- Email: [email protected]
Assessing the burden of Clostridium difficile infections for hospitals
Accepted Manuscript Assessing the burden of Clostridium difficile infections for hospitals Elise Hebbinckuys, Pharma.D, Jean-Pierre Marissal, Ph.D, Cristian Preda, Ph.D, Valérie Leclercq, MD PII:
S0195-6701(17)30467-X
DOI:
10.1016/j.jhin.2017.08.023
Reference:
YJHIN 5212
To appear in:
Journal of Hospital Infection
Received Date: 18 July 2017 Accepted Date: 29 August 2017
Please cite this article as: Hebbinckuys E, Marissal J-P, Preda C, Leclercq V, Assessing the burden of Clostridium difficile infections for hospitals, Journal of Hospital Infection (2017), doi: 10.1016/ j.jhin.2017.08.023. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. 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.
ACCEPTED MANUSCRIPT TITLE : Assessing the burden of Clostridium difficile infections for hospitals SHORT TITLE : Cost of Clostridium difficile AUTHORS: Elise HEBBINCKUYS, Pharma.D (1), Jean-Pierre MARISSAL, Ph.D (1), Cristian PREDA, Ph.D (3), Valérie LECLERCQ, MD (4)
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(1) Centre hospitalier de St Philibert– 115 rue du Grand But– 59160 Lomme– France : [email protected]; (2) Faculté de Gestion, d’Economie et de Sciences – Institut catholique de Lille – 60 boulevard Vauban – CS 40109 – 59016 Lille Cedex – France; [email protected]; (3) Laboratoire de Mathématiques Paul Painlevé (UMR-CNRS 8524) – Bâtiment M2 – Cité Scientifique – 59655 Villeneuve-d'Ascq – France; Institute of Mathematical Statistics and Applied Mathematics – Romanian Academy; [email protected] (4) Centre Hospitalier Saint-Philibert – 115, rue du Grand But – 59160 Lomme – France : [email protected].
CORRESPONDANCE
All correspondence should be sent to:
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Jean-Pierre Marissal
Faculté de Gestion, d’Economie et de Sciences Institut Catholique de Lille
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CS 40109 59016 Lille Cedex
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France.
Mail : [email protected]
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ACCEPTED MANUSCRIPT ABSTRACT: Background: Nosocomial infections place a heavy burden on the healthcare system. However, quantifying the burden raises many questions, ranging from the way to accurately estimate the extra length of stay at hospital to defining and costing the preventative methods among the different care providers.
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Method: We used multi state modeling based on Markov processes and bootstraping to derive individual estimates of the prolongation of stay at hospital associated with Clostridium difficile infection (CDI). We then computed indicators of cost for hospitals, including an estimation of the productivity losses derived from DRG-based payment systems.
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Population: Patients aged 55 and over, admitted in two hospital facilities in Lille, Saint Philibert, Lomme and Saint Vincent de Paul, Lille, North of France, with and without an episode of CDI from January 1st 2013 to September 15th 2014.
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Results: A total of 52 episodes were screened during the study period. The estimated mean cost of CDI was approximately €23,909 (SD = 17,458) for an extended length of hospital stay (N = 27). In the case of a reduced length of the hospital stay (N = 25), the mean cost was approximately € –14,697 (SD = 16,936), which represents net savings for the hospitals. The main cost / savings driver was the productivity losses / gains resulting from the nosocomial infection. A sensitivity analysis showed that the main factor explaining the amount of costs or savings due to nosocomial infections was the length of the hospital stay.
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Conclusion: We discuss the notion of productivity gains in the case of deaths as a factor revealing the incompleteness of the payment systems. We then discuss the methodological issues associated with the statistical method used to control for temporality bias.
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Keywords: Cost, measurement bias, nosocomial infection. JEL classification : I12 I18.
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ACCEPTED MANUSCRIPT 1. Introduction Estimation of the cost of hospital-acquired infections raises two important questions dealing with both the quality and the nature of the measurements to be made. These questions relate not only to the costing methodology but also to the computation of the extra days at hospital.
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The latter question deals with how to measure, with a minimum level of bias, the effect of a particular episode of nosocomial infection on the length of a hospital stay. The literature on this topic offers a number of possible approaches. The first statistical attempt to measure the prolongation of hospital stay dates from the 1980s, with the pioneering works by Cruse and Foord [1] and Haley et al [2]. The authors used an analysis based on the comparison between infected persons (cases) and non-infected ones (controls) matched according to a limited number of relevant criteria (e.g., age and type of surgery). The main problem posed by this method lies in its low level of control of factors that are likely to affect the overall length of the stay. In fact, to compute the extra hospital days would require samples of cases and controls in each configuration defined by crossing relevant factors. In practice, this is almost impossible due to the relatively low rates of incidence of nosocomial infections.
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Another approach to estimating the extra hospital days uses econometrics, a set of methods aimed at decomposing the variance of a phenomenon. The difficulty here is to take into account the specificities of the statistical distribution of the lengths of hospital stays, namely a long tailed distribution. This led to methods ranging from the use of a simple log transformation of the length of hospital stays [3] to the use of specific statistical distributions (e.g., a gamma or a log-normal distribution) [4, 5].
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The main advantage of the econometric approach is its capability to control for the impact of several factors that are likely to explain the length of the stay. In this case, the estimated net effect of the nosocomial infection on the length of hospital stays is captured by the weight of a dichotomous variable (infected / non-infected) or, if available, of a polytomous variable introducing the severity of the episode. This method has, however, two limits. First, it requires a large number of cases to capture with accuracy the net impact of nosocomial infections on the length of hospital stays. Second, this approach (like the case-control approach) doesn’t control for temporality biases [6]. Such temporality biases arise when time is a relevant factor in the explanation of both the incidence of the infections and the length of hospital stays [7, 8]. Time may indeed affect the estimates through two main sources: (i) the time at which the infection is declared during an hospitalisation – the consequences may differ if an infection is declared at the beginning of the hospitalisation or at the end, when other medical factors have been fixed –, and (ii) the time when hospitalisation occurs – there may be periods of general increase in the length of stay in some wards. The method used to control for the temporality biases relies on Markov processes and 3
ACCEPTED MANUSCRIPT survival analysis. These methods aim at computing the expectation of the extra length of hospital stays taking into account the time of infection through the definition of multiple states (basically, infected / not infected, and alive at discharge / dead) [9, 10]. The individual estimates (pseudo-values) are derived from the average estimate by decomposing this average with bootstrap methods [11].
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In response to an increase in the frequency and severity of Clostridium difficile infections (CDI) observed in our hospitals, associated with the emergence of hypervirulent C. difficile 027, we aimed to estimate cost of nosocomial infection of C. difficile to inform the hospital managers. We used a multi-state modeling approach based on Markov processes in order to estimate the cost of Clostridium difficilerelated nosocomial infections in two hospitals of Lille (North of France). We first defined some economic indicators aiming at capturing the dimensions of the burden of nosocomial infections for hospitals, based on the use of some properties of the diagnosed-related groups (DRGs). We then produced estimates of the extra hospital days due to CDI during the period January 1st 2013 to September 15th 2014. We then provide data on the costs of these infections according to the domains of burden we previously defined. Finally, we discuss the results and highlight a possible bias of the method, namely the absence of control of other interfering factors, which may lead to biased estimates when analyzing at the ward level.
2.1 Setting
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2. Methods
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The GHICL (Catholic Institute of Lille) consists of two hospitals in Lille (Saint-Philibert and Saint-Vincent de Paul) and a clinic (Sainte Marie) in the neighbouring town of Cambrai. Saint-Philibert Hospital (SP) focuses on adult specialty activities and had 352 beds in 2013, and Saint-Vincent de Paul Hospital is positioned as a general hospital with a high-level mother-child center and had 284 beds in 2013. The total number of employees is about 2,200, 42,000 hospitalizations, over 120,000 outpatient visits, 66,000 emergency visits per year. 2.2 Assessing the impact on hospital productivity Time is a central variable in the computation of the cost of nosocomial infections. It affects the measurements by defining the period of time during which costs have to be applied (the extra days at hospital). It is also a factor that is characterized by multiproducts. Indeed, time can be the source of numerous and simultaneous effects related to different cost domains, then defining a set of concomitant cost drivers for the hospital. An additional complexity to take into account relates to the properties of DRG-based payment systems as cost drivers for the hospital. DRG-based payment systems are used in many Western countries like France. They consist in defining a link between 4
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the payment of a hospital stay on one hand, and the length of the hospital stay and the medical complexity of the case (e.g., main and associated diagnoses, age, etc.) on the other hand. Such systems aim at driving a reduction in length of stay, providing absolute references presented as thresholds. Not only does this kind of payment system provide data that can be used as references for all hospital structures, but DRG-based payments also allow us to define an indicator of productivity loss for the hospitals facing episodes of nosocomial infection.
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In a basic DRG-based system in which a given hospital stay i is associated with a certain amount or payment Pi, which is modulated on the basis of the length of hospital stay. Let us consider that the system defines two bounds: a lower bound of length (LBi) and an upper bound of length (UBi). The principle is to define a system of payment incentivizing hospitals to reduce the length of hospital stays towards the lower bound. This is why most of the systems define low payments in the case of a length below the lower bound, and, in the case of the French system, an additional fee for each additional day over the upper bound. In this context, the productivity in value of an hospital admission may be expressed as the ratio of the payment to the number of days at hospital, with the following relationship: > + − 1 ×
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where ti is the total length of hospital stay, and fi the fee per day over the upper bound.
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The classical problem posed by nosocomial infections is that it increases the length of a hospital stay. Let us denote by ei the estimated prolongation of a stay due to a particular episode of nosocomial infection occurring during the stay i. Then we can write = + , where is the length of hospital stay explained by other medical factors. Three cases must be considered.
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If > 0 – meaning that a nosocomial infection leads to an increase in the length of a hospital stay –, one has a loss of productivity when !"# ×$
−
' !"# ×$ %& '
> 0,
where ()*+, = 1 when the condition -./0 is met, = 0 otherwise. This leads to the definition of an indicator of the loss of productivity in value, given by: '
( =
− 1 × 1 2 − ( '3"# 1 + − 2 − ( 3"# 1 − 2 × ,
where ( is the loss of productivity indicator associated with the stay i.
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ACCEPTED MANUSCRIPT The second case to be considered is when > 0 and the payment system introduces special fees accounting for extra charges induced by a nosocomial infection, which is the case in France as Clostridium difficile is concerned. Let us consider a system in which a special fee is paid in case of a stay i. Let us also assume that this episode increases the payment from 1 2 to 1 + 2. In such a situation, the ( is given by the following system:
− 1 × 1 2 − 1 + 2 − 1 2 − ( ' 3"# 1 + − 2 −
( 3"# 1 − 2 × ,
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'
( =
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The last case to be considered corresponds to a reduction in the length of the hospital stay, that is, < 0. In this case, the ( is
( = 1 − ' × 1 2 − 1 2 − 1 + 2 − ( ' 3"# 1 + − 2 −
( 3"# 1 − 2 × .
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This expression is the consequence of a change in the reference situation, which becomes 1 + 2 instead of in the case of a reduced length of a hospital stay 1 < 02.
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2.3 Assessing the opportunity cost of nosocomial infections
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As stated earlier, time may affect hospital costs in several ways. One of these is through productivity, but time is also associated to opportunity costs due to the fact that a bed may be used for several medical purposes. Using a bed for a certain motive or blocking a bed because of a nosocomial infection forbids its use for a different medical purpose. 6
For example, each hospital stay k in a specific ward (j) is associated with 05 days of 6
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hospitalization, leading to an income 5 . In this case, an extension of the length of hospital stay is associated with an opportunity cost that is classically computed as: 6
78 =
∑5 56
∑5 056
6
6
× : × /
6
where 786 is the opportunity cost for ward j, is the extension of the length of the 6
hospital stay associated with the Ith episode in ward j, and / the number of beds in the room involved in the process of isolation of the Ith episode in ward j. The overall opportunity cost of nosomial infections for the hospital is then trivially given by 78 = ∑6 786 . 6
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<
∑; ;
< ∑; ,;
6
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× × / will exhibit a negative value, indicating a gain in terms of
economic opportunities for the ward and the hospital.
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2.4 Direct costs of nosocomial infections Nosocomial infections exhibit direct costs in the form of treatment costs, mostly antibiotics in the case of CDI, screening costs, medical supervision, and decontamination.
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Treatment costs are classically computed by multiplying the cost per dose by the number of doses units per day and the number of days of treatment during the period of hospitalization.
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The computation of the cost of screening is directly derived from the application of the guidelines relating to the screening for C. difficile [12] and a specific fee per screening used in the two hospitals used in the empirical analysis. The cost of medical supervision and prophylaxis is derived from an ad hoc empirical study performed in the studied hospitals.
2.5 Data collection
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Table I summarizes the assumptions used in the computation of the direct hospital costs of nosocomial infections for the two hospital structures analysed.
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We prospectively and exhaustively collected medical, administrative and payment data on all cases of CDI declared in our two hospitals at least 48 hours after admission, and whose hospitalisations led to a DRG-based payment , from January 1st 2013 to September 15th 2014. We also collected medical and administrative data on 10,341 hospitalised patients who declared no episode of CDI during the same time period, aged 55 to 104 to match the age range of the infected cases. 3. Results
3.1 Clostridium difficile nosocomial infections During the study period, a total of 52 patients were had CDI in Saint Philibert and Saint Vincent hospitals. Their median age was 77.7 years, ranging from 56 to 104. The median length of hospital stay was 18.5 days, ranging from 6 to 132 (mean = 39.5 days). The infected patients were mostly admitted to the general medicine ward (19%), the intensive care unit (11%), the cardiology intensive care unit (10%), the 7
ACCEPTED MANUSCRIPT digestive surgery ward (10%), and to the palliative care unit (10%) at the time of the episode. Eighteen out of the 52 infected patients died during their hospitalization.
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The estimated average extra lengths of hospital stay, assessed by the multi-state model [10], were, respectively, 7.756 days (standard deviation (SD) = 1.22) in the case of deceased patients (18 infected versus 620 non-infected patients), and 6.953 days (SD = 0.11) in the case of patients living at discharge (34 infected versus 9,721 non-infected patients).
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The bootstrap decomposition of these two estimated averages, aimed at deriving estimates of the prolongation of stay at the individual level, leads to a median individual prolongation of hospital stay of 12.5 days among deceased patients (N = 18), and 0.0 day among living patients (N = 34) (Figure 1).
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3.2 Burden of CDI
The assessment of the burden of CDI in the two hospitals had to take into account the existence of an extension 1 > 02 or a reduction 1 < 02 in the length of the hospital stay in the presence of an infection.
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The mean burden per episode in the case of an extension of the length of stay (N = 27) was estimated to be €23,909 (SD = 17,458; 95% confidence interval (CI) ranging from €1,312 to €74,571). Figure 2 displays a decomposition of the average burden of CDI, showing that the productivity losses due to an episode of nosocomial infection account for 40.8% of the total costs. This chart also shows that all the financial devices aimed at compensating for the consequences of a nosocomial infection – namely the specific fee for nosocomial infection and the daily fee in the case where the length of stay exceeds the upper bound – have a relatively limited compensating power.
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The mean positive economic impact per episode in the case of a reduced length of stay (N = 25) was estimated to be €14,697 (SD = 16,936; 95% CI = €–92 (net cost) to €84,043). Savings occured in both infections leading to death (N = 8; mean cost savings = €10,003; SD = 8,905; 95% CI = €–92 to €25,002), and infections leading to survival at discharge (N = 17; mean cost savings = €16,906; SD = 19,477; 95% CI = €833 to €31,498). Figure 3 provides a decomposition of the average net savings produced by CDI, showing that the productivity gains account for 53.0% of the total savings. In all, the overall burden of the 52 cases of CDI for the two studied hospitals was approximately €278,111 during the study period, corresponding to an average burden per episode estimated to be €5,348.
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ACCEPTED MANUSCRIPT 3.3 Sensitivity analysis Table II provides the results of a sensitivity analysis of both the probability to sustain a reduced duration of stay due to a C. difficile-related nosocomial infection and the estimated average burden of infection for the studied hospitals.
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The variables used for the sensitivity analysis were: (1) age (under 80, and 80 & over); (2) the Charlson score, capturing the complexity of the medical context, classified by tertile; (3) the length of the hospital stay classified by tertile.
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The analysis shows that the only statistically significant explanatory variable of both the probability of a decreased length of stay and the existence of cost savings is the length of hospital stay under 19 days, age and Charlson score having no significant impact on the dependant variables.
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These results lend credence to the hypothesis that the methodology used to compute the extra hospital days due to nosocomial infection is sensitive to the average population-based length of a hospital stay, and that the estimation for a particular individual is biased downward in the case of wards with a relatively shorter mean length of stay.
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4. Discussion
4.1. On the importance of productivity losses
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Our work introduced a specific indicator to capture the effect of nosocomial infections on the ability of an hospital to provide health care in conditions ensuring the minimum of length of stay. We used the properties of DRG-related payments to estimate an indicator of productivity losses using a reference that is common to hospitals (the lower and the upper bounds of length of stay defined for a particular care), ensuring its use as a tool for comparing hospitals in their performance regarding the prevention and management of nosocomial infections. We showed that an indicator of productivity loss is a significant addition to the commonly used cost drivers in the field of the computation of the costs of nosocomial infections for hospitals. In fact, more than 40% of the total losses or gains associated with nosocomial CDI are attributable to the inability (respectively, the ability) of a ward to increase (respectively, reduce) the length of stay in the case of an infection.
4.2. On the existence of savings The existence of savings in the case of nosocomial infections must be debated because it highlights two important limits. The first limit is related to the benefits 9
ACCEPTED MANUSCRIPT exhibited by a reduced length of stay in the case of deaths, highlighting the incompleteness of the current payment systems. The second limit concerns the benefits associated with a reduced length of stay in the case of living patients, pointing to the limitations of the statistical method used.
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Speaking of savings associated with the death of patients may be considered as a raw economic thinking, but it gives an interesting insight into the limits of the current hospital payment systems. Indeed, current systems do not take into account the whole range of effects of nosocomial infections, assuming a strict and positive link between the existence of an episode and the length of the hospital stay. Our analysis shows that this relationship is not necessary true, particularly in the case of the premature death of patients.
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The question is then how to take into account the fact that nosocomial infections may be beneficial to the system in cases where they obviously represent a failure in the process of care. In this case, an estimation of the savings derived from such events may be used to reduce the financial and productivity advantages derived from the occurrence of death from nosocomial infections. A consistent analysis of both the cost and saving drivers may then be used to adjust the payments to hospitals via penalty and reward systems, particularly in a situation where few incentives exist to promote the prevention of nosocomial infections.
∑5 5 + ∑5> 5 1/ − 12 × ̅+! = = + / / / /
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̅ =
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The question of the existence of benefits from a reduced length of a hospital stay among living patients raises specific questions about the statistical method used to exhibit individual extensions from the average length of the prolongation of stay. The method used is a decomposition of the mean extension ̅ with a bootstraping approach. The idea is here to find the individual value of a particular episode I by considering that:
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It then becomes possible to compute the pseudo-value for each individual episode by computing the average of length of stay without each episode 1̅+! 2 and by computing the following relationship: = / × ̅ − 1/ − 12 × ̅+! . The key values in this system are the estimated ̅ and the variance of the lengths of hospital stay, because the variance of the lengths of hospital stay ?,@ will inevitably affect the estimation of the ̅+! . The problem here is that both ̅ and ?,@ are derived from survival functions computed on the whole population, which could lead to either overestimate the prolongation of hospital stays in wards characterized by a relatively longer length of hospital stays compared to the average population-based length of stay, and underestimate the true prolongation of hospital stays among wards that are characterized by a relatively
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ACCEPTED MANUSCRIPT shorter length of hospital stays compared to the average population-based length of hospital stay.
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This conclusion echoes the recent work by van Kleef et al [13], who proposed to estimate the excess length of stay due to Clostridium difficile among groups of cases and controls sharing the same set of characteristics (e.g., age group and number of comorbidities). The idea of defining such sets of characteristics is the consequence of a limitation of the multi state approach, that is the assumption that the only variable affecting the population-based expected excess length of stay is time. The authors proposed to reduce this bias by computing expected excess lengths of stay by groups of characteristics, introducing de facto a control for other variables that may interfere with the length of stay.
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Our work suggests that the problems are not concentrated on the sole estimation of the expected excess length of stay at the population or group level, but also in the computation of individual excess lengths of stay from the population-based or groupbased expected excess length of stay. As our results indicate, the relative average length of stay of the ward as compared to the overall length of stay is an additional variable to be introduced in the set of variables defining the groups into which the multi state estimations are performed.
5. Acknowledgements
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In many respects, the introduction of multi state models in the measurement of the impact of nosocomial infections on the length of stay at hospital leads to a situation that is not quite different to what case-control studies faced, except that one key factor is analysed with precision, namely time.
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The authors would like to express their acknowledgements to the Direction of Medical Information, particularly Drs Maryse Germain Alonso and Aurélien Schaffar, and the Department of Medical Research, particularly Dr Amélie Lansiaux and Mr Julien Pamelard, of the Hospital Community of the Catholic Institute of Lille, for their invaluable help in the management of the project and the collection of data.
6. Ethics
This work is the result of a grant-free research based on a doctorate dissertation publicly presented by Miss Elise Choquet at the Faculty of Pharmacy of the University of Lille II, France, on September 9th 2016. The dissertation was supervised by Dr Valérie Leclercq (for the medical aspects), Mr Jean-Pierre Marissal (for the economic aspects), and Mr Cristian Preda (for the statistical aspects).
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ACCEPTED MANUSCRIPT The study complies with all the requirements on ethical matters, as stated by the decision n°2015/03/01 published on March 9 th 2015 by the Committee on ethics of the Hospital Community of the Catholic Institute of Lille.
7. References
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[1] Cruse PJ, Foord R. The epidemiology of wound infection. A 10-year prospective study of 62,939 wounds. Surgical clinics of North America 1980; 60: 2740.
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[2] Haley RW, Schaberg DR, Crossley KB, Von Allmen SD, McGowan JE Jr. Extra charges and prolongation of stay attributable to nosocomial infections: a prospective interhospital comparison. American journal of medicine 1981; 70: 51-8.
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[3] Manning WG, Mullahy J. Estimating log models: to transform or not to transform? Journal of health economics 2001: 21: 461-94. [4] Manning WG, Basu A, Mullahy J. Generalized modeling approaches to risk adjustment of skewed outcomes data. Journal of health economics 2005; 24: 465-88. [5] Fukuda H, Lee J, Imanaka Y. Variations in analytical methodology for estimating costs of hospital-acquired infections: A systematic review. Journal of hospital infection 2011; 77: 93-105.
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[6] Van Walraven C, Davis D, Forster A, Wells G. Time-dependent bias was common in survival analysis published in leading clinical journals. Journal of clinical epidemiology 2004; 57: 672-82.
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[7] Beyersmann J, Gastmeier P, Wolkewitz M, Schumacher M. An easy mathematical proof showed that time-dependent bias inevitably leads to biased effect estimation. Journal of clinical epidemiology 2008; 61: 1216-21.
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[8] Barnett AG, Beuersmann J, Allignol A, Rosenthal VD, Graves N, Wolkewitz M. The time-dependent bias and its effect on extra length of stay due to nosocomial infection. Value in health 2011; 14: 381-6. [9] Rosenthal VD, Dwivedy A, Rodriguez Calderon ME, Esen S, Torres Hernandez H, Abougal R, Medeiros EA, Atencio Espinoza T, Kanj SS, Gikas A, Barnett AG, Graves N, International nosocomial infection control consortium (INICC) members. Time-dependent analysis of length of stay and mortality due to urinary tract infections in ten developing countries: INICC findings. Journal of infection 2011; 62: 136-41. [10] Beyersmann J, Gastmeier P, Grundmann H, Bärwolff S, Geffers C, Behnke M, Rüden H, Schumacher M. Use of multistate models to assess prolongation of
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ACCEPTED MANUSCRIPT intensive care unit stay due to nosocomial infection. Infection control and hospital epidemiology 2006; 27(5): 493-9. [11] Andersen PK, Klein JP. Regression analysis for multistate models based on a pseudo-value approach, with applications to bone marrow transplantation studies. Scandinavian journal of statistics 2007; 34 (1): 3-16.
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[12] Réseau d’Alerte, d’Investigation et de Surveillance des Infections Nosocomiales. Conduite à tenir : diagnostic, investigation, surveillance, et principes de prévention et de maîtrise des infections à Clostridium difficile. Paris, Réseau d’Alerte, d’Investigation et de Surveillance des Infections Nosocomiales, 2006.
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[13] van Kleef E, Green N, Goldenberg SD, Robotham JV, Cookson B, Jit M, Edmunds WJ, Deeny SR. Excess length of stay and mortality due to Clostridium difficile infection: a multi-state modelling approach. Journal of hospital infection 2014; 88: 213-7.
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ACCEPTED MANUSCRIPT Table 1 : Data used in the computation of hospital direct costs
Direct costs Per dose
0.150
Metronidazole 250 mg
Per dose
0.470
Vancomycine IV 500 mg / 100 ml
Per dose
Screening test
Per visit
Wash / wastes
Per day
Thermometer
Per isolation
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1.550
20.253
Single use equipment
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Medical supervision / prophylaxis
Per test
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Metronidazole 250 mg
1.660
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Antibiotics
Cost (€ 2014)
0.517 2.705
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Table 2 : Decomposition of the probability to have a decreased length of stay due to Clostridium difficile and of the burden of nosocomial infection among patients living at discharge (N = 34)
< 80
61.1%
80 & +
37.5%
<4
60.0%
4–5
50.0%
6&+
40.0%
Length of stay < 19 days 19 – 39.9 days > 39.9 days
92.3%
Chi-2 test Mean
95% CI min (*)
Burden of nosocomial infection 95% CI max (*)
0.189 0.634
0.622
< 0.001
< 0.001
0.647
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Charlson score
% with a decreased length of stay
33.3% 0.0%
Mean (€ 2014)
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Age group
Category
< 0.001
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Variable
-1,271
17,972
5,043
34,676
1,392
17,411
6,768
28,186
-5,186
33,290
-18,059
23,345
8,129
16,660
28,440
26,282
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(*) Confidence intervals obtained via a Monte Carlo simulation with 10,000 replications.
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SD
Non parametric tests MannWhitney 0.330
KruskalWallis
0,854
< 0.001
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Figure 1 : Distribution of the estimations of the prolongation of hospital stay from a bootstrap decomposition of the average prolongation of stay
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from fi -2 517 Gains €
Specific fee for infection -114 €
Other direct costs
Loss of opportunities - 2nd bed
1 135 €
Productivity loss
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981 €
Supervision & prophylaxis
Série1
10 763 €
Loss of opportunity - infected bed
€-
€2 000
€4 000
€6 000
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€(4 000) €(2 000)
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68 €
€8 000
13 593 €
€10 000 €12 000 €14 000 €16 000
Figure 2 : Decomposition of the overall burden of Clostridium difficile in the case of an extension of the length of stay (N = 27) (€ 2014)
Note:
is the daily fee attributed to hospitals in the case of a length of stay exceeding the upper
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bound of the DRG.
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Loss in fi
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855 €
Loss of opportunities - 2nd bed
610 €
Supervision & prophylaxis
404 €
Other direct costs
31 €
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Série1
Productivity gains
-8 631 €
Increase in opportunities - infected bed
-7 059 €
-10 000 €
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Specific fee for infection -610 €
-8 000 €
-6 000 €
-4 000 €
-2 000 €
- €
2 000 €
Note:
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Figure 3 : Decomposition of the overall burden of Clostridium difficile in the case of a reduced length of stay (N = 25) (€ 2014)
is the daily fee attributed to hospitals in the case of a length of stay exceeding the upper
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bound of the DRG
S0195-6701(17)30467-X
DOI:
10.1016/j.jhin.2017.08.023
Reference:
YJHIN 5212
To appear in:
Journal of Hospital Infection
Received Date: 18 July 2017 Accepted Date: 29 August 2017
Please cite this article as: Hebbinckuys E, Marissal J-P, Preda C, Leclercq V, Assessing the burden of Clostridium difficile infections for hospitals, Journal of Hospital Infection (2017), doi: 10.1016/ j.jhin.2017.08.023. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. 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.
ACCEPTED MANUSCRIPT TITLE : Assessing the burden of Clostridium difficile infections for hospitals SHORT TITLE : Cost of Clostridium difficile AUTHORS: Elise HEBBINCKUYS, Pharma.D (1), Jean-Pierre MARISSAL, Ph.D (1), Cristian PREDA, Ph.D (3), Valérie LECLERCQ, MD (4)
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(1) Centre hospitalier de St Philibert– 115 rue du Grand But– 59160 Lomme– France : [email protected]; (2) Faculté de Gestion, d’Economie et de Sciences – Institut catholique de Lille – 60 boulevard Vauban – CS 40109 – 59016 Lille Cedex – France; [email protected]; (3) Laboratoire de Mathématiques Paul Painlevé (UMR-CNRS 8524) – Bâtiment M2 – Cité Scientifique – 59655 Villeneuve-d'Ascq – France; Institute of Mathematical Statistics and Applied Mathematics – Romanian Academy; [email protected] (4) Centre Hospitalier Saint-Philibert – 115, rue du Grand But – 59160 Lomme – France : [email protected].
CORRESPONDANCE
All correspondence should be sent to:
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Jean-Pierre Marissal
Faculté de Gestion, d’Economie et de Sciences Institut Catholique de Lille
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CS 40109 59016 Lille Cedex
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France.
Mail : [email protected]
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ACCEPTED MANUSCRIPT ABSTRACT: Background: Nosocomial infections place a heavy burden on the healthcare system. However, quantifying the burden raises many questions, ranging from the way to accurately estimate the extra length of stay at hospital to defining and costing the preventative methods among the different care providers.
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Method: We used multi state modeling based on Markov processes and bootstraping to derive individual estimates of the prolongation of stay at hospital associated with Clostridium difficile infection (CDI). We then computed indicators of cost for hospitals, including an estimation of the productivity losses derived from DRG-based payment systems.
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Population: Patients aged 55 and over, admitted in two hospital facilities in Lille, Saint Philibert, Lomme and Saint Vincent de Paul, Lille, North of France, with and without an episode of CDI from January 1st 2013 to September 15th 2014.
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Results: A total of 52 episodes were screened during the study period. The estimated mean cost of CDI was approximately €23,909 (SD = 17,458) for an extended length of hospital stay (N = 27). In the case of a reduced length of the hospital stay (N = 25), the mean cost was approximately € –14,697 (SD = 16,936), which represents net savings for the hospitals. The main cost / savings driver was the productivity losses / gains resulting from the nosocomial infection. A sensitivity analysis showed that the main factor explaining the amount of costs or savings due to nosocomial infections was the length of the hospital stay.
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Conclusion: We discuss the notion of productivity gains in the case of deaths as a factor revealing the incompleteness of the payment systems. We then discuss the methodological issues associated with the statistical method used to control for temporality bias.
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Keywords: Cost, measurement bias, nosocomial infection. JEL classification : I12 I18.
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ACCEPTED MANUSCRIPT 1. Introduction Estimation of the cost of hospital-acquired infections raises two important questions dealing with both the quality and the nature of the measurements to be made. These questions relate not only to the costing methodology but also to the computation of the extra days at hospital.
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The latter question deals with how to measure, with a minimum level of bias, the effect of a particular episode of nosocomial infection on the length of a hospital stay. The literature on this topic offers a number of possible approaches. The first statistical attempt to measure the prolongation of hospital stay dates from the 1980s, with the pioneering works by Cruse and Foord [1] and Haley et al [2]. The authors used an analysis based on the comparison between infected persons (cases) and non-infected ones (controls) matched according to a limited number of relevant criteria (e.g., age and type of surgery). The main problem posed by this method lies in its low level of control of factors that are likely to affect the overall length of the stay. In fact, to compute the extra hospital days would require samples of cases and controls in each configuration defined by crossing relevant factors. In practice, this is almost impossible due to the relatively low rates of incidence of nosocomial infections.
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Another approach to estimating the extra hospital days uses econometrics, a set of methods aimed at decomposing the variance of a phenomenon. The difficulty here is to take into account the specificities of the statistical distribution of the lengths of hospital stays, namely a long tailed distribution. This led to methods ranging from the use of a simple log transformation of the length of hospital stays [3] to the use of specific statistical distributions (e.g., a gamma or a log-normal distribution) [4, 5].
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The main advantage of the econometric approach is its capability to control for the impact of several factors that are likely to explain the length of the stay. In this case, the estimated net effect of the nosocomial infection on the length of hospital stays is captured by the weight of a dichotomous variable (infected / non-infected) or, if available, of a polytomous variable introducing the severity of the episode. This method has, however, two limits. First, it requires a large number of cases to capture with accuracy the net impact of nosocomial infections on the length of hospital stays. Second, this approach (like the case-control approach) doesn’t control for temporality biases [6]. Such temporality biases arise when time is a relevant factor in the explanation of both the incidence of the infections and the length of hospital stays [7, 8]. Time may indeed affect the estimates through two main sources: (i) the time at which the infection is declared during an hospitalisation – the consequences may differ if an infection is declared at the beginning of the hospitalisation or at the end, when other medical factors have been fixed –, and (ii) the time when hospitalisation occurs – there may be periods of general increase in the length of stay in some wards. The method used to control for the temporality biases relies on Markov processes and 3
ACCEPTED MANUSCRIPT survival analysis. These methods aim at computing the expectation of the extra length of hospital stays taking into account the time of infection through the definition of multiple states (basically, infected / not infected, and alive at discharge / dead) [9, 10]. The individual estimates (pseudo-values) are derived from the average estimate by decomposing this average with bootstrap methods [11].
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In response to an increase in the frequency and severity of Clostridium difficile infections (CDI) observed in our hospitals, associated with the emergence of hypervirulent C. difficile 027, we aimed to estimate cost of nosocomial infection of C. difficile to inform the hospital managers. We used a multi-state modeling approach based on Markov processes in order to estimate the cost of Clostridium difficilerelated nosocomial infections in two hospitals of Lille (North of France). We first defined some economic indicators aiming at capturing the dimensions of the burden of nosocomial infections for hospitals, based on the use of some properties of the diagnosed-related groups (DRGs). We then produced estimates of the extra hospital days due to CDI during the period January 1st 2013 to September 15th 2014. We then provide data on the costs of these infections according to the domains of burden we previously defined. Finally, we discuss the results and highlight a possible bias of the method, namely the absence of control of other interfering factors, which may lead to biased estimates when analyzing at the ward level.
2.1 Setting
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2. Methods
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The GHICL (Catholic Institute of Lille) consists of two hospitals in Lille (Saint-Philibert and Saint-Vincent de Paul) and a clinic (Sainte Marie) in the neighbouring town of Cambrai. Saint-Philibert Hospital (SP) focuses on adult specialty activities and had 352 beds in 2013, and Saint-Vincent de Paul Hospital is positioned as a general hospital with a high-level mother-child center and had 284 beds in 2013. The total number of employees is about 2,200, 42,000 hospitalizations, over 120,000 outpatient visits, 66,000 emergency visits per year. 2.2 Assessing the impact on hospital productivity Time is a central variable in the computation of the cost of nosocomial infections. It affects the measurements by defining the period of time during which costs have to be applied (the extra days at hospital). It is also a factor that is characterized by multiproducts. Indeed, time can be the source of numerous and simultaneous effects related to different cost domains, then defining a set of concomitant cost drivers for the hospital. An additional complexity to take into account relates to the properties of DRG-based payment systems as cost drivers for the hospital. DRG-based payment systems are used in many Western countries like France. They consist in defining a link between 4
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the payment of a hospital stay on one hand, and the length of the hospital stay and the medical complexity of the case (e.g., main and associated diagnoses, age, etc.) on the other hand. Such systems aim at driving a reduction in length of stay, providing absolute references presented as thresholds. Not only does this kind of payment system provide data that can be used as references for all hospital structures, but DRG-based payments also allow us to define an indicator of productivity loss for the hospitals facing episodes of nosocomial infection.
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In a basic DRG-based system in which a given hospital stay i is associated with a certain amount or payment Pi, which is modulated on the basis of the length of hospital stay. Let us consider that the system defines two bounds: a lower bound of length (LBi) and an upper bound of length (UBi). The principle is to define a system of payment incentivizing hospitals to reduce the length of hospital stays towards the lower bound. This is why most of the systems define low payments in the case of a length below the lower bound, and, in the case of the French system, an additional fee for each additional day over the upper bound. In this context, the productivity in value of an hospital admission may be expressed as the ratio of the payment to the number of days at hospital, with the following relationship: > + − 1 ×
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where ti is the total length of hospital stay, and fi the fee per day over the upper bound.
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The classical problem posed by nosocomial infections is that it increases the length of a hospital stay. Let us denote by ei the estimated prolongation of a stay due to a particular episode of nosocomial infection occurring during the stay i. Then we can write = + , where is the length of hospital stay explained by other medical factors. Three cases must be considered.
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If > 0 – meaning that a nosocomial infection leads to an increase in the length of a hospital stay –, one has a loss of productivity when !"# ×$
−
' !"# ×$ %& '
> 0,
where ()*+, = 1 when the condition -./0 is met, = 0 otherwise. This leads to the definition of an indicator of the loss of productivity in value, given by: '
( =
− 1 × 1 2 − ( '3"# 1 + − 2 − ( 3"# 1 − 2 × ,
where ( is the loss of productivity indicator associated with the stay i.
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ACCEPTED MANUSCRIPT The second case to be considered is when > 0 and the payment system introduces special fees accounting for extra charges induced by a nosocomial infection, which is the case in France as Clostridium difficile is concerned. Let us consider a system in which a special fee is paid in case of a stay i. Let us also assume that this episode increases the payment from 1 2 to 1 + 2. In such a situation, the ( is given by the following system:
− 1 × 1 2 − 1 + 2 − 1 2 − ( ' 3"# 1 + − 2 −
( 3"# 1 − 2 × ,
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'
( =
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The last case to be considered corresponds to a reduction in the length of the hospital stay, that is, < 0. In this case, the ( is
( = 1 − ' × 1 2 − 1 2 − 1 + 2 − ( ' 3"# 1 + − 2 −
( 3"# 1 − 2 × .
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This expression is the consequence of a change in the reference situation, which becomes 1 + 2 instead of in the case of a reduced length of a hospital stay 1 < 02.
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2.3 Assessing the opportunity cost of nosocomial infections
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As stated earlier, time may affect hospital costs in several ways. One of these is through productivity, but time is also associated to opportunity costs due to the fact that a bed may be used for several medical purposes. Using a bed for a certain motive or blocking a bed because of a nosocomial infection forbids its use for a different medical purpose. 6
For example, each hospital stay k in a specific ward (j) is associated with 05 days of 6
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hospitalization, leading to an income 5 . In this case, an extension of the length of hospital stay is associated with an opportunity cost that is classically computed as: 6
78 =
∑5 56
∑5 056
6
6
× : × /
6
where 786 is the opportunity cost for ward j, is the extension of the length of the 6
hospital stay associated with the Ith episode in ward j, and / the number of beds in the room involved in the process of isolation of the Ith episode in ward j. The overall opportunity cost of nosomial infections for the hospital is then trivially given by 78 = ∑6 786 . 6
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<
∑; ;
< ∑; ,;
6
6
× × / will exhibit a negative value, indicating a gain in terms of
economic opportunities for the ward and the hospital.
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2.4 Direct costs of nosocomial infections Nosocomial infections exhibit direct costs in the form of treatment costs, mostly antibiotics in the case of CDI, screening costs, medical supervision, and decontamination.
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Treatment costs are classically computed by multiplying the cost per dose by the number of doses units per day and the number of days of treatment during the period of hospitalization.
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The computation of the cost of screening is directly derived from the application of the guidelines relating to the screening for C. difficile [12] and a specific fee per screening used in the two hospitals used in the empirical analysis. The cost of medical supervision and prophylaxis is derived from an ad hoc empirical study performed in the studied hospitals.
2.5 Data collection
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Table I summarizes the assumptions used in the computation of the direct hospital costs of nosocomial infections for the two hospital structures analysed.
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We prospectively and exhaustively collected medical, administrative and payment data on all cases of CDI declared in our two hospitals at least 48 hours after admission, and whose hospitalisations led to a DRG-based payment , from January 1st 2013 to September 15th 2014. We also collected medical and administrative data on 10,341 hospitalised patients who declared no episode of CDI during the same time period, aged 55 to 104 to match the age range of the infected cases. 3. Results
3.1 Clostridium difficile nosocomial infections During the study period, a total of 52 patients were had CDI in Saint Philibert and Saint Vincent hospitals. Their median age was 77.7 years, ranging from 56 to 104. The median length of hospital stay was 18.5 days, ranging from 6 to 132 (mean = 39.5 days). The infected patients were mostly admitted to the general medicine ward (19%), the intensive care unit (11%), the cardiology intensive care unit (10%), the 7
ACCEPTED MANUSCRIPT digestive surgery ward (10%), and to the palliative care unit (10%) at the time of the episode. Eighteen out of the 52 infected patients died during their hospitalization.
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The estimated average extra lengths of hospital stay, assessed by the multi-state model [10], were, respectively, 7.756 days (standard deviation (SD) = 1.22) in the case of deceased patients (18 infected versus 620 non-infected patients), and 6.953 days (SD = 0.11) in the case of patients living at discharge (34 infected versus 9,721 non-infected patients).
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The bootstrap decomposition of these two estimated averages, aimed at deriving estimates of the prolongation of stay at the individual level, leads to a median individual prolongation of hospital stay of 12.5 days among deceased patients (N = 18), and 0.0 day among living patients (N = 34) (Figure 1).
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3.2 Burden of CDI
The assessment of the burden of CDI in the two hospitals had to take into account the existence of an extension 1 > 02 or a reduction 1 < 02 in the length of the hospital stay in the presence of an infection.
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The mean burden per episode in the case of an extension of the length of stay (N = 27) was estimated to be €23,909 (SD = 17,458; 95% confidence interval (CI) ranging from €1,312 to €74,571). Figure 2 displays a decomposition of the average burden of CDI, showing that the productivity losses due to an episode of nosocomial infection account for 40.8% of the total costs. This chart also shows that all the financial devices aimed at compensating for the consequences of a nosocomial infection – namely the specific fee for nosocomial infection and the daily fee in the case where the length of stay exceeds the upper bound – have a relatively limited compensating power.
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The mean positive economic impact per episode in the case of a reduced length of stay (N = 25) was estimated to be €14,697 (SD = 16,936; 95% CI = €–92 (net cost) to €84,043). Savings occured in both infections leading to death (N = 8; mean cost savings = €10,003; SD = 8,905; 95% CI = €–92 to €25,002), and infections leading to survival at discharge (N = 17; mean cost savings = €16,906; SD = 19,477; 95% CI = €833 to €31,498). Figure 3 provides a decomposition of the average net savings produced by CDI, showing that the productivity gains account for 53.0% of the total savings. In all, the overall burden of the 52 cases of CDI for the two studied hospitals was approximately €278,111 during the study period, corresponding to an average burden per episode estimated to be €5,348.
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ACCEPTED MANUSCRIPT 3.3 Sensitivity analysis Table II provides the results of a sensitivity analysis of both the probability to sustain a reduced duration of stay due to a C. difficile-related nosocomial infection and the estimated average burden of infection for the studied hospitals.
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The variables used for the sensitivity analysis were: (1) age (under 80, and 80 & over); (2) the Charlson score, capturing the complexity of the medical context, classified by tertile; (3) the length of the hospital stay classified by tertile.
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The analysis shows that the only statistically significant explanatory variable of both the probability of a decreased length of stay and the existence of cost savings is the length of hospital stay under 19 days, age and Charlson score having no significant impact on the dependant variables.
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These results lend credence to the hypothesis that the methodology used to compute the extra hospital days due to nosocomial infection is sensitive to the average population-based length of a hospital stay, and that the estimation for a particular individual is biased downward in the case of wards with a relatively shorter mean length of stay.
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4. Discussion
4.1. On the importance of productivity losses
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Our work introduced a specific indicator to capture the effect of nosocomial infections on the ability of an hospital to provide health care in conditions ensuring the minimum of length of stay. We used the properties of DRG-related payments to estimate an indicator of productivity losses using a reference that is common to hospitals (the lower and the upper bounds of length of stay defined for a particular care), ensuring its use as a tool for comparing hospitals in their performance regarding the prevention and management of nosocomial infections. We showed that an indicator of productivity loss is a significant addition to the commonly used cost drivers in the field of the computation of the costs of nosocomial infections for hospitals. In fact, more than 40% of the total losses or gains associated with nosocomial CDI are attributable to the inability (respectively, the ability) of a ward to increase (respectively, reduce) the length of stay in the case of an infection.
4.2. On the existence of savings The existence of savings in the case of nosocomial infections must be debated because it highlights two important limits. The first limit is related to the benefits 9
ACCEPTED MANUSCRIPT exhibited by a reduced length of stay in the case of deaths, highlighting the incompleteness of the current payment systems. The second limit concerns the benefits associated with a reduced length of stay in the case of living patients, pointing to the limitations of the statistical method used.
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Speaking of savings associated with the death of patients may be considered as a raw economic thinking, but it gives an interesting insight into the limits of the current hospital payment systems. Indeed, current systems do not take into account the whole range of effects of nosocomial infections, assuming a strict and positive link between the existence of an episode and the length of the hospital stay. Our analysis shows that this relationship is not necessary true, particularly in the case of the premature death of patients.
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The question is then how to take into account the fact that nosocomial infections may be beneficial to the system in cases where they obviously represent a failure in the process of care. In this case, an estimation of the savings derived from such events may be used to reduce the financial and productivity advantages derived from the occurrence of death from nosocomial infections. A consistent analysis of both the cost and saving drivers may then be used to adjust the payments to hospitals via penalty and reward systems, particularly in a situation where few incentives exist to promote the prevention of nosocomial infections.
∑5 5 + ∑5> 5 1/ − 12 × ̅+! = = + / / / /
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̅ =
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The question of the existence of benefits from a reduced length of a hospital stay among living patients raises specific questions about the statistical method used to exhibit individual extensions from the average length of the prolongation of stay. The method used is a decomposition of the mean extension ̅ with a bootstraping approach. The idea is here to find the individual value of a particular episode I by considering that:
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It then becomes possible to compute the pseudo-value for each individual episode by computing the average of length of stay without each episode 1̅+! 2 and by computing the following relationship: = / × ̅ − 1/ − 12 × ̅+! . The key values in this system are the estimated ̅ and the variance of the lengths of hospital stay, because the variance of the lengths of hospital stay ?,@ will inevitably affect the estimation of the ̅+! . The problem here is that both ̅ and ?,@ are derived from survival functions computed on the whole population, which could lead to either overestimate the prolongation of hospital stays in wards characterized by a relatively longer length of hospital stays compared to the average population-based length of stay, and underestimate the true prolongation of hospital stays among wards that are characterized by a relatively
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ACCEPTED MANUSCRIPT shorter length of hospital stays compared to the average population-based length of hospital stay.
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This conclusion echoes the recent work by van Kleef et al [13], who proposed to estimate the excess length of stay due to Clostridium difficile among groups of cases and controls sharing the same set of characteristics (e.g., age group and number of comorbidities). The idea of defining such sets of characteristics is the consequence of a limitation of the multi state approach, that is the assumption that the only variable affecting the population-based expected excess length of stay is time. The authors proposed to reduce this bias by computing expected excess lengths of stay by groups of characteristics, introducing de facto a control for other variables that may interfere with the length of stay.
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Our work suggests that the problems are not concentrated on the sole estimation of the expected excess length of stay at the population or group level, but also in the computation of individual excess lengths of stay from the population-based or groupbased expected excess length of stay. As our results indicate, the relative average length of stay of the ward as compared to the overall length of stay is an additional variable to be introduced in the set of variables defining the groups into which the multi state estimations are performed.
5. Acknowledgements
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In many respects, the introduction of multi state models in the measurement of the impact of nosocomial infections on the length of stay at hospital leads to a situation that is not quite different to what case-control studies faced, except that one key factor is analysed with precision, namely time.
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The authors would like to express their acknowledgements to the Direction of Medical Information, particularly Drs Maryse Germain Alonso and Aurélien Schaffar, and the Department of Medical Research, particularly Dr Amélie Lansiaux and Mr Julien Pamelard, of the Hospital Community of the Catholic Institute of Lille, for their invaluable help in the management of the project and the collection of data.
6. Ethics
This work is the result of a grant-free research based on a doctorate dissertation publicly presented by Miss Elise Choquet at the Faculty of Pharmacy of the University of Lille II, France, on September 9th 2016. The dissertation was supervised by Dr Valérie Leclercq (for the medical aspects), Mr Jean-Pierre Marissal (for the economic aspects), and Mr Cristian Preda (for the statistical aspects).
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ACCEPTED MANUSCRIPT The study complies with all the requirements on ethical matters, as stated by the decision n°2015/03/01 published on March 9 th 2015 by the Committee on ethics of the Hospital Community of the Catholic Institute of Lille.
7. References
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[1] Cruse PJ, Foord R. The epidemiology of wound infection. A 10-year prospective study of 62,939 wounds. Surgical clinics of North America 1980; 60: 2740.
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[2] Haley RW, Schaberg DR, Crossley KB, Von Allmen SD, McGowan JE Jr. Extra charges and prolongation of stay attributable to nosocomial infections: a prospective interhospital comparison. American journal of medicine 1981; 70: 51-8.
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[3] Manning WG, Mullahy J. Estimating log models: to transform or not to transform? Journal of health economics 2001: 21: 461-94. [4] Manning WG, Basu A, Mullahy J. Generalized modeling approaches to risk adjustment of skewed outcomes data. Journal of health economics 2005; 24: 465-88. [5] Fukuda H, Lee J, Imanaka Y. Variations in analytical methodology for estimating costs of hospital-acquired infections: A systematic review. Journal of hospital infection 2011; 77: 93-105.
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[6] Van Walraven C, Davis D, Forster A, Wells G. Time-dependent bias was common in survival analysis published in leading clinical journals. Journal of clinical epidemiology 2004; 57: 672-82.
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[7] Beyersmann J, Gastmeier P, Wolkewitz M, Schumacher M. An easy mathematical proof showed that time-dependent bias inevitably leads to biased effect estimation. Journal of clinical epidemiology 2008; 61: 1216-21.
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[8] Barnett AG, Beuersmann J, Allignol A, Rosenthal VD, Graves N, Wolkewitz M. The time-dependent bias and its effect on extra length of stay due to nosocomial infection. Value in health 2011; 14: 381-6. [9] Rosenthal VD, Dwivedy A, Rodriguez Calderon ME, Esen S, Torres Hernandez H, Abougal R, Medeiros EA, Atencio Espinoza T, Kanj SS, Gikas A, Barnett AG, Graves N, International nosocomial infection control consortium (INICC) members. Time-dependent analysis of length of stay and mortality due to urinary tract infections in ten developing countries: INICC findings. Journal of infection 2011; 62: 136-41. [10] Beyersmann J, Gastmeier P, Grundmann H, Bärwolff S, Geffers C, Behnke M, Rüden H, Schumacher M. Use of multistate models to assess prolongation of
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ACCEPTED MANUSCRIPT intensive care unit stay due to nosocomial infection. Infection control and hospital epidemiology 2006; 27(5): 493-9. [11] Andersen PK, Klein JP. Regression analysis for multistate models based on a pseudo-value approach, with applications to bone marrow transplantation studies. Scandinavian journal of statistics 2007; 34 (1): 3-16.
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[12] Réseau d’Alerte, d’Investigation et de Surveillance des Infections Nosocomiales. Conduite à tenir : diagnostic, investigation, surveillance, et principes de prévention et de maîtrise des infections à Clostridium difficile. Paris, Réseau d’Alerte, d’Investigation et de Surveillance des Infections Nosocomiales, 2006.
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[13] van Kleef E, Green N, Goldenberg SD, Robotham JV, Cookson B, Jit M, Edmunds WJ, Deeny SR. Excess length of stay and mortality due to Clostridium difficile infection: a multi-state modelling approach. Journal of hospital infection 2014; 88: 213-7.
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ACCEPTED MANUSCRIPT Table 1 : Data used in the computation of hospital direct costs
Direct costs Per dose
0.150
Metronidazole 250 mg
Per dose
0.470
Vancomycine IV 500 mg / 100 ml
Per dose
Screening test
Per visit
Wash / wastes
Per day
Thermometer
Per isolation
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1.550
20.253
Single use equipment
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Medical supervision / prophylaxis
Per test
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Metronidazole 250 mg
1.660
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Antibiotics
Cost (€ 2014)
0.517 2.705
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Table 2 : Decomposition of the probability to have a decreased length of stay due to Clostridium difficile and of the burden of nosocomial infection among patients living at discharge (N = 34)
< 80
61.1%
80 & +
37.5%
<4
60.0%
4–5
50.0%
6&+
40.0%
Length of stay < 19 days 19 – 39.9 days > 39.9 days
92.3%
Chi-2 test Mean
95% CI min (*)
Burden of nosocomial infection 95% CI max (*)
0.189 0.634
0.622
< 0.001
< 0.001
0.647
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Charlson score
% with a decreased length of stay
33.3% 0.0%
Mean (€ 2014)
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Age group
Category
< 0.001
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Variable
-1,271
17,972
5,043
34,676
1,392
17,411
6,768
28,186
-5,186
33,290
-18,059
23,345
8,129
16,660
28,440
26,282
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(*) Confidence intervals obtained via a Monte Carlo simulation with 10,000 replications.
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SD
Non parametric tests MannWhitney 0.330
KruskalWallis
0,854
< 0.001
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Figure 1 : Distribution of the estimations of the prolongation of hospital stay from a bootstrap decomposition of the average prolongation of stay
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from fi -2 517 Gains €
Specific fee for infection -114 €
Other direct costs
Loss of opportunities - 2nd bed
1 135 €
Productivity loss
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981 €
Supervision & prophylaxis
Série1
10 763 €
Loss of opportunity - infected bed
€-
€2 000
€4 000
€6 000
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€(4 000) €(2 000)
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68 €
€8 000
13 593 €
€10 000 €12 000 €14 000 €16 000
Figure 2 : Decomposition of the overall burden of Clostridium difficile in the case of an extension of the length of stay (N = 27) (€ 2014)
Note:
is the daily fee attributed to hospitals in the case of a length of stay exceeding the upper
AC C
EP
bound of the DRG.
ACCEPTED MANUSCRIPT
Loss in fi
RI PT
855 €
Loss of opportunities - 2nd bed
610 €
Supervision & prophylaxis
404 €
Other direct costs
31 €
SC
Série1
Productivity gains
-8 631 €
Increase in opportunities - infected bed
-7 059 €
-10 000 €
M AN U
Specific fee for infection -610 €
-8 000 €
-6 000 €
-4 000 €
-2 000 €
- €
2 000 €
Note:
TE D
Figure 3 : Decomposition of the overall burden of Clostridium difficile in the case of a reduced length of stay (N = 25) (€ 2014)
is the daily fee attributed to hospitals in the case of a length of stay exceeding the upper
AC C
EP
bound of the DRG