in clinical thinking.
6 7
We used a simulation procedure to describe a large number of allocation decisions which differ in
8
terms of ∆E and ∆C and also levels of variability in ∆E and ∆C (Figure 5). We also performed a
9
logistic regression to analyse agreement between PVFNOLIN and PVFLIN for the benchmark decision
10
rule.
11 12
The simulation was conducted as follows:
13
(i)
The uncertainty about the potential consequences of each allocation decision was described with a bivariate normal distribution
14 15
μ∆ σ∆ ∆E ! # ~Normal !μ $ , B ∆C ∆& ∆ ∆&
16
B∆ ∆& σ∆& $#
(3)
17 18
Where µ∆E is the mean ∆E, µ∆C is the mean ∆C, σ∆E is the variance of ∆E, σ∆C is the variance of ∆C
19
and σ∆C∆C is the covariance of ∆E and ∆C. The covariance is given by σ∆ ∆& = ρσ∆ σ∆& , where ρ is
20
the correlation between ∆E and ∆C.
21 22 23
(ii)
We added two proportionality constraints (τ∆ ; τ∆ ) such that the variances (σ∆ , σ∆& ) couldn’t represent less than 10% and more than 200% of the means (μ∆ , μ∆& ):
24 25
σ∆ = μ∆ τ∆
(4a)
26
σ∆& = μ∆& τ∆&
(4b)
27 12
1
(iii)
We specified uniform distributions for the simulation parameters (μ∆ ; μ∆& ; τ∆ ;τ∆ ; ρ).
2
Manipulating these parameters allow obtaining allocation decisions with different shapes of
3
potential outcomes as illustrated in Figure 3. The choice of values for the parameters of the
4
uniform distributions is largely based on values used in Gafni et al (2013) and also had to
5
satisfy a constraint of plausibility/realism (i.e., unlikely that in practice ∆E and ∆C are either
6
perfectly correlated (|ρ|=1) or uncorrelated (ρ=0); unlikely that variances of ∆E and ∆C are
7
null (τE=τC=0)).
8 9
μ∆ ~Uniform<−4, 4?
(5a)
10
μ∆& ~Uniform<−4, 4?
(5b)
11
τ∆ ~Uniform<0.1, 2?
(5c)
12
τ∆& ~Uniform<0.1, 2?
(5d)
13
ρ~Uniform<−0.9, 0.9?
(5e)
14 15
(iv)
We drew 5,000 allocation decisions from these uniform distributions.
(v)
For each allocation decision, we then simulated 10,000 potential outcomes (t) using the
16 17
bivariate normal distribution (Eq. 4).
18 19 20
(vi)
We applied PVFLIN and PVFNOLIN to obtain a subjective valuation of each potential outcome and computed the expected value (EV) of each allocation decision.
21 22
23
<∆E EVJ = K, ∑K, , ∆C ? M PVF
24
<∆E EVJ = K, ∑K, , ∆C ? M PVF
(7a)
(7b)
25 26 27
(vii)
The decision rule that we used is to recommend re-allocation of healthcare resources when the EV of the allocation decision is positive. Therefore, for each PVF, we computed the 13
1
percent of allocation decisions with a positive EV. We then used the Kappa coefficient to
2
measure the level of agreement between the two PVFs. We then performed a logistic
3
regression to investigate the effects of changes in the simulation parameters on the level of
4
agreement.
5 6
P
(8)
7 8
4.2: Results
9
Regarding the PVFNOLIN function, 28.1% of the situations had a positive expected value. This
10
proportion increased to 50.1% with the PVFLIN function. The level of agreement (after accounting for
11
agreement by chance) was moderate with a Kappa coefficient of 0.56. Whilst the choice of the
12
decision rule had a large effect on these proportions of cases where resources should be re-allocated
13
(i.e., Rule #2: {PVFNOLIN = 34.62%, PVFLIN = 50.18%}, and Rule #3: {PVFNOLIN = 4.18%, PVFLIN =
14
13.02%}), the PVFLIN function appeared to provide higher estimates of the proportion of cases in
15
which resources should be re-allocated.
16 17
The results for the logistic regression of agreement are presented in Table 3. The results show that the
18
probability of agreement between the two functions is mainly driven by the distribution of the net
19
changes in health outcomes (∆E). When increasing the size of the improvements in health outcomes,
20
the PVFNOLIN and PVFLIN functions become more likely to provide different recommendations
21
regarding the allocation of healthcare resources. At the opposite, when the potential health outcomes
22
become more variable, the two methods are more likely to agree (i.e., a 1-unit increase in σ∆E is
23
associated with a +5% increase in the agreement probability).
24 25
5: Discussion
26
14
1
The objective of our study was to identify a public valuation function (PVF) that describes how a
2
representative sample of the French population values potential outcomes stemming from a decision
3
to reallocate healthcare resources. To the best of our knowledge, it is the first attempt to identify such
4
function. In line with Gafni et al (2013) arguments, our results show that the valuation of outcomes
5
stemming from resources reallocation is shaped by both a within-quadrant effect (the magnitude of
6
the potential gains or losses) and a between-quadrant effect (the direction of potential outcome).
7
These effects were captured by a non-linear valuation function largely inspired by the prospect theory
8
(Kahneman & Tversky, 1979). We showed that such non-linear function provided a better account of
9
the resources reallocation decisions. We then illustrated the consequences of this public valuation
10
function in terms of recommendations regarding the decision to reallocate resources across different
11
healthcare interventions. In a simulation study, we showed that ignoring non-linearities in public
12
preferences by assuming a linear function could lead to different results.
13 14
This study contributes to the literature in different ways. First, it illustrates how to operationalize the
15
measurement of a PVF and that it is feasible to do it for a representative sample of the population. It
16
demonstrates how public preferences could be used to inform the health policy-making process. The
17
importance of taking into account the public views in the organisation of the healthcare system has
18
been widely acknowledged. However, in practice this might be difficult to achieve as one first needs
19
to determine how to measure/describe users’ views and then identify a mechanism to incorporate
20
these views in the decision-making. By building a valuation space based on public preferences, our
21
study provides a tool which can inform the decision whether to reallocate resources or not. Past
22
studies tried to achieve this objective by investigating public preferences for how healthcare resources
23
should be used (i.e., who should benefit from the scarce resources in priority) (Erdem & Thompson,
24
2014; Green & Gerard, 2009; Scuffham et al, 2014; Skedgel et al, 2015). Second, study results
25
contribute to the literature on the measurement of non-linearities in health-related preferences (Holte
26
et al, 2016; van der Pol et al, 2014; Torres et al, 2011). The third contribution is demonstrating the
27
importance of measuring a PVF rather than assuming one. Our simulation study demonstrates the
15
1
potential for a large effect on the decision whether to continue with resource allocation or not for a
2
given distribution of potential outcome.
3 4
One potential limitation of this study is the absence of information regarding the types of
5
treatments and the population treated (e.g. age, gender, size of the population) involved in the decision
6
to reallocate healthcare resources. Our approach obtains a generic set of results to inform health
7
policy making under the common assumption that a unit of health outcome (e.g., HYE, QALY) is
8
valued the same regardless of who gains it or loses it (Whitehead & Ali, 2010). This may have
9
reduced the credibility of our choice experiment for some participants and/or decision makers who do
10
not subscribe to this assumption. In line with the assumption that the application area does not affect
11
the valuation of allocation decisions, we provided no information regarding the type of treatments to
12
be implemented/cancelled and explicitly instructed the participants to consider this information as
13
irrelevant. However, we have no information about respondents’ understanding of this choice setting
14
and some might still have envisaged particular decision contexts when they participated in the
15
experiment. Future studies could look at the impact of making the choice context case specific (e.g.,
16
whether it matters or not, how it affects). Similarly, the size of the different subgroups of patients was
17
“made irrelevant” by providing individual-level information (e.g., 20,000 euros increase in medical
18
expenditures per person) to the participants rather than aggregated information (e.g., 200 million
19
euros increase in medical expenditures). This was done to make the figures easier to understand for
20
the participants and to avoid potential distributional issues (i.e., the same figure can hide different
21
repartitions of the effects across patients’ subgroups). We tried to preserve the collective nature of the
22
decision problem by (i) instructing participants to assume the role of a health decision maker when
23
making their decisions, and (ii) framing the individual-level values as average consequences of the
24
decision to re-allocate healthcare resources per person. However, we could not verify whether the
25
participants followed these instructions. Future research should look for other ways to present the
26
information at an aggregated level that will be understandable to individuals.
27
16
1
The study results could also have been influenced by the hypothetical nature of the choice
2
questions (Hensher, 2010; Loomis, 2011). Future research could test the robustness of our study
3
results to hypothetical biases by using cheap-talk script or oath priming (de-Magistris & Pascucci,
4
2014; Carlsson et al, 2013). Such hypothetical bias may explain why net changes in population health
5
appeared to be more important than net changes in the level of medical expenditures in respondents’
6
choices. We attempted to mitigate a potential hypothetical bias by carefully explaining to the
7
participants the decision context and that increase in the size of the healthcare budget might be at the
8
expense of other public sectors such as education.
9 10
The study results may suffer from a lack of sample representativeness. Whilst our sample
11
appears to be an acceptable representation of the French population in terms of age, gender and
12
geographical spread, the descriptive analysis of some other personal characteristics showed significant
13
departures from the national population in terms of education attainment (i.e., our sample appears to
14
be more qualified) and self-reported health status (i.e., our sample appears to be in a more deteriorated
15
health). This lack of representativeness is likely to be caused by the use of an online panel. However,
16
it is unclear a priori how the personal characteristics of the respondents would influence the
17
preferences for the allocation of healthcare resources in a generic context. We leave this issue for
18
future research.
19 20
Future research should also assess the impact of different decision rules on the policy
21
recommendations. Following Gafni et al (2013), we summarised all the information about potential
22
situations by computing the expected value of the decision (Rule #1). However, other decision rules
23
can be envisaged. To test the sensitivity of our finding to the choice of a decision rule we tried two
24
other decision rules based on the “50% of the potential outcomes being positive” (Rule #2) and “95%
25
of potential outcomes being positive” (Rule #3), and the results showed that important differences in
26
the percentage of cases where resources should be re-allocated. However, the proportions obtained
27
with the linear public valuation function were higher in the linear case than those obtained with its
28
non-linear counterpart, in the three decision rules compared. 17
1 2
6: Conclusion
3
In this study we have demonstrated how a valuation function, that describes the preferences (or values
4
attributed) for every potential outcome in each quadrant of the DMP, can be obtained from a
5
representative sample of the population (i.e., France in our example). Our study demonstrates the
6
importance of measuring such function rather than assuming one. We do not feel that our work is
7
necessarily providing the final answer. It is the first step and calls for more research that should
8
explore the effects (if there are) of other factors (e.g., which treatment is added to what disease and
9
which treatment is cancel for what disease to free up the required resources) on the public preferences.
10
18
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53
References Bekker-Grob, Esther W. de, Mandy Ryan, and Karen Gerard. 2012. “Discrete Choice Experiments in Health Economics: A Review of the Literature.” Health Economics 21 (2): 145–72. https://doi.org/10.1002/hec.1697. Birch, S., and A. Gafni. 1992. “Cost Effectiveness/Utility Analyses. Do Current Decision Rules Lead Us to Where We Want to Be?” Journal of Health Economics 11 (3): 279–96. Campbell, Danny, Marco Boeri, Edel Doherty, and W. George Hutchinson. 2015. “Learning, Fatigue and Preference Formation in Discrete Choice Experiments.” Journal of Economic Behavior & Organization 119 (November): 345–63. https://doi.org/10.1016/j.jebo.2015.08.018. Carlsson, Fredrik, Mitesh Kataria, Alan Krupnick, Elina Lampi, Åsa Löfgren, Ping Qin, and Thomas Sterner. 2013. “The Truth, the Whole Truth, and Nothing but the Truth—A Multiple Country Test of an Oath Script.” Journal of Economic Behavior & Organization 89 (May): 105–21. https://doi.org/10.1016/j.jebo.2013.02.003. Clark, Michael D., Domino Determann, Stavros Petrou, Domenico Moro, and Esther W. de BekkerGrob. 2014. “Discrete Choice Experiments in Health Economics: A Review of the Literature.” PharmacoEconomics 32 (9): 883–902. https://doi.org/10.1007/s40273-014-0170x. Erdem, Seda, and Carl Thompson. 2014. “Prioritising Health Service Innovation Investments Using Public Preferences: A Discrete Choice Experiment.” BMC Health Services Research 14 (1). https://doi.org/10.1186/1472-6963-14-360. Gafni, Amiram, and Stephen Birch. 1993. “Guidelines for the Adoption of New Technologies: A Prescription for Uncontrolled Growth in Expenditures and How to Avoid the Problem.” Canadian Medical Association Journal 148 (6): 913–917. ———. 1997. “QALYs and HYEs Spotting the Differences.” Journal of Health Economics 16 (5): 601–8. https://doi.org/10.1016/S0167-6296(96)00527-9. ———. 2006. “Incremental Cost-Effectiveness Ratios (ICERs): The Silence of the Lambda.” Social Science & Medicine 62 (9): 2091–2100. https://doi.org/10.1016/j.socscimed.2005.10.023. Gafni, Amiram, Stephen Walter, and Stephen Birch. 2013. “UNCERTAINTY AND THE DECISION MAKER: ASSESSING AND MANAGING THE RISK OF UNDESIRABLE OUTCOMES: UNCERTAINTY AND THE DECISION MAKER.” Health Economics 22 (11): 1287–94. https://doi.org/10.1002/hec.2883. Green, Colin, and Karen Gerard. 2009. “Exploring the Social Value of Health-Care Interventions: A Stated Preference Discrete Choice Experiment.” Health Economics 18 (8): 951–76. https://doi.org/10.1002/hec.1414. Hensher, David A. 2010. “Hypothetical Bias, Choice Experiments and Willingness to Pay.” Transportation Research Part B: Methodological 44 (6): 735–52. https://doi.org/10.1016/j.trb.2009.12.012. Holte, Jon Helgheim, Peter Sivey, Birgit Abelsen, and Jan Abel Olsen. 2016. “Modelling Nonlinearities and Reference Dependence in General Practitioners’ Income Preferences: GPs’ Income Preferences.” Health Economics 25 (8): 1020–38. https://doi.org/10.1002/hec.3208. Kahneman, Daniel, and Amos Tversky. 1979. “Prospect Theory: An Analysis of Decision under Risk.” Econometrica 47 (2): 263. https://doi.org/10.2307/1914185. Krucien, Nicolas, Nathalie Pelletier-Fleury, and Amiram Gafni. 2018. “Measuring Public Preferences for Health Outcomes and Expenditures in a Context of Healthcare Resource Re-Allocation.” PharmacoEconomics, November. https://doi.org/10.1007/s40273-018-0751-1. Loomis, John. 2011. “WHAT’S TO KNOW ABOUT HYPOTHETICAL BIAS IN STATED PREFERENCE VALUATION STUDIES?: HYPOTHETICAL BIAS IN STATED PREFERENCE VALUATION STUDIES.” Journal of Economic Surveys 25 (2): 363–70. https://doi.org/10.1111/j.1467-6419.2010.00675.x. Magistris, Tiziana de-, and Stefano Pascucci. 2014. “The Effect of the Solemn Oath Script in Hypothetical Choice Experiment Survey: A Pilot Study.” Economics Letters 123 (2): 252–55. https://doi.org/10.1016/j.econlet.2014.02.016.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
Mehrez, Abraham, and Amiram Gafni. 1989. “Quality-Adjusted Life Years, Utility Theory, and Healthy-Years Equivalents.” Medical Decision Making 9 (2): 142–49. https://doi.org/10.1177/0272989X8900900209. Pol, Marjon van der, Gillian Currie, Seija Kromm, and Mandy Ryan. 2014. “Specification of the Utility Function in Discrete Choice Experiments.” Value in Health 17 (2): 297–301. https://doi.org/10.1016/j.jval.2013.11.009. Ryan, Mandy, Nicolas Krucien, and Frouke Hermens. 2018. “The Eyes Have It: Using Eye Tracking to Inform Information Processing Strategies in Multi-Attributes Choices.” Health Economics 27 (4): 709–21. https://doi.org/10.1002/hec.3626. Savage, Scott J., and Donald M. Waldman. 2008. “Learning and Fatigue during Choice Experiments: A Comparison of Online and Mail Survey Modes.” Journal of Applied Econometrics 23 (3): 351–71. https://doi.org/10.1002/jae.984. Scuffham, Paul A, Julie Ratcliffe, Elizabeth Kendall, Paul Burton, Andrew Wilson, Kalipso Chalkidou, Peter Littlejohns, and Jennifer A Whitty. 2014. “Engaging the Public in Healthcare Decision-Making: Quantifying Preferences for Healthcare through Citizens’ Juries.” BMJ Open 4 (5): e005437. https://doi.org/10.1136/bmjopen-2014-005437. Skedgel, Chris, Allan Wailoo, and Ron Akehurst. 2015. “Societal Preferences for Distributive Justice in the Allocation of Health Care Resources: A Latent Class Discrete Choice Experiment.” Medical Decision Making 35 (1): 94–105. https://doi.org/10.1177/0272989X14547915. Torres, Cati, Nick Hanley, and Antoni Riera. 2011. “How Wrong Can You Be? Implications of Incorrect Utility Function Specification for Welfare Measurement in Choice Experiments.” Journal of Environmental Economics and Management 62 (1): 111–21. https://doi.org/10.1016/j.jeem.2010.11.007. Train, Kenneth. 2009. Discrete Choice Methods with Simulation. 2nd ed. Cambridge ; New York: Cambridge University Press. Weinstein, Milton, and Richard Zeckhauser. 1973. “Critical Ratios and Efficient Allocation.” Journal of Public Economics 2 (2): 147–57. https://doi.org/10.1016/0047-2727(73)90002-9. Whitehead, S. J., and S. Ali. 2010. “Health Outcomes in Economic Evaluation: The QALY and Utilities.” British Medical Bulletin 96 (1): 5–21. https://doi.org/10.1093/bmb/ldq033. Williams, A. 1983. “The Economic Role of Health Indicators.” In Measuring the Social Benefits of Medicine, 63–67. London: Office of Health Economic: G. Teeling Smith.
20
Table 1. Descriptive analysis of personal characteristics of the respondents (N=995) % 1. Personal characteristics Health status Very good Good Fair/Bad/Very bad Education No formal qualifications & Other Secondary or high school qualifications University or College degree Gender Male Female Chronic conditions None At least one Prefer not to say Involvement *** Undecided (4-6) No (<= 3) Yes (>= 7) Satisfaction *** Neither satisfied, nor unsatisfied (4-6) Unsatisfied (<= 3) Satisfied (>= 7) Age Mean (SD) 2. Feedback about the questionnaire Interest *** Intermediate (4-6) Not interesting (<= 3) Interesting (>= 7) Difficulty *** Intermediate (4-6) Difficult (<= 3) Easy (>= 7) Quality *** Intermediate (4-6) Good (<= 3) Bad (>= 7)
22.9 52 25.1 9.4 16.5 74.1 48.8 51.2 57.9 37.9 4.2 23.3 3.6 73.1 36.9 6.1 57 43.68 (14.18) 19.5 6 74.5 34.8 8.2 57 28.2 24.4 47.3
*** Involvement: Do you think the public should be involved in the decisions to fund new medical interventions? [11-points rating scale ranging from "not at all" (0) to "yes quite" (10)]; Satisfaction: How satisfied are you with the healthcare system? [11-points rating scale ranging from "Fully unsatisfied" (0) to "Fully satisfied" (10)]; Quality: How would you rate the quality of this questionnaire? [11-points rating scale ranging from "Extremely good" (0) to "Extremely bad" (10)]; Interest: How would you rate the interest of this questionnaire? [11-points rating scale ranging from "Not at all interesting" (0) to "Extremely interesting" (10)]; Difficulty: How would you rate the difficulty of this questionnaire? [11-points rating scale ranging from "Extremely difficult" (0) to "Extremely easy" (10)]
Table 2. Estimation of public preferences for net changes in health outcomes and medical expenditures VLIN
VLIN+NS
VNOLIN
-
-0.7491 (0.0352) ***
-0.6152 (0.0509) ***
∆E
0.3297 (0.0046) ***
0.3184 (0.0046) ***
0.5251 (0.0358) ***
∆C
-0.0995 (0.0023) ***
-0.097 (0.0023) ***
-0.0547 (0.019) ***
∆E x ∆C
-
-
0.0003 (0.0005)
LA_∆E
-
-
1.4045 (0.0575) ***
LA_∆C
-
-
0.7255 (0.07) ***
MS_∆E
-
-
0.6562 (0.0337) ***
MS_∆C
-
-
1.2773 (0.1457) ***
1.123 (0.0409) ***
0.7767 (0.0389) ***
0.7806 (0.0393) ***
995
995
995
11,940
11,940
11,940
# Parameters
3
4
9
Log-likelihood
-8,291.5
-8,108.4
-8,008.9
BIC
16,611.2
16,254.4
16,102.3
1. Model parameters (MLE (SE)) ASC
SD_panel 2. Model statistics # Individuals # Observations
MLE: maximum likelihood estimate; SE: standard error; P: P-value; ∆E: Net change in health outcomes; ∆C: Net change in health expenditures; SD: standard deviation; ASC: Alternative specific constant; LA: Loss aversion; MS: Marginal sensitivity; BIC: Bayesian information criteria. *** P-value < 1%; ** P-value < 5%; * P-value < 10%
Table 3. Logistic regression of the agreements between the recommendations of the VNOLIN and VLIN public valuation functions MLE
SE
P
AME
Constant
0.685
0.065
< 0.001
-
mE
-0.311
0.019
< 0.001
-0.049
mC
-0.015
0.016
0.363
-0.002
sE
0.318
0.025
< 0.001
0.050
sC
0.085
0.021
< 0.001
0.013
sEC
0.078
0.070
0.265
0.012
Model statistics: Log-likelihood = -2,400.2; # Observations = 5,000 (# 1's = 3,900); # Parameters = 6 MLE: maximum likelihood estimate; SE: Standard error; P: P-value; AME: Average marginal effect; mE & sE: Respectively mean and standard deviation of net changes in population health; mC & sC: Respectively mean and standard deviation of net changes in medical expenditures; sEC: Covariance of net changes in population health and medical expenditures.
Figure 1. Representation of the decision to reallocate healthcare resources in the decisionmaking plane (DMP) Panel A: Decision-making plane
Panel B: Uncertainty in the consequences of the decision to re-allocate healthcare resources
Source: Sendi, P., Gafni, A. & Birch, S. Opportunity costs and uncertainty in the economic evaluation of health care interventions. Health Econ. 11, 23–31 (2002). Reading: ∆C(A) indicates the incremental costs for programme A; ∆C(B) indicates the incremental costs for programme B; ∆E(A) indicates the incremental health outcomes for programme A; ∆E(B) indicates the incremental health outcomes for programme B; The Latin numbers (I, II, III, IV) are used to describe the four quadrants of the DMP: {Increase in health outcomes; Decrease in medical expenditures}; {Decrease in health outcomes; Decrease in medical expenditures}; {Decrease in health outcomes; Increase in medical expenditures}; {Increase in health outcomes; Increase in medical expenditures}. Panel B illustrates the posterior joint distribution taken from an example used in Sendi et al (2002) of introducing programme A and cancelling programme B in the decision-making plane.
Figure 2. Illustration of the choice task format
Figure 3. Visual representation of non-linearities in public preferences for ∆E and ∆C
Figure 4. Using public preferences to transform the decision making plane into a valuation space Panel A: Linear function (PVFLIN)
Panel B: Linear function allowing for a neutral situation bias (PVFLIN+NS)
Panel C: Non-linear function allowing for a Panel D: Contour plot representing the neutral situation bias, asymmetric preferences valuation space once non-linear public between positive and negative changes and non- preferences for ∆E and ∆C are considered constant marginal sensitivity to changes (PVFNOLIN)
Legend Coloured areas in panels A-C represent the potential outcomes {∆E; ∆C} which would be positively (Grey) and negatively (White) valued by the public. Dotted green line in panels B-D corresponds to the indifference curve associated with PVFLIN. Dotted red line in panels C-D corresponds to the indifference curve associated with PVFLIN+NS. Panel D describes how public valuation changes across the decision-making plane – Within each colour band the exact valuations also differ.
Figure 5. Illustration of potential outcomes for different RADs *
Legend: mE = mean of net changes in health outcomes (∆E); mC = mean of net changes in medical expenditures (∆C); sE = variance of ∆E; sC = variance of ∆C; sEC = covariance of ∆E and ∆C. The ellipses around the dots correspond to the 95% confidence ellipses. [Situation #1] mE=1.767; mC=-2.553; sE=0.864; sC=0.091; sEC=0.009; [Situation #2] mE=3.006; mC=-2.490; sE=4.145; sC=2.311; sEC=8.576; [Situation #3] mE=2.008; mC=1.816; sE=3.631; sC=2.881; sEC=3.815; [Situation #4] mE=3.089; mC=-3.755; sE=6.062; sC=0.873; sEC=4.328. * To improve the readability of this illustration we only drew 100 potential outcomes for each RAD.
Research highlights • A public valuation function to support reallocation of healthcare resources • Evidence of non-linearities in public valuation of health outcomes and expenditures • Public gives 10 times more weight to health outcomes than expenditures • Non-linearities in public preferences matter for the resource allocation decisions
Amiram Gafni: Conceptualization; Methodology; Writing - Review & Editing. Sebastian Heidenreich: Formal analysis; Writing - Review & Editing. Nicolas Krucien: Conceptualization; Methodology; Formal analysis; Writing - Original Draft; Writing - Review & Editing; Project administration. Nathalie Pelletier-Fleury: Conceptualization; Methodology; Resources; Writing - Review & Editing.
S0277-9536(19)30770-1
DOI:
https://doi.org/10.1016/j.socscimed.2019.112775
Reference:
SSM 112775
To appear in:
Social Science & Medicine
Received Date: 17 May 2019 Revised Date:
16 December 2019
Accepted Date: 20 December 2019
Please cite this article as: Krucien, N., Heidenreich, S., Gafni, A., Pelletier-Fleury, N., Measuring public preferences in France for potential consequences stemming from re-allocation of healthcare resources, Social Science & Medicine (2020), doi: https://doi.org/10.1016/j.socscimed.2019.112775. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd.
Cover page Manuscript number SSM-D-19-01573R2 Title Measuring public preferences in France for potential consequences stemming from re-allocation of healthcare resources List of authors Nicolas KRUCIEN(1) Sebastian HEIDENREICH(1) Amiram GAFNI(2) Nathalie PELLETIER-FLEURY(3) (1)
Patient-Centered Research, Evidera Ltd, London, United Kingdom Centre for Health Economics and Policy Analysis, Department of Clinical Epidemiology and Biostatistics, McMaster University, Hamilton, Canada (3) Centre de Recherche en Epidemiologie et Santé des Populations, Université Paris-Sud, UVSQ, INSERM, Université Paris-Saclay, Villejuif, France (2)
Corresponding author Nicolas KRUCIEN Patient-Centered Research Evidera Ltd The Ark 201 Talgarth Road London W6 8BJ United Kingdom Tel: +44 20 8576 5000 Email: [email protected] Acknowledgments We thank all participants who took part in the study.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
Abstract When deciding which new programme to implement and where the additional resources, if needed, will come from, the decision makers need to accommodate the uncertainty of the potential changes in population health and medical expenditures that can occur. They also need to determine the value of these potential changes. The objective of this study is to identify a public valuation function measuring how the public values changes in population health and medical expenditures when healthcare resources are re-allocated. We report the results of a choice experiment conducted in March 2016 in a representative sample of the population living in France (N=1,008). The main results indicate that the public is more sensitive to changes in population health than changes in the level of medical expenditures. There is a non-linear valuation of these changes with evidence of asymmetric preferences and non-constant marginal sensitivity. The public gives 1.4 times more weight to decrease in population health than for the same-size increase. The public becomes less sensitive to marginal changes in population health as the level of changes increases. In a simulation study of 5,000 resource allocation decisions, we show that non-linearities in public valuation of population health and medical expenditures matters. The linear and non-linear public valuation functions were associated with respectively 50.1% and 28.1% of situations of acceptable outcome of the reallocation of resources. The level of agreement between these two functions was moderate with a Kappa coefficient of 0.56, and the probability of agreement was mainly driven by the distribution of net changes in population health. This study provides a method and an estimation of a public valuation function that describes the preferences (or values attributed) for every potential outcome stemming from the reallocation of healthcare resources. The results show the importance of measuring such function rather than assuming one. Keywords France; Stated preferences; Choice experiment; Choices modelling; Resources allocation; Economic evaluation
1
1
1: Introduction
2 3
If healthcare budgets were unlimited, the most effective treatments could be adopted. However,
4
resources allocated to healthcare are scarce, hence health policy decision-makers (hereafter decision
5
makers) need to decide how to best allocate them. Resources scarcity can occur in different contexts
6
(i.e., fixed budgets, shrinking budget with less resources allocated to healthcare, growing budget with
7
more resources allocated to healthcare) as long as the total amount of resources available is not
8
sufficient to support the implementation of all the most effective treatments. As a result of scarcity,
9
decision makers need to determine where the resources should come from to fund the implementation
10
of new treatments to replace or complement existing treatments. For example, in the case of a fixed
11
budget, decision makers may decide to cancel existing treatment(s) in order to free up resources to
12
implement the new treatment(s). In the case of a growing budget, because not all new treatments can
13
be implemented, decision makers would still need to decide which new treatment(s) to implement and
14
which ones not to implement.
15 16
The decisions to allocate healthcare resources (hereafter allocation decisions) are challenging because
17
they typically require to trade off potential health gains for patients who will benefit from the new
18
treatment against potential health losses for those who will see their current treatment being cancelled
19
or replaced (or potential new treatment not adopted). In this context, decision makers need to consider
20
the opportunity costs of their decisions. In a world where full information about all the potential
21
programs for cancellation is not available, a second best option is to “ensure that the value of what is
22
gained from an activity [e.g., implementing the new treatment] outweighs the value of what has to be
23
sacrificed [e.g., cancelling a different treatment]” (Williams, 1983; page 63).
24 25
Cost–effectiveness analysis (CEA) is widely advocated as a tool to inform this allocation decision in a
26
way that maximizes the health benefits produced to the population from the available resources. The
27
analytical tool of CEA is the incremental cost-effectiveness ratio (ICER), which is compared to a
28
threshold value (λ) to determine whether the new treatment should be implemented. Assuming that 2
1
healthcare resources were efficiently used, this λ should in principle correspond to the ICER of the
2
last treatment adopted (Weinstein & Zeckhauser, 1973) and would then correspond to the shadow
3
price of the budget constraint. However, this approach would lead to an optimal use of healthcare
4
resources only under strong assumptions of perfect divisibility and constant returns to scale of all
5
programs (Gafni & Birch, 2006; Birch & Gafni, 1992; Gafni & Birch, 1993). Birch & Gafni (B&G)
6
have suggested an alternative approach which relaxes these two assumptions. The differences are: (i)
7
it does not require to subscribe to the assumptions of perfect divisibility and constant returns to scale,
8
and (ii) it does not require the use of an ICER and cost-effectiveness threshold. This approach
9
requires the identification of the source of the additional resource requirements for the new program
10
and bases the recommendation regarding the adoption of the new program on a direct comparison of
11
the total additional benefits produced from the new program with the total benefits forgone. In doing
12
so it ensures, that if followed and under conditions of certainty, “the value of what is gained from an
13
activity outweighs the value of what has to be sacrificed” (Williams, 1983; page 63).
14 15
In the past two decades it has been recognized that both costs and effects of all programs are
16
stochastic. The B&G approach has been extended to account for the uncertainty in costs and effects
17
of re-allocating resources (Sendi et al, 2002). Visually, it takes the form of a decision-making plane
18
(DMP) allowing to describe all the possible potential outcomes stemming from resource reallocation
19
due to the uncertainty. In contrast, the cost-effectiveness plane (CEP) describes only the difference in
20
health outcomes (E) and costs (C) of a candidate treatment for implementation (A1) with a reference
21
one (A0) using measures of incremental effectiveness (∆E = E − E ) and increment costs
22
(∆C = C − C ). Those measures are used to compute the ICER and compare it to the ICER
23
threshold. The DMP “extends” the CEP by also comparing a candidate treatment for cancellation
24
(B1) with another reference treatment (B0) (i.e., the explicit consideration of the source of additional
25
resources), leading thus to another set of incremental effects (∆E = E − E ) and costs (∆C =
26
C − C ). The DMP can also be extended to the case where more than one existing treatment have
27
to be replaced in order to free up resources for the implement of the new treatment. All these
3
1
incremental measures are used to compute net changes in health outcomes (∆E = ∆E − ∆E ) and
2
costs (∆C = ∆C − ∆C ) which are then mapped into the DMP (Figure 1A). The DMP is divided into
3
four quadrants which will affect the allocation decision. Quadrant I (QI) describes situations where the
4
joint decision to replace A0 by A1 and B1 by B0 allows improving the population health (i.e., ∆E > 0)
5
and an overall lower level of medical expenditures (i.e., ∆C < 0). At the opposite, quadrant III (QIII)
6
describes situations where population health is decreased (i.e., ∆E < 0) and medical expenditures
7
increased (i.e., ∆C > 0). Quadrant II (QII) describes situations where both the population health and
8
level of medical expenditures are decreased (i.e., ∆E < 0; ∆C < 0). Quadrant IV (QIV) describes
9
situations where both the population health and level of medical expenditures are increased (i.e., ∆E >
10
0; ∆C > 0).
11 12
Assuming decision makers want to improve the health of the population from the available resources,
13
the decision to replace existing treatment(s) in order to free up resources for the implementation of a
14
new treatment should be made only if the final outcome {∆E; ∆C} will be located in QI. However,
15
this cannot be guaranteed because of the uncertainty in net changes which exposes decision makers to
16
the risk of dealing with a consequence that was not intended (i.e., the consequence of the reallocation
17
of the resources does not fall in QI). Visually this uncertainty takes the form of a joint distribution of
18
all potential outcomes in the DMP (Figure 1B). In order to assist the decision makers in dealing with
19
the uncertainty stemming from the allocation decision, Sendi et al (2002) suggested that decision
20
makers might use as a decision rule the following one: healthcare resources should be re-allocated if
21
more than 95% of the potential outcomes fall into QI.
22 23
Gafni et al (2013) noted that this decision rule may be too restrictive because it implicitly assumes
24
that all potential outcomes within the same quadrant are equally desirable (i.e., the rule ignores the
25
magnitude of the potential outcomes). It also assumes that all outcomes falling outside QI are equally
26
undesirable. The valuation of a potential outcome is likely to depend on both the specific quadrant
27
that it falls in (i.e., between-quadrant effect), and the exact location within the quadrant (i.e., within4
1
quadrant effect). In order to account for these between-quadrant and within-quadrant effects, and not
2
just the probability of where all potential outcome fall, one needs information about decision makers’
3
preferences for each potential outcome (i.e., net changes in ∆E and ∆C). This information can then be
4
used to help decision makers deal with the uncertainty of the final outcome by using a decision rules
5
which avoid the assumptions mentioned (e.g., proceed to re-allocation of resources only if expected
6
value of the allocation decision is positive). To the best of our knowledge such valuation function,
7
that describes the preferences (or value attributed) for every potential outcome in each quadrant of the
8
DMP, does not exist. The goal of this study is to illustrate how such function can be obtained.
9
Assuming that the decision maker is interested in public preferences for the potential outcomes of
10
resources reallocation, in this study we describe how such “public valuation function” (PVF) can be
11
measured.
12 13
In the present study we use a previously developed preferences-elicitation instrument (Krucien et al,
14
2018) to measure preferences for ∆E and ∆C of a representative sample of the French population.
15
When looking for the best PVF, we were also interested in investigating the likelihood of non-
16
linearities in public preferences, such as asymmetric preferences (i.e., higher sensitivity to negative
17
changes compared to same-size positive changes) and non-constant marginal sensitivity (i.e., marginal
18
sensitivity to changes increase/decrease with their magnitude). We used a non-linear specification of
19
the PVF and assessed its statistical performance in comparison with a linear specification. This
20
comparison showed that the non-linear PVF significantly outperformed its linear counterpart. In a
21
simulation study, we also compared the linear and non-linear PVFs in terms of the effect on the
22
decision regarding the decision to re-allocate of healthcare resources.
23 24
The remainder of this article is as follows: Section 2 explains the preference elicitation instrument and
25
how data was collected. Section 3 compares alternative functional forms of the PVF. Section 4
26
describes the simulation study. Section 5 discusses the findings and limitations of the study.
27
5
1
2: Experimental setup
2 3
2.1: Design
4
We conducted a choice experiment (CE) to measure how the public values net changes in health
5
outcomes (∆E) and costs (∆C). CEs are frequently used in health economics to investigate patients’,
6
public, and health professionals’ preferences for a wide range of topics (de Bekker-Grob et al, 2012;
7
Clark et al, 2014).
8 9
Following the concept of Healthy Years Equivalent (Gafni & Birch 1997; Mehrez & Gafni 1989), we
10
used changes in the “equivalent number of years in good health” to describe ∆E. ∆C was defined as
11
net changes in the level of medical expenditures (in euros). Based on our pre-test of the CE, attribute
12
levels were defined per person to make the values easier to understand by participants: ∆E = {-8; -4;
13
0; +4; +8}; ∆C = {-120,000; -60,000; 0; +60,000; +120,000}. These values represented the total net
14
change for the whole population affected divided by the number of people affected. Once multiplied
15
by the size of the population affected, positive values of ∆E and ∆C indicated an improvement in
16
population health and decrease (or no change) in the level of medical expenditures respectively. These
17
attributes’ levels were combined into scenarios describing potential outcomes stemming from the
18
decision to re-allocate resources. Every choice task included three choice options, with one option
19
describing a “neutral situation” (NS) with null net changes (i.e., ∆E = ∆C = 0), and the participants
20
were asked to choose their preferred option (Figure 2).
21 22
Twelve choice tasks were generated using a D-efficient design with Bayesian priors optimised for a
23
multinomial logit (MNL) model. The order of the twelve experimental tasks was randomised across
24
participants to mitigate the influence of order biases such as learning/fatigue (Savage & Waldman,
25
2008; Campbell et al, 2015). The order of the choice options within the tasks was also randomised to
26
mitigate the influence of decision biases associated with a left-to-right processing of the information
6
1
(Ryan et al, 2018). The participants were also asked questions about their socio-demographic
2
characteristics and understanding of the choice context.
3 4
2.2: Sampling
5
A commercially managed online access panel was used to recruit a sample of the population living in
6
France that is representative of the general population in terms of age, gender and geographical spread
7
(n=1,008). The survey was administered to the participants as an online questionnaire. The inclusion
8
criteria were to be older than 18 years and to be able to read the questionnaire. A descriptive analysis
9
of respondents’ personal characteristics can be found in Table 1.
10
The institutional review board (IRB00003888, IORG0003254, FWA00005831) of the French Institute
11
of Medical Research and Health has reviewed this project and attested that this kind of research did
12
not need an opinion of a research ethics committee according to the French law. Moreover, the project
13
was in accordance with the French Law concerning personal data protection at the time of data
14
collection.
15 16
2.3: Data quality
17
In addition to the 12 experimental tasks we included three non-experimental tasks to control the
18
quality of choice data: (i) one warm-up task (Task #1) to familiarise the participants with the task
19
format; (ii) one stability test (Task #14 as repetition of Task #1); (iii) one monotonicity test (Task
20
#15) with one option being superior to the others in terms of ∆E and ∆C. We also checked the quality
21
of the choice data by analysing variability in the choices. A respondent was identified as a “serial non-
22
participant” (SNP) if she always selected the neutral situation as most preferred option in all 12
23
experimental tasks. This absence of variability in the choices is an indication of low engagement in
24
the CE. Only 13 (1.3%) individuals were identified as SNPs, and it was decided to remove them from
25
the analyses as they don’t provide a meaningful information about underlying preferences for ∆E and
26
∆C (A sensitivity analysis of preferences including/excluding serial non-participants can be found in:
27
[INSERT LINK TO FILE [Online supplementary material]).
7
1 2
3: Modelling public preferences for ∆E and ∆C
3 4
3.1: Method
5
We estimate a public valuation function (PVF) from the CE data using a multinomial logit (MNL)
6
model (Train 2009). Given that net changes in population health (∆E) and medical expenditure (∆C)
7
differ in magnitude and direction, sensitivity to marginal changes is unlikely to be constant. Hence,
8
we suggest a function that can account for potential non-linearities in the valuation of ∆E and ∆C (Eq.
9
1).
10
∆ PVF = ρASC + β I ∆E
11
'
∆& β% δ% !1 − I ∆C #
∆ − δ !I − 1 ∆E # $ + '
∆& − −I ∆C $ + φ∆E ∆C + τ
(1)
12 13
∆ ∆& The I and I terms are two binary variables indicating whether the re-allocation of healthcare
14
∆ resources improves population health (i.e., I =1 when ∆Entj ≥ 0) and decreases medical expenditures
15
∆& (i.e., I =1 when ∆Cntj ≤ 0).
16 17
Regarding the model parameters, β1 and β2 capture the respondents’ preferences for a 1-unit change in
18
∆E and ∆C. To make the estimates more comparable, the ∆C attribute is rescaled by dividing its
19
values by 10,000, such that a 1-unit change in rescaled ∆C indicates an increase/decrease of medical
20
expenditures by 10,000 euros. We expected respondents to prefer a higher level of population health
21
(∆E > 0) and a lower level of medical expenditures (∆C < 0) (i.e., H1a: β1 > 0; H1b: β2 < 0). The α1 and
22
α2 parameters allow for non-constant marginal sensitivities. We expected respondents to become
23
marginally less sensitive to changes in both population health and medical expenditures (i.e., H2a: α1
24
< 1; H2b: α2 < 1). The δ1 and δ2 parameters allow for a change of preferences between positive and
25
negative changes in ∆E and ∆C. We expected individuals to give more weight to negative than same-
8
1
size positive changes (i.e., H3, : δ > 1; H31 : δ% > 1). The ρ parameter captures a systematic
2
preference for a situation of non-neutral changes. We expected individuals’ choices to be biased
3
towards the neutral situation (i.e., H4: ρ < 0). The φ parameters allows for an interaction between the
4
valuation of ∆E and ∆C. We expected preferences for ∆E and ∆C to be linked, and more specifically
5
we expect to observe a positive interaction effect (i.e., H5: φ > 0). As each respondent completed 12
6
choice tasks, we accounted for potential correlation in the data by specifying an additional error term
7
(τ ) which is normally distributed with null mean and standard deviation to be estimated (i.e.,
8
τ ~Normal<0, σ ?).
9 10
Starting from this general specification, it was possible to apply constraints to obtain more
11
parsimonious specifications. For instance, a linear and additive weighting of ∆E and ∆C (Eq. 2) could
12
be obtained with the following constraints: ρ = α = δ = φ = 0.
13 14
PVF = β ∆E + β% ∆C + τ
(2)
15 16
We determined whether allowing for non-linearities in the valuation of ∆E and ∆C improved the
17
modelling of the choices by comparing statistical performance of the PVFNOLIN and PVFLIN
18
specifications.
19 20
3.2: Results
21
Regarding the quality checks, 127 (12.6%) and 208 (20.6%) individuals failed the monotonicity and
22
stability tests respectively. As anticipated, the PVFNOLIN significantly outperformed its linear
23
counterpart (Log-likelihood ratio test: Deviance = 565.2; P < 0.001). The results are presented in
24
Table 2. Respondents positively value an improvement in population health and a reduction of
25
medical expenditures (i.e., cost saving). The estimate for ∆E appeared to be relatively large compared
26
to ∆C, indicating that individuals gave more weight to net changes in health than expenditures (i.e.,
27
0.525/0.055 ≈ 10). The estimate for the ρ parameter is negative and significant, indicating that
9
1
respondents did not want to re-allocate resources ceteris paribus. All four parameters allowing for
2
non-linearities in preferences reached significance. The results showed evidence of loss aversion in
3
valuation of ∆E with losses being 1.4 times more valued than equivalent gains. At the opposite,
4
individuals appeared to give less weight to losses in ∆C compared to gains. There is also evidence of
5
non-constant marginal sensitivity to changes in both ∆E and ∆C. Individuals exhibited diminishing
6
marginal sensitivity in their valuation of ∆E and increasing marginal sensitivity in their valuation of
7
∆C (Figure 3).
8 9
The non-linearities in the PVF resulted in a transformation of the valuation space. Panel A in Figure
10
4 is based on the results from the PVFLIN function and describes the valuation space once public
11
preferences for ∆E and ∆C are taken into account. The grey area describes potential outcomes that
12
would be positively valued by the public. This valuation frontier describes all {∆E; ∆C} outcomes
13
which would be associated with a null valuation and can be interpreted as an indifference curve.
14
Given that preferences were assumed to be linear, this curve takes the form of a straight line, and its
15
slope corresponds to the marginal rate of substitution between ∆E and ∆C (i.e., one needs to increase
16
∆C by 3.31 units to compensate the positive effect of increasing ∆E by 1 unit). Outcomes falling in QI
17
are positively valued by the public. Conversely, all potential outcomes belonging to QIII are negatively
18
valued. This result was anticipated by Sendi et al (2002) who suggested that healthcare resources
19
should be reallocated if more than 95% of the potential outcomes fall within QI. Our study results
20
suggest that this decision rule could be over-cautious because some outcomes in QII and QIV are also
21
positively valued. QIV has a larger share of positively valued outcomes than QII because public gives
22
more weight to ∆E than ∆C.
23 24
Panel B corresponds to a modified version of linear function allowing public preferences to be biased
25
towards the NS (PVFLIN+NS). As the valuation function remains additive in its arguments, we only
26
observe a horizontal translation of the grey area. This translation has two major implications. First, all
27
outcomes in QI are no longer unambiguously good. Second, the NS preference significantly decreases
10
1
the probability of finding improvements in the allocation of healthcare resources (i.e. positively
2
valued outcomes). In Panel A, the grey surface represented approximately 50.3% of the valuation
3
space. In Panel B, this proportion decreased to 35%. Regarding QI, the NS bias represents a 19.3%
4
loss of optimality. The optimality loss is represented by the white surface within QI. Panel C is
5
obtained with the non-linear valuation function (PVFNOLIN). Due to non-linearities in the preferences
6
for ∆E and ∆C, the marginal rate of substitution between these two quantities is no longer constant.
7
The results show that the non-linearities in preferences reduce the impact of the NS effect on the
8
valuation space, as the optimality loss decreases to 8.4%. Panel D is a contour plot of the valuation
9
space. Altogether these results show the importance of allowing for both between-quadrant and
10
within-quadrant effects when exploring public preferences for the allocation of healthcare resources.
11 12
4: Implications of non-linearities in preferences on the allocation decision
13 14
4.1 Method
15
Whilst the non-linearities in public preferences for ∆E and ∆C significantly improved the statistical
16
representation of respondents’ choices, there is a priori no guarantee that these would significantly
17
influence the allocation decision (i.e., whether the uncertainty is acceptable or not). In a simulation
18
study we compared the PVFLIN and PVFNOLIN using 5,000 allocation decisions. For each allocation
19
decision, we simulate a large number of potential outcomes and then apply the PVFLIN and PVFNOLIN
20
functions. The goal is to compare the effect on the decision to re-allocate healthcare resources or not.
21
As a benchmark decision rule we assumed that the decision makers would compute the expected
22
value of the potential outcomes and decide to re-allocate resources only if this expected value is
23
positive (Rule #1). However, to check the sensitivity of our finding to a change in the decision rule,
24
we also tested two additional rules: “Proceeding to re-allocation if at least 50% of the potential
25
outcomes are positive (i.e., median value > 0)” (Rule #2) and “Proceeding to re-allocation if at least
26
95% of the potential outcomes are positive” (Rule #3). We chose these two alternative rules for the
27
following reasons. A comparison based on the median value, instead of the mean (expected) value,
11
1
could be more appropriate in cases of large departures from normality in the distribution of the
2
potential outcomes as the median is less influenced by extreme values. The second rule (rule #3) was
3
chosen following the rule suggested by Sendi et al where the health decision maker will accept the
4
reallocation of resources when 95% or more of the outcomes fall into the Quadrant I of the DMP,
5
which is similar to the rule used in clinical thinking.
6 7
We used a simulation procedure to describe a large number of allocation decisions which differ in
8
terms of ∆E and ∆C and also levels of variability in ∆E and ∆C (Figure 5). We also performed a
9
logistic regression to analyse agreement between PVFNOLIN and PVFLIN for the benchmark decision
10
rule.
11 12
The simulation was conducted as follows:
13
(i)
The uncertainty about the potential consequences of each allocation decision was described with a bivariate normal distribution
14 15
μ∆ σ∆ ∆E ! # ~Normal !μ $ , B ∆C ∆& ∆ ∆&
16
B∆ ∆& σ∆& $#
(3)
17 18
Where µ∆E is the mean ∆E, µ∆C is the mean ∆C, σ∆E is the variance of ∆E, σ∆C is the variance of ∆C
19
and σ∆C∆C is the covariance of ∆E and ∆C. The covariance is given by σ∆ ∆& = ρσ∆ σ∆& , where ρ is
20
the correlation between ∆E and ∆C.
21 22 23
(ii)
We added two proportionality constraints (τ∆ ; τ∆ ) such that the variances (σ∆ , σ∆& ) couldn’t represent less than 10% and more than 200% of the means (μ∆ , μ∆& ):
24 25
σ∆ = μ∆ τ∆
(4a)
26
σ∆& = μ∆& τ∆&
(4b)
27 12
1
(iii)
We specified uniform distributions for the simulation parameters (μ∆ ; μ∆& ; τ∆ ;τ∆ ; ρ).
2
Manipulating these parameters allow obtaining allocation decisions with different shapes of
3
potential outcomes as illustrated in Figure 3. The choice of values for the parameters of the
4
uniform distributions is largely based on values used in Gafni et al (2013) and also had to
5
satisfy a constraint of plausibility/realism (i.e., unlikely that in practice ∆E and ∆C are either
6
perfectly correlated (|ρ|=1) or uncorrelated (ρ=0); unlikely that variances of ∆E and ∆C are
7
null (τE=τC=0)).
8 9
μ∆ ~Uniform<−4, 4?
(5a)
10
μ∆& ~Uniform<−4, 4?
(5b)
11
τ∆ ~Uniform<0.1, 2?
(5c)
12
τ∆& ~Uniform<0.1, 2?
(5d)
13
ρ~Uniform<−0.9, 0.9?
(5e)
14 15
(iv)
We drew 5,000 allocation decisions from these uniform distributions.
(v)
For each allocation decision, we then simulated 10,000 potential outcomes (t) using the
16 17
bivariate normal distribution (Eq. 4).
18 19 20
(vi)
We applied PVFLIN and PVFNOLIN to obtain a subjective valuation of each potential outcome and computed the expected value (EV) of each allocation decision.
21 22
23
<∆E EVJ = K, ∑K, , ∆C ? M PVF
24
<∆E EVJ = K, ∑K, , ∆C ? M PVF
(7a)
(7b)
25 26 27
(vii)
The decision rule that we used is to recommend re-allocation of healthcare resources when the EV of the allocation decision is positive. Therefore, for each PVF, we computed the 13
1
percent of allocation decisions with a positive EV. We then used the Kappa coefficient to
2
measure the level of agreement between the two PVFs. We then performed a logistic
3
regression to investigate the effects of changes in the simulation parameters on the level of
4
agreement.
5 6
P
(8)
7 8
4.2: Results
9
Regarding the PVFNOLIN function, 28.1% of the situations had a positive expected value. This
10
proportion increased to 50.1% with the PVFLIN function. The level of agreement (after accounting for
11
agreement by chance) was moderate with a Kappa coefficient of 0.56. Whilst the choice of the
12
decision rule had a large effect on these proportions of cases where resources should be re-allocated
13
(i.e., Rule #2: {PVFNOLIN = 34.62%, PVFLIN = 50.18%}, and Rule #3: {PVFNOLIN = 4.18%, PVFLIN =
14
13.02%}), the PVFLIN function appeared to provide higher estimates of the proportion of cases in
15
which resources should be re-allocated.
16 17
The results for the logistic regression of agreement are presented in Table 3. The results show that the
18
probability of agreement between the two functions is mainly driven by the distribution of the net
19
changes in health outcomes (∆E). When increasing the size of the improvements in health outcomes,
20
the PVFNOLIN and PVFLIN functions become more likely to provide different recommendations
21
regarding the allocation of healthcare resources. At the opposite, when the potential health outcomes
22
become more variable, the two methods are more likely to agree (i.e., a 1-unit increase in σ∆E is
23
associated with a +5% increase in the agreement probability).
24 25
5: Discussion
26
14
1
The objective of our study was to identify a public valuation function (PVF) that describes how a
2
representative sample of the French population values potential outcomes stemming from a decision
3
to reallocate healthcare resources. To the best of our knowledge, it is the first attempt to identify such
4
function. In line with Gafni et al (2013) arguments, our results show that the valuation of outcomes
5
stemming from resources reallocation is shaped by both a within-quadrant effect (the magnitude of
6
the potential gains or losses) and a between-quadrant effect (the direction of potential outcome).
7
These effects were captured by a non-linear valuation function largely inspired by the prospect theory
8
(Kahneman & Tversky, 1979). We showed that such non-linear function provided a better account of
9
the resources reallocation decisions. We then illustrated the consequences of this public valuation
10
function in terms of recommendations regarding the decision to reallocate resources across different
11
healthcare interventions. In a simulation study, we showed that ignoring non-linearities in public
12
preferences by assuming a linear function could lead to different results.
13 14
This study contributes to the literature in different ways. First, it illustrates how to operationalize the
15
measurement of a PVF and that it is feasible to do it for a representative sample of the population. It
16
demonstrates how public preferences could be used to inform the health policy-making process. The
17
importance of taking into account the public views in the organisation of the healthcare system has
18
been widely acknowledged. However, in practice this might be difficult to achieve as one first needs
19
to determine how to measure/describe users’ views and then identify a mechanism to incorporate
20
these views in the decision-making. By building a valuation space based on public preferences, our
21
study provides a tool which can inform the decision whether to reallocate resources or not. Past
22
studies tried to achieve this objective by investigating public preferences for how healthcare resources
23
should be used (i.e., who should benefit from the scarce resources in priority) (Erdem & Thompson,
24
2014; Green & Gerard, 2009; Scuffham et al, 2014; Skedgel et al, 2015). Second, study results
25
contribute to the literature on the measurement of non-linearities in health-related preferences (Holte
26
et al, 2016; van der Pol et al, 2014; Torres et al, 2011). The third contribution is demonstrating the
27
importance of measuring a PVF rather than assuming one. Our simulation study demonstrates the
15
1
potential for a large effect on the decision whether to continue with resource allocation or not for a
2
given distribution of potential outcome.
3 4
One potential limitation of this study is the absence of information regarding the types of
5
treatments and the population treated (e.g. age, gender, size of the population) involved in the decision
6
to reallocate healthcare resources. Our approach obtains a generic set of results to inform health
7
policy making under the common assumption that a unit of health outcome (e.g., HYE, QALY) is
8
valued the same regardless of who gains it or loses it (Whitehead & Ali, 2010). This may have
9
reduced the credibility of our choice experiment for some participants and/or decision makers who do
10
not subscribe to this assumption. In line with the assumption that the application area does not affect
11
the valuation of allocation decisions, we provided no information regarding the type of treatments to
12
be implemented/cancelled and explicitly instructed the participants to consider this information as
13
irrelevant. However, we have no information about respondents’ understanding of this choice setting
14
and some might still have envisaged particular decision contexts when they participated in the
15
experiment. Future studies could look at the impact of making the choice context case specific (e.g.,
16
whether it matters or not, how it affects). Similarly, the size of the different subgroups of patients was
17
“made irrelevant” by providing individual-level information (e.g., 20,000 euros increase in medical
18
expenditures per person) to the participants rather than aggregated information (e.g., 200 million
19
euros increase in medical expenditures). This was done to make the figures easier to understand for
20
the participants and to avoid potential distributional issues (i.e., the same figure can hide different
21
repartitions of the effects across patients’ subgroups). We tried to preserve the collective nature of the
22
decision problem by (i) instructing participants to assume the role of a health decision maker when
23
making their decisions, and (ii) framing the individual-level values as average consequences of the
24
decision to re-allocate healthcare resources per person. However, we could not verify whether the
25
participants followed these instructions. Future research should look for other ways to present the
26
information at an aggregated level that will be understandable to individuals.
27
16
1
The study results could also have been influenced by the hypothetical nature of the choice
2
questions (Hensher, 2010; Loomis, 2011). Future research could test the robustness of our study
3
results to hypothetical biases by using cheap-talk script or oath priming (de-Magistris & Pascucci,
4
2014; Carlsson et al, 2013). Such hypothetical bias may explain why net changes in population health
5
appeared to be more important than net changes in the level of medical expenditures in respondents’
6
choices. We attempted to mitigate a potential hypothetical bias by carefully explaining to the
7
participants the decision context and that increase in the size of the healthcare budget might be at the
8
expense of other public sectors such as education.
9 10
The study results may suffer from a lack of sample representativeness. Whilst our sample
11
appears to be an acceptable representation of the French population in terms of age, gender and
12
geographical spread, the descriptive analysis of some other personal characteristics showed significant
13
departures from the national population in terms of education attainment (i.e., our sample appears to
14
be more qualified) and self-reported health status (i.e., our sample appears to be in a more deteriorated
15
health). This lack of representativeness is likely to be caused by the use of an online panel. However,
16
it is unclear a priori how the personal characteristics of the respondents would influence the
17
preferences for the allocation of healthcare resources in a generic context. We leave this issue for
18
future research.
19 20
Future research should also assess the impact of different decision rules on the policy
21
recommendations. Following Gafni et al (2013), we summarised all the information about potential
22
situations by computing the expected value of the decision (Rule #1). However, other decision rules
23
can be envisaged. To test the sensitivity of our finding to the choice of a decision rule we tried two
24
other decision rules based on the “50% of the potential outcomes being positive” (Rule #2) and “95%
25
of potential outcomes being positive” (Rule #3), and the results showed that important differences in
26
the percentage of cases where resources should be re-allocated. However, the proportions obtained
27
with the linear public valuation function were higher in the linear case than those obtained with its
28
non-linear counterpart, in the three decision rules compared. 17
1 2
6: Conclusion
3
In this study we have demonstrated how a valuation function, that describes the preferences (or values
4
attributed) for every potential outcome in each quadrant of the DMP, can be obtained from a
5
representative sample of the population (i.e., France in our example). Our study demonstrates the
6
importance of measuring such function rather than assuming one. We do not feel that our work is
7
necessarily providing the final answer. It is the first step and calls for more research that should
8
explore the effects (if there are) of other factors (e.g., which treatment is added to what disease and
9
which treatment is cancel for what disease to free up the required resources) on the public preferences.
10
18
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53
References Bekker-Grob, Esther W. de, Mandy Ryan, and Karen Gerard. 2012. “Discrete Choice Experiments in Health Economics: A Review of the Literature.” Health Economics 21 (2): 145–72. https://doi.org/10.1002/hec.1697. Birch, S., and A. Gafni. 1992. “Cost Effectiveness/Utility Analyses. Do Current Decision Rules Lead Us to Where We Want to Be?” Journal of Health Economics 11 (3): 279–96. Campbell, Danny, Marco Boeri, Edel Doherty, and W. George Hutchinson. 2015. “Learning, Fatigue and Preference Formation in Discrete Choice Experiments.” Journal of Economic Behavior & Organization 119 (November): 345–63. https://doi.org/10.1016/j.jebo.2015.08.018. Carlsson, Fredrik, Mitesh Kataria, Alan Krupnick, Elina Lampi, Åsa Löfgren, Ping Qin, and Thomas Sterner. 2013. “The Truth, the Whole Truth, and Nothing but the Truth—A Multiple Country Test of an Oath Script.” Journal of Economic Behavior & Organization 89 (May): 105–21. https://doi.org/10.1016/j.jebo.2013.02.003. Clark, Michael D., Domino Determann, Stavros Petrou, Domenico Moro, and Esther W. de BekkerGrob. 2014. “Discrete Choice Experiments in Health Economics: A Review of the Literature.” PharmacoEconomics 32 (9): 883–902. https://doi.org/10.1007/s40273-014-0170x. Erdem, Seda, and Carl Thompson. 2014. “Prioritising Health Service Innovation Investments Using Public Preferences: A Discrete Choice Experiment.” BMC Health Services Research 14 (1). https://doi.org/10.1186/1472-6963-14-360. Gafni, Amiram, and Stephen Birch. 1993. “Guidelines for the Adoption of New Technologies: A Prescription for Uncontrolled Growth in Expenditures and How to Avoid the Problem.” Canadian Medical Association Journal 148 (6): 913–917. ———. 1997. “QALYs and HYEs Spotting the Differences.” Journal of Health Economics 16 (5): 601–8. https://doi.org/10.1016/S0167-6296(96)00527-9. ———. 2006. “Incremental Cost-Effectiveness Ratios (ICERs): The Silence of the Lambda.” Social Science & Medicine 62 (9): 2091–2100. https://doi.org/10.1016/j.socscimed.2005.10.023. Gafni, Amiram, Stephen Walter, and Stephen Birch. 2013. “UNCERTAINTY AND THE DECISION MAKER: ASSESSING AND MANAGING THE RISK OF UNDESIRABLE OUTCOMES: UNCERTAINTY AND THE DECISION MAKER.” Health Economics 22 (11): 1287–94. https://doi.org/10.1002/hec.2883. Green, Colin, and Karen Gerard. 2009. “Exploring the Social Value of Health-Care Interventions: A Stated Preference Discrete Choice Experiment.” Health Economics 18 (8): 951–76. https://doi.org/10.1002/hec.1414. Hensher, David A. 2010. “Hypothetical Bias, Choice Experiments and Willingness to Pay.” Transportation Research Part B: Methodological 44 (6): 735–52. https://doi.org/10.1016/j.trb.2009.12.012. Holte, Jon Helgheim, Peter Sivey, Birgit Abelsen, and Jan Abel Olsen. 2016. “Modelling Nonlinearities and Reference Dependence in General Practitioners’ Income Preferences: GPs’ Income Preferences.” Health Economics 25 (8): 1020–38. https://doi.org/10.1002/hec.3208. Kahneman, Daniel, and Amos Tversky. 1979. “Prospect Theory: An Analysis of Decision under Risk.” Econometrica 47 (2): 263. https://doi.org/10.2307/1914185. Krucien, Nicolas, Nathalie Pelletier-Fleury, and Amiram Gafni. 2018. “Measuring Public Preferences for Health Outcomes and Expenditures in a Context of Healthcare Resource Re-Allocation.” PharmacoEconomics, November. https://doi.org/10.1007/s40273-018-0751-1. Loomis, John. 2011. “WHAT’S TO KNOW ABOUT HYPOTHETICAL BIAS IN STATED PREFERENCE VALUATION STUDIES?: HYPOTHETICAL BIAS IN STATED PREFERENCE VALUATION STUDIES.” Journal of Economic Surveys 25 (2): 363–70. https://doi.org/10.1111/j.1467-6419.2010.00675.x. Magistris, Tiziana de-, and Stefano Pascucci. 2014. “The Effect of the Solemn Oath Script in Hypothetical Choice Experiment Survey: A Pilot Study.” Economics Letters 123 (2): 252–55. https://doi.org/10.1016/j.econlet.2014.02.016.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
Mehrez, Abraham, and Amiram Gafni. 1989. “Quality-Adjusted Life Years, Utility Theory, and Healthy-Years Equivalents.” Medical Decision Making 9 (2): 142–49. https://doi.org/10.1177/0272989X8900900209. Pol, Marjon van der, Gillian Currie, Seija Kromm, and Mandy Ryan. 2014. “Specification of the Utility Function in Discrete Choice Experiments.” Value in Health 17 (2): 297–301. https://doi.org/10.1016/j.jval.2013.11.009. Ryan, Mandy, Nicolas Krucien, and Frouke Hermens. 2018. “The Eyes Have It: Using Eye Tracking to Inform Information Processing Strategies in Multi-Attributes Choices.” Health Economics 27 (4): 709–21. https://doi.org/10.1002/hec.3626. Savage, Scott J., and Donald M. Waldman. 2008. “Learning and Fatigue during Choice Experiments: A Comparison of Online and Mail Survey Modes.” Journal of Applied Econometrics 23 (3): 351–71. https://doi.org/10.1002/jae.984. Scuffham, Paul A, Julie Ratcliffe, Elizabeth Kendall, Paul Burton, Andrew Wilson, Kalipso Chalkidou, Peter Littlejohns, and Jennifer A Whitty. 2014. “Engaging the Public in Healthcare Decision-Making: Quantifying Preferences for Healthcare through Citizens’ Juries.” BMJ Open 4 (5): e005437. https://doi.org/10.1136/bmjopen-2014-005437. Skedgel, Chris, Allan Wailoo, and Ron Akehurst. 2015. “Societal Preferences for Distributive Justice in the Allocation of Health Care Resources: A Latent Class Discrete Choice Experiment.” Medical Decision Making 35 (1): 94–105. https://doi.org/10.1177/0272989X14547915. Torres, Cati, Nick Hanley, and Antoni Riera. 2011. “How Wrong Can You Be? Implications of Incorrect Utility Function Specification for Welfare Measurement in Choice Experiments.” Journal of Environmental Economics and Management 62 (1): 111–21. https://doi.org/10.1016/j.jeem.2010.11.007. Train, Kenneth. 2009. Discrete Choice Methods with Simulation. 2nd ed. Cambridge ; New York: Cambridge University Press. Weinstein, Milton, and Richard Zeckhauser. 1973. “Critical Ratios and Efficient Allocation.” Journal of Public Economics 2 (2): 147–57. https://doi.org/10.1016/0047-2727(73)90002-9. Whitehead, S. J., and S. Ali. 2010. “Health Outcomes in Economic Evaluation: The QALY and Utilities.” British Medical Bulletin 96 (1): 5–21. https://doi.org/10.1093/bmb/ldq033. Williams, A. 1983. “The Economic Role of Health Indicators.” In Measuring the Social Benefits of Medicine, 63–67. London: Office of Health Economic: G. Teeling Smith.
20
Table 1. Descriptive analysis of personal characteristics of the respondents (N=995) % 1. Personal characteristics Health status Very good Good Fair/Bad/Very bad Education No formal qualifications & Other Secondary or high school qualifications University or College degree Gender Male Female Chronic conditions None At least one Prefer not to say Involvement *** Undecided (4-6) No (<= 3) Yes (>= 7) Satisfaction *** Neither satisfied, nor unsatisfied (4-6) Unsatisfied (<= 3) Satisfied (>= 7) Age Mean (SD) 2. Feedback about the questionnaire Interest *** Intermediate (4-6) Not interesting (<= 3) Interesting (>= 7) Difficulty *** Intermediate (4-6) Difficult (<= 3) Easy (>= 7) Quality *** Intermediate (4-6) Good (<= 3) Bad (>= 7)
22.9 52 25.1 9.4 16.5 74.1 48.8 51.2 57.9 37.9 4.2 23.3 3.6 73.1 36.9 6.1 57 43.68 (14.18) 19.5 6 74.5 34.8 8.2 57 28.2 24.4 47.3
*** Involvement: Do you think the public should be involved in the decisions to fund new medical interventions? [11-points rating scale ranging from "not at all" (0) to "yes quite" (10)]; Satisfaction: How satisfied are you with the healthcare system? [11-points rating scale ranging from "Fully unsatisfied" (0) to "Fully satisfied" (10)]; Quality: How would you rate the quality of this questionnaire? [11-points rating scale ranging from "Extremely good" (0) to "Extremely bad" (10)]; Interest: How would you rate the interest of this questionnaire? [11-points rating scale ranging from "Not at all interesting" (0) to "Extremely interesting" (10)]; Difficulty: How would you rate the difficulty of this questionnaire? [11-points rating scale ranging from "Extremely difficult" (0) to "Extremely easy" (10)]
Table 2. Estimation of public preferences for net changes in health outcomes and medical expenditures VLIN
VLIN+NS
VNOLIN
-
-0.7491 (0.0352) ***
-0.6152 (0.0509) ***
∆E
0.3297 (0.0046) ***
0.3184 (0.0046) ***
0.5251 (0.0358) ***
∆C
-0.0995 (0.0023) ***
-0.097 (0.0023) ***
-0.0547 (0.019) ***
∆E x ∆C
-
-
0.0003 (0.0005)
LA_∆E
-
-
1.4045 (0.0575) ***
LA_∆C
-
-
0.7255 (0.07) ***
MS_∆E
-
-
0.6562 (0.0337) ***
MS_∆C
-
-
1.2773 (0.1457) ***
1.123 (0.0409) ***
0.7767 (0.0389) ***
0.7806 (0.0393) ***
995
995
995
11,940
11,940
11,940
# Parameters
3
4
9
Log-likelihood
-8,291.5
-8,108.4
-8,008.9
BIC
16,611.2
16,254.4
16,102.3
1. Model parameters (MLE (SE)) ASC
SD_panel 2. Model statistics # Individuals # Observations
MLE: maximum likelihood estimate; SE: standard error; P: P-value; ∆E: Net change in health outcomes; ∆C: Net change in health expenditures; SD: standard deviation; ASC: Alternative specific constant; LA: Loss aversion; MS: Marginal sensitivity; BIC: Bayesian information criteria. *** P-value < 1%; ** P-value < 5%; * P-value < 10%
Table 3. Logistic regression of the agreements between the recommendations of the VNOLIN and VLIN public valuation functions MLE
SE
P
AME
Constant
0.685
0.065
< 0.001
-
mE
-0.311
0.019
< 0.001
-0.049
mC
-0.015
0.016
0.363
-0.002
sE
0.318
0.025
< 0.001
0.050
sC
0.085
0.021
< 0.001
0.013
sEC
0.078
0.070
0.265
0.012
Model statistics: Log-likelihood = -2,400.2; # Observations = 5,000 (# 1's = 3,900); # Parameters = 6 MLE: maximum likelihood estimate; SE: Standard error; P: P-value; AME: Average marginal effect; mE & sE: Respectively mean and standard deviation of net changes in population health; mC & sC: Respectively mean and standard deviation of net changes in medical expenditures; sEC: Covariance of net changes in population health and medical expenditures.
Figure 1. Representation of the decision to reallocate healthcare resources in the decisionmaking plane (DMP) Panel A: Decision-making plane
Panel B: Uncertainty in the consequences of the decision to re-allocate healthcare resources
Source: Sendi, P., Gafni, A. & Birch, S. Opportunity costs and uncertainty in the economic evaluation of health care interventions. Health Econ. 11, 23–31 (2002). Reading: ∆C(A) indicates the incremental costs for programme A; ∆C(B) indicates the incremental costs for programme B; ∆E(A) indicates the incremental health outcomes for programme A; ∆E(B) indicates the incremental health outcomes for programme B; The Latin numbers (I, II, III, IV) are used to describe the four quadrants of the DMP: {Increase in health outcomes; Decrease in medical expenditures}; {Decrease in health outcomes; Decrease in medical expenditures}; {Decrease in health outcomes; Increase in medical expenditures}; {Increase in health outcomes; Increase in medical expenditures}. Panel B illustrates the posterior joint distribution taken from an example used in Sendi et al (2002) of introducing programme A and cancelling programme B in the decision-making plane.
Figure 2. Illustration of the choice task format
Figure 3. Visual representation of non-linearities in public preferences for ∆E and ∆C
Figure 4. Using public preferences to transform the decision making plane into a valuation space Panel A: Linear function (PVFLIN)
Panel B: Linear function allowing for a neutral situation bias (PVFLIN+NS)
Panel C: Non-linear function allowing for a Panel D: Contour plot representing the neutral situation bias, asymmetric preferences valuation space once non-linear public between positive and negative changes and non- preferences for ∆E and ∆C are considered constant marginal sensitivity to changes (PVFNOLIN)
Legend Coloured areas in panels A-C represent the potential outcomes {∆E; ∆C} which would be positively (Grey) and negatively (White) valued by the public. Dotted green line in panels B-D corresponds to the indifference curve associated with PVFLIN. Dotted red line in panels C-D corresponds to the indifference curve associated with PVFLIN+NS. Panel D describes how public valuation changes across the decision-making plane – Within each colour band the exact valuations also differ.
Figure 5. Illustration of potential outcomes for different RADs *
Legend: mE = mean of net changes in health outcomes (∆E); mC = mean of net changes in medical expenditures (∆C); sE = variance of ∆E; sC = variance of ∆C; sEC = covariance of ∆E and ∆C. The ellipses around the dots correspond to the 95% confidence ellipses. [Situation #1] mE=1.767; mC=-2.553; sE=0.864; sC=0.091; sEC=0.009; [Situation #2] mE=3.006; mC=-2.490; sE=4.145; sC=2.311; sEC=8.576; [Situation #3] mE=2.008; mC=1.816; sE=3.631; sC=2.881; sEC=3.815; [Situation #4] mE=3.089; mC=-3.755; sE=6.062; sC=0.873; sEC=4.328. * To improve the readability of this illustration we only drew 100 potential outcomes for each RAD.
Research highlights • A public valuation function to support reallocation of healthcare resources • Evidence of non-linearities in public valuation of health outcomes and expenditures • Public gives 10 times more weight to health outcomes than expenditures • Non-linearities in public preferences matter for the resource allocation decisions
Amiram Gafni: Conceptualization; Methodology; Writing - Review & Editing. Sebastian Heidenreich: Formal analysis; Writing - Review & Editing. Nicolas Krucien: Conceptualization; Methodology; Formal analysis; Writing - Original Draft; Writing - Review & Editing; Project administration. Nathalie Pelletier-Fleury: Conceptualization; Methodology; Resources; Writing - Review & Editing.