Development and validation of a new population-based simulation model of osteoarthritis in New Zealand

Accepted Manuscript Development and validation of a new population-based simulation model of osteoarthritis in New Zealand Ross Wilson, J. Haxby Abbott PII:

S1063-4584(18)30014-1

DOI:

10.1016/j.joca.2018.01.004

Reference:

YJOCA 4142

To appear in:

Osteoarthritis and Cartilage

Received Date: 26 May 2017 Revised Date:

19 November 2017

Accepted Date: 2 January 2018

Please cite this article as: Wilson R, Haxby Abbott J, Development and validation of a new populationbased simulation model of osteoarthritis in New Zealand, Osteoarthritis and Cartilage (2018), doi: 10.1016/j.joca.2018.01.004. 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

2

Development and validation of a new population-based simulation model of osteoarthritis in New Zealand

3

Ross Wilson1, J. Haxby Abbott2

4 5

Centre for Musculoskeletal Outcomes Research, Department of Surgical Sciences, Dunedin School of Medicine, University of Otago, Dunedin, New Zealand

6

1

Corresponding author: Centre for Musculoskeletal Outcomes Research

7

Department of Surgical Sciences

8

University of Otago

9

PO Box 56, Dunedin 9054, New Zealand

10

RI PT

1

Email: [email protected]

11

Phone: +64 3 474 0999 ext. 58613

12

2

13

ABSTRACT

14

Objective

15 16 17

To describe the construction and preliminary validation of a new population-based microsimulation model developed to analyse the health and economic burden and cost-effectiveness of treatments for knee osteoarthritis (OA) in New Zealand (NZ).

18

Method

19 20 21 22

We developed the New Zealand Management of Osteoarthritis (NZ-MOA) model, a discrete-time statetransition microsimulation model of the natural history of radiographic knee OA. In this article, we report on the model structure, derivation of input data, validation of baseline model parameters against external data sources, and validation of model outputs by comparison of the predicted population health loss with previous estimates.

23

Results

24 25 26 27 28 29 30

The NZ-MOA model simulates both the structural progression of radiographic knee OA and the stochastic development of multiple disease symptoms. Input parameters were sourced from NZ population-based data where possible, and from international sources where NZ-specific data were not available. The predicted distributions of structural OA severity and health utility detriments associated with OA were externally validated against other sources of evidence, and uncertainty resulting from key input parameters was quantified. The resulting lifetime and current population health-loss burden was consistent with estimates of previous studies.

31

Conclusion

32 33 34 35

The new NZ-MOA model provides reliable estimates of the health loss associated with knee OA in the NZ population. The model structure is suitable for analysis of the effects of a range of potential treatments, and will be used in future work to evaluate the cost-effectiveness of recommended interventions within the NZ healthcare system.

36

KEYWORDS

37

Osteoarthritis; Simulation modelling; Microsimulation; Quality of life

38

Running title: Simulation model of OA in New Zealand

AC C

EP

TE D

M AN U

SC

Email: [email protected]

39

1

ACCEPTED MANUSCRIPT INTRODUCTION

41

Simulation modelling is a powerful tool that is being increasingly used to analyse the population health impact

42

of disease.[1, 2] Such models combine data on disease prevalence, the distribution of risk factors in the

43

population, and the impact of the condition on health-related quality of life (HRQoL) to quantify the population

44

health burden of disease. By incorporating estimates of the effects of existing and proposed prevention and

45

treatment strategies, simulation models can be used to evaluate the cost-effectiveness of healthcare interventions

46

under a variety of scenarios.

47

Simulation modelling can also be used to estimate the future burden of disease for health policy planning or the

48

evaluation of preventive public health measures. For example, modelling expected future changes in risk

49

factors—such as, in the case of osteoarthritis (OA), structural injury, the ageing population, and increasing

50

prevalence of obesity—can provide policy-relevant estimates of future disease burden.[3-5] Simulation methods

51

also lend themselves naturally to equity analysis, a growing area of concern in healthcare evaluation. For

52

example, in New Zealand (NZ) it is known that Māori (NZ’s indigenous population) have worse health

53

outcomes than the non-Māori population,[6] including higher (age-standardised) prevalence of OA.[7] By

54

analysing separately the impact of diseases and interventions on potentially disadvantaged subpopulations, such

55

as ethnic minorities, rural residents, or socio-economically deprived groups, modelling can be used to evaluate

56

the effectiveness of targeted interventions to reduce disparities in health outcomes.

57

Advances in computing power have made possible the development of large-scale microsimulation models,

58

which simulate health trajectories at the individual level and evaluate population health outcomes by

59

aggregating the outcomes of large numbers of randomly-generated individual simulations. Such

60

microsimulation methods, unlike group-based approaches such as Markov cohort models, have the advantages

61

of being able to incorporate a larger number of patient-level characteristics and risk factors at a finer level of

62

detail, to model dynamic intervention strategies dependent on both past and present characteristics and disease

63

states, and to evaluate the distribution of outcomes and patient-level heterogeneity as well as group-level

64

means.[8, 9] Recent microsimulation models used in the analysis of OA include the Osteoarthritis Policy

65

(OAPol) model,[10, 11] a state-transition model of OA progression and OA-related pain in the US, and

66

POHEM-OA,[12] a continuous-time simulation of OA incidence and risk factors in the Canadian population.

67

This study reports on the development of the New Zealand Management of Osteoarthritis (NZ-MOA) model, a

68

population-based microsimulation model of the burden and treatment of knee OA in NZ. Two novel features of

69

NZ-MOA are an explicit focus on the stochastic progression of HRQoL outcomes along with radiographically-

70

described structural OA progression, and multidimensional health state modelling to capture the breadth of the

71

HRQoL impacts of OA. As we demonstrate in this preliminary study, these features allow, for example, the

72

evaluation of interventions provided to a subset of OA patients meeting defined, clinically-relevant criteria, such

73

as limitations in physical functioning, bodily pain, or structural joint deterioration.

74

The remainder of this paper presents the model structure and the derivation of input parameters, and reports

75

preliminary analyses to establish the validity of model outputs. We conclude by discussing the model’s strengths

76

and limitations, highlighting potential future developments, and previewing planned applications of the model

77

for evaluating the cost-effectiveness of treatment strategies for knee OA in NZ.

AC C

EP

TE D

M AN U

SC

RI PT

40

2

ACCEPTED MANUSCRIPT METHOD

79

Model structure

80

NZ-MOA is a population-based state-transition model of the natural history of radiographic knee OA. The

81

model simulates the incidence, structural progression, and health-related quality of life outcomes of knee OA in

82

a large cohort representative of the NZ adult population. NZ-MOA is a microsimulation model: it simulates the

83

health trajectories of randomly-generated heterogeneous individuals, based on a set of defined probability

84

distributions and input parameters, and aggregates the outcomes of individual trials (microsimulations) to

85

estimate population-level quantities.

86

The model consists of two layers (Figure 1): first, structural disease progression is modelled dependent on

87

individual characteristics; second, HRQoL outcomes and healthcare costs are assigned to the resulting disease

88

states. The remainder of this sub-section details the model structure and the flow of simulated individuals

89

through the model; the following sub-section then describes the data sources and derivation of input parameters

90

used to populate the model.

91

[Figure 1 about here]

92

Structural progression

93

Structural disease states are defined by Kellgren-Lawrence (K-L) grade, from grades 0/1 indicating no/doubtful

94

radiographic OA to grade 4 indicating severe OA.[13] Each simulated individual, randomly drawn from the NZ

95

adult population, is followed through a sequence of annual probabilistic transitions between these health states:

96

in each period they either remain at the same K-L grade or progress by a single step, determined by transition

97

probabilities dependent on age, sex, ethnicity, and BMI. Death can occur in any period, up to a maximum age of

98

100.

99

Health-related quality of life

TE D

M AN U

SC

RI PT

78

In each period, a HRQoL valuation is probabilistically assigned to the individual’s disease state, using the SF-

101

6D instrument. The SF-6D is a six-dimensional health-status classification (Physical Functioning, Role

102

Limitations, Social Functioning, Pain, Mental Health, and Vitality) with an associated HRQoL score index,

103

derived from the 12-item SF-12 questionnaire.[14] At baseline, each individual is randomly generated an SF-6D

104

profile (i.e. levels on each of the six SF-6D dimensions), conditional on their age, sex, ethnicity, BMI, and OA

105

status, and receives the associated HRQoL value. The SF-6D profile, and hence HRQoL value, is

106

probabilistically updated each year, dependent on the individual’s OA status and other characteristics.

107

Healthcare treatments

108

In both the structural disease progression and HRQoL valuation steps presented in Figure 1, outcomes are

109

dependent on the course of treatment being followed. In each period, individuals may be allocated to a treatment

110

regimen if they meet specified criteria regarding structural OA severity (defined by K-L grade) and symptomatic

111

severity (defined by SF-6D profile). Treatment effects may involve a combination of weight loss (reduction in

112

BMI), retardation of structural OA progression, or mitigation of OA symptoms (modelled as a reduction in the

113

HRQoL detriments of having OA). The healthcare costs associated with the treatment regimen being followed

AC C

EP

100

3

ACCEPTED MANUSCRIPT (which may vary according to individuals’ other characteristics such as age, sex, ethnicity, obesity, and K-L

115

grade) are also recorded in each period.

116

The model computes two outcome paths for each individual, corresponding to ‘business-as-usual’ (i.e. reflecting

117

current patterns of treatment and healthcare utilization) and the intervention under study (for example,

118

incorporating a new treatment or sequence of treatments into the business-as-usual scenario). By running the

119

same individuals through both pathways, the incremental QALY gains and costs of the intervention can be

120

assessed.

121

Model output

122

At death (or age 100), the individual’s total quality-adjusted life years (QALYs) lived (the sum of annual

123

HRQoL values recorded in each year of life) are computed, along with details of OA status and any healthcare

124

costs incurred, and the model is repeated for another randomly-drawn individual. A large number of simulated

125

individuals are used to provide stable estimates of population-wide average QALY losses and costs. (The results

126

reported here use a sample size of 5 million trials for each model run.) The incremental QALYs gained and

127

costs incurred by the intervention relative to the business-as-usual case are used to assess population health

128

impacts and cost-effectiveness.

129

Key input parameters and data sources

130

The model relies on a large number of input parameters and distributions from a variety of sources. Where

131

possible, NZ population-based data were used to provide model inputs; where NZ-specific data were not

132

available, international data were used, sourced both from published literature and estimated directly from

133

publicly-available datasets. Summaries of input parameters and distributions are provided below, and in greater

134

detail in Appendix A (Tables A1-A5).

135

Population distribution of age, sex, and ethnicity

136

The 2013 NZ Census was used to define the starting population cohort.[15] For the current study, we used the

137

population aged 35–99, stratified by sex and ethnicity. In the Census, individuals were able to report affiliation

138

with multiple ethnic identities; the model uses the total ethnic group definition recommended by Statistics New

139

Zealand,[16] identifying as Māori all of those reporting Māori ethnicity, with or without any other ethnic

140

affiliations.

141

Body Mass Index (BMI)

142

The baseline distribution of BMI was estimated from the New Zealand Health Survey (NZHS) 2013/14.[17] A

143

lognormal distribution was assumed for BMI, following inspection of the empirical distribution function, and fit

144

to age, sex, and ethnicity. In each subsequent annual cycle, individuals’ BMI was assumed to follow the current

145

(sex- and ethnicity-specific) population average trajectory of BMI with age, plus a secular trend increase of 0.3

146

percent per year (extrapolating observed trends over recent decades[18]).

AC C

EP

TE D

M AN U

SC

RI PT

114

4

ACCEPTED MANUSCRIPT Mortality Rates

148

Population annual mortality rates, stratified by age, sex, and ethnicity, were obtained from the New Zealand

149

Period Life Tables 2012–14.[19] To model the increased mortality risk for obese individuals, estimates of the

150

relative risk of mortality for different levels of BMI, derived from the US population,[20] were used to adjust

151

these baseline rates. Future mortality rates were assumed to decrease by 2.25 percent per annum for Māori and

152

1.75 percent per annum for non-Māori until 2026, and remain constant thereafter.[21] Beyond the differences in

153

mortality attributable to age, sex, ethnicity, and obesity, no attempt was made to model excess mortality

154

associated with radiographic knee OA, as the evidence for OA-related mortality is equivocal.[22]

155

Prevalence of radiographic knee osteoarthritis

156

Data on the prevalence of radiographically-defined knee OA are not available for the NZ population. NZ-MOA

157

therefore relies on information on the prevalence of self-reported all-site doctor-diagnosed OA, for which data

158

were obtained from NZHS 2013/14.[17] To obtain estimates of radiographic OA prevalence, these rates were

159

first adjusted for the ratio of knee OA to all-site OA, estimated from US population data.[23] The estimated

160

knee OA prevalence rates were then further adjusted to reflect differences between prevalence estimates based

161

on self-reported doctor-diagnosed OA and radiographically-defined OA, using relative prevalence ratios

162

estimated by the Global Burden of Disease (GBD) study.[22] Annual incidence rates were backed out from

163

these data to ensure a constant conditional prevalence rate over time (within age/sex/ethnicity/obesity sub-

164

groups).

165

Structural progression of radiographic knee osteoarthritis

166

Estimates of annual progression rates of knee OA were obtained from a previous simulation model of the burden

167

of knee OA in the US population.[4] These data were originally derived from two prospective population-based

168

studies of knee OA incidence and progression in the US and the UK.[24, 25] Progression rates were stratified by

169

sex, obesity status, and K-L grade (i.e. progression from K-L grade 2 to 3 and from grade 3 to 4).

170

Health-related quality of life

171

The distribution of SF-6D health profiles in the NZ population, by age, sex, ethnicity, and obesity, was derived

172

from NZHS 2013/14. As data on the impact of radiographic knee OA on SF-6D health status are not available

173

for the NZ population, these effects were estimated using data from the Osteoarthritis Initiative (OAI), a large

174

longitudinal cohort study of those with or at risk of knee OA in the US population (http://www.oai.ucsf.edu). To

175

capture the progressive nature of OA symptoms, the effects were modelled as annual rates of progression on

176

each SF-6D dimension, conditional on radiographic OA status (see Appendix B). These rates represent HRQoL

177

progression under standard background conservative treatment regimes, but exclude outcomes following total

178

knee replacement (TKR).

179

Interventions

180

The primary means of treating knee OA in the NZ population at present is provision of TKR for late-stage

181

disease, following conservative care consisting predominantly of the prescription of analgesics or non-steroidal

182

anti-inflammatory drugs for pain relief during early to mid-stage disease progression. In the current study, we

AC C

EP

TE D

M AN U

SC

RI PT

147

5

ACCEPTED MANUSCRIPT therefore assumed that all OA patients receive the package of conservative care only until meeting pre-specified

184

eligibility criteria for TKR. Based on national prioritization criteria for provision of TKR in NZ,[26] individuals

185

were assumed to be eligible for surgery if they showed limitations in physical functioning, role limitations due

186

to physical health, and moderate or greater pain (SF-6D dimensions PF 2+, RL 2 or 4, and PAIN 3+), together

187

with radiographic knee OA at K-L grade 3 or higher.

188

As the crude application of these criteria is likely to overestimate surgical provision—some of those eligible for

189

TKR on these criteria will not undergo surgery due to, for example, contraindications from other health

190

conditions or patients’ unwillingness to have surgery—the model was calibrated to match observed provision

191

rates (sourced from the New Zealand Joint Registry[27]) by varying the annual probability with which surgery

192

was performed, conditional on meeting the pre-specified eligibility criteria.

193

In the present analysis, HRQoL losses associated with knee OA were only estimated under background

194

conservative care, prior to the provision of TKR; explicit modelling of costs and outcomes following subsequent

195

treatment regimens, including TKR, will be included in future cost-effectiveness analyses using the model.

196

Derivation of baseline distributions

197

For structural OA progression, OA-related HRQoL losses, and TKR provision, the input data used in the model

198

were specified as annual rates of incidence or progression. The baseline distributions of OA severity, HRQoL

199

losses among those with radiographic OA, and prevalence of pre-existing TKR at each year of age therefore had

200

to be derived from these annual rates. We specified a starting cohort with all individuals at age 30, which was

201

then followed through until death (or age 100), recording the radiographic OA, HRQoL, and TKR outcomes in

202

each year of life from age 35 to 99 to obtain the baseline distributions to be applied to the full population cohort.

203

Analysis and model validation

204

This article reports on several preliminary analyses to investigate the performance and validity of the NZ-MOA

205

model. First, the provision of TKR surgery in the model was examined and calibrated to observed provision

206

rates in the NZ population. We initially modelled the expected provision rates in 2015 under the assumption that

207

all eligible patients would receive TKR; these were then compared with observed rates, and the model estimates

208

calibrated by varying the probability, conditional on age and sex, of surgery being offered to (and accepted by)

209

patients meeting the specified eligibility criteria.

210

Next, the derived baseline distributions of structural OA severity and HRQoL outcomes—excluding those with

211

a previous TKR—were examined, and compared with available data from alternative sources to establish the

212

validity of our input parameters for OA progression and development of symptoms.

213

Cross-model validation was undertaken by running the model for the 2006 NZ population, for which alternative

214

estimates of the health-loss burden of OA are available for comparison. Two alternative estimates of the

215

population health burden of OA were used. First, the OAPol model, an established, well-validated computer

216

simulation model of symptomatic OA originally developed for the US population,[10, 11] was recently used to

217

provide estimates of the lifetime QALY losses due to OA for the 2006 NZ population aged 40–84.[23, 28] Two

218

approaches were used for the valuation of HRQoL in those studies: the Visual Analogue Scale (VAS)-based NZ

219

EQ-5D tariff,[29] and a power transformation of the VAS tariff to more closely approximate preference-based

AC C

EP

TE D

M AN U

SC

RI PT

183

6

ACCEPTED MANUSCRIPT weights commonly obtained in international valuation studies.[30] The estimates produced by the OAPol studies

221

correspond to QALY losses associated with the natural history of disease progression among the current cohort

222

of prevalent knee OA, without interventions; we therefore computed QALY losses for initial prevalent cases

223

only (excluding future incidence) and excluded provision of TKR for these cross-model comparisons.

224

Second, the New Zealand Burden of Diseases, Injuries and Risk Factors Study (NZBD), as part of the GBD

225

project, provides estimates of the single-year disability-adjusted life-years (DALYs) attributable to a number of

226

conditions in 2005, including all-site symptomatic OA.[31] DALYs are an alternative approach to calculating

227

the population-level health-loss burden of disease, combining estimates of the morbidity loss due to living with

228

disease and years of life lost due to disease-related premature mortality (the latter assumed to be zero for

229

OA[22]). To estimate the DALY burden attributable to knee OA only, we applied the same ratio of knee OA to

230

all-site OA used in the NZ-MOA model. These were compared with the NZ-MOA predicted QALY losses in a

231

single-year model run for the 2006 population (adjusted for population growth between 2005 and 2006).

232

To investigate the sensitivity of the model estimates to the input parameters used, we also conducted one-way

233

sensitivity analyses on the population BMI, OA prevalence, structural OA progression, and HRQoL progression

234

parameters. Each parameter was varied to the lower and upper bounds of the corresponding 95% confidence

235

intervals (estimated from the data for BMI, OA prevalence, and HRQoL progression rates, and obtained from

236

the literature[4] for OA structural progression), and the resulting population lifetime QALY loss associated with

237

knee OA was modelled. Results were collated into a tornado plot for visual analysis.

238

RESULTS

239

Calibration of total knee replacement surgery

240

Initial results, under the assumption that all eligible patients would receive TKR, showed the expected increase

241

in provision rates with age, up to approximately age 80 (Figure 2). Modelled provision was higher than observed

242

rates, as predicted; the discrepancy was highest in the youngest (< 50 years) and, especially, the oldest (> 80

243

years) age groups and was higher for women than for men. By applying age- and sex-varying probabilities of

244

surgery being offered to, and accepted by, patients who meet the clinical and radiographic OA criteria, we were

245

able to accurately match the observed provision rates in the population. The resulting calibrated probabilities are

246

shown in Table A6 in Appendix A.

247

[Figure 2 about here]

248

Modelled distributions of total knee replacement, radiographic knee OA severity, and health-

249

related quality of life losses associated with OA

250

Using these calibrated rates, 2.4 percent of the baseline population were estimated to have previously received a

251

TKR. As expected, this proportion was increasing in both age and obesity (Table 1); it was slightly lower for

252

women than for men, and was similar for Māori compared to non-Māori (after controlling for differences in the

253

distributions of age, obesity, and sex).

254

[Table 1 about here]

AC C

EP

TE D

M AN U

SC

RI PT

220

7

ACCEPTED MANUSCRIPT The baseline prevalence of radiographic knee OA, excluding those having previously had a TKR, was estimated

256

to be 9.7 percent, of which 65 percent was at K-L grade 2, 30 percent at grade 3, and 5 percent at grade 4. The

257

average severity level was increasing with age and obesity, and was greater for women than for men (Table 2).

258

There are limited population-based data on the distribution of radiographic grades available to provide

259

validation of these estimates, and none for the NZ population. Data from NHANES-III,[32] a US population-

260

based survey conducted between 1988 and 1994, show 73 percent of radiographic OA at K-L grade 2, 21

261

percent at grade 3, and 6 percent at grade 4, in the population aged 60–90 (radiographs were only taken from

262

those aged 60+). These shares are generally comparable with those found in NZ-MOA for the same age group,

263

although the model projections showed slightly fewer in K-L grade 2 (64%) and more in K-L grade 3 (31%).

264

[Table 2 about here]

265

The average health utility detriment associated with radiographic OA was 0.03, increasing from 0.02 at K-L

266

grade 2 to 0.05 at grade 3 and 0.10 at grade 4. In line with the differences found in the distribution of

267

radiographic severity, the average utility detriment was increasing in age and obesity, and was higher for women

268

than for men (Table 3). These values were lower than previous estimates of the HRQoL loss associated with OA

269

in the US population (0.06),[33] and those reported in the Global Burden of Disease 2013 study for

270

‘musculoskeletal problems: legs’ (0.02 for ‘mild’ problems, 0.08 for ‘moderate’ problems, and 0.17 for ‘severe’

271

problems; weighted average of 0.04).[34, 35] As both of these previous estimates refer to symptomatic OA only,

272

the differences observed here are likely due to a proportion of those with radiographic OA being asymptomatic.

273

There is mixed evidence regarding the proportion of those with radiographic OA showing clinical symptoms,

274

but the ratio of approximately 50 percent implied by comparing the US population-based estimates[33] with our

275

model estimates is consistent with previous studies.[36-38]

276

[Table 3 about here]

277

Cross-model validation

278

For the 2006 NZ population aged 40–84 with OA, the projected total lifetime health loss was 307,000 QALYs

279

(Table 4). The corresponding estimates from the OAPol model were 467,000 QALYs using the original VAS-

280

based valuations and 224,000 QALYs using the power-transformed valuations. The pattern of health losses was

281

generally consistent across the population distribution of age, sex, and ethnicity for the two models, although

282

NZ-MOA provided relatively lower estimates of the health-loss burden among older Māori women (Figure 3).

283

In 2005, the single-year population health loss due to knee OA was 5700 QALYs in NZ-MOA (Table 4),

284

slightly higher than the 4500 DALYs reported in the NZBD study (after adjustments to estimate the burden

285

attributable to knee OA only); the disability weights estimated for OA by the GBD study do not explicitly

286

account for mental or emotional aspects of health,[34, 35] which may help to explain their somewhat lower

287

health-loss values.

288

[Table 4 about here]

289

[Figure 3 about here]

AC C

EP

TE D

M AN U

SC

RI PT

255

8

ACCEPTED MANUSCRIPT Sensitivity analysis

291

Imprecision in estimates of the HRQoL trajectories associated with OA was the largest source of uncertainty in

292

the projected population lifetime QALYs lost to OA (Figure 4). Estimates of OA structural progression rates and

293

population OA prevalence were the next largest sources of uncertainty, and population BMI had very little

294

impact on modelled population QALY losses.

295

[Figure 4 about here]

296

DISCUSSION

297

This article has described the structure, input parameters, and preliminary concurrent and predictive validation

298

of a new microsimulation model of knee OA in NZ. The NZ-MOA model provides estimates of the population

299

health burden of knee OA, and will be used to assess the health gains and cost-effectiveness of specified

300

treatment strategies. The preliminary specification of the model presented here was able to provide estimates of

301

the total health-loss burden of OA comparable to previous studies, and to accurately model the aggregate

302

provision of TKR surgery in NZ.

303

Key innovations in NZ-MOA include the modelling of the multidimensional HRQoL impacts of knee OA using

304

the SF-6D instrument and the explicit modelling of the stochastic progression of both radiographic and

305

symptomatic OA. These features allowed the modelling of TKR provision according to multidimensional

306

criteria involving physical functioning, bodily pain, and structural joint deterioration, in line with clinical

307

practice. This multidimensional approach to the provision of interventions will be extended in future work, to

308

evaluate the effectiveness and cost-effectiveness of ongoing treatment strategies involving potentially several

309

sequential disease states and treatments.

310

Limitations of the analysis reflect several limitations in available data for model input parameters, particularly

311

pertaining to the NZ population. There are no population-based data on the prevalence or severity distribution of

312

radiographic knee OA specific to the NZ population. The model therefore relies on a population-based survey of

313

self-reported doctor-diagnosed OA, with additional assumptions required to derive estimates of the prevalence

314

of radiographic knee OA, while structural severity was derived from progression rates observed in US- and UK-

315

based cohort studies.

316

There are also limited data available on the trajectories of OA symptoms over time, and none for the NZ

317

population. Previous studies of pain and physical function trajectories in OA have reported mixed results,[39-

318

42] while very few results have been reported for other dimensions of HRQoL affected by OA. The estimates of

319

symptomatic progression used here, however, which were derived from publically-available data from the OAI,

320

gave outcomes consistent with previously-reported cross-sectional data,[33-35] and previous model-based

321

estimates of the population health loss attributable to knee OA.[23, 28, 31]

322

The model validation analyses reported here have estimated outcomes under generic ‘conservative care’ only,

323

prior to the provision of TKR in late-stage OA. Further model development will incorporate other treatments

324

used in current practice in NZ, including modelling of post-TKR outcomes and subsequent demand for TKR

325

revision surgery. The results shown here demonstrate the validity of the preliminary natural history model of

AC C

EP

TE D

M AN U

SC

RI PT

290

9

ACCEPTED MANUSCRIPT OA progression and the suitability of the model structure for the evaluation of current and recommended

327

treatment options. In line with clinical practice, simulated treatment assignment can be made on the basis of

328

both clinical and radiographic outcomes, and multiple treatment effects—weight loss, reduction in OA incidence

329

or progression, or mitigation of OA symptoms—can be assessed. Future work will apply the model to the

330

analysis of the cost-effectiveness of various interventions, and a recommended strategy consisting of potentially

331

multiple sequential interventions, within the New Zealand healthcare system.

332

ACKNOWLEDGMENTS

333

This research was funded by a grant from the Health Research Council of New Zealand (#15/263). The funding

334

body played no role in study design, analysis, writing of the manuscript, or the decision to submit for

335

publication.

336

We would like to thank Elena Losina for advice on model structure and development, and Tony Blakely and

337

Giorgi Kvizhinadze for helpful comments on an earlier draft of this manuscript. We also thank David Gwynne-

338

Jones for providing informative data on the provision of knee replacement surgery in the New Zealand public

339

health system.

340

This study uses data from the OAI public use data set. The OAI is a public-private partnership comprised of five

341

contracts (N01-AR-2-2258; N01-AR-2-2259; N01-AR-2-2260; N01-AR-2-2261; N01-AR-2-2262) funded by

342

the National Institutes of Health, a branch of the Department of Health and Human Services, and conducted by

343

the OAI Study Investigators. Private funding partners include Merck Research Laboratories; Novartis

344

Pharmaceuticals Corporation, GlaxoSmithKline; and Pfizer, Inc. Private sector funding for the OAI is managed

345

by the Foundation for the National Institutes of Health. The manuscript does not necessarily reflect the opinions

346

or views of the OAI investigators, the NIH, or the private funding partners.

347

AUTHOR CONTRIBUTIONS

348

RW developed the model, ran the analyses, and drafted the manuscript. HA obtained study funding, led the

349

conceptualization of the study, and contributed to model development. Both authors critically revised the

350

manuscript for important intellectual content, and read and approved the final version submitted for publication.

351

RW is guarantor.

352

COMPETING INTERESTS

353

We have no competing interests to declare.

354

REFERENCES

355

1.

356

AC C

EP

TE D

M AN U

SC

RI PT

326

Petrou S, Gray A. Economic evaluation using decision analytical modelling: design, conduct, analysis, and reporting. BMJ 2011; 342: d1766.

10

ACCEPTED MANUSCRIPT 357

2.

Caro JJ, Briggs AH, Siebert U, Kuntz KM, on behalf of the ISPOR-SMDM Modeling Good Research

358

Practices Task Force. Modeling Good Research Practices - Overview: A Report of the ISPOR-SMDM

359

Modeling Good Research Practices Task Force-1. Value in Health 2012; 15: 796-803.

360

3.

Suter LG, Smith SR, Katz JN, Englund M, Hunter DJ, Frobell R, et al. Projecting Lifetime Risk of

361

Symptomatic Knee Osteoarthritis and Total Knee Replacement in Individuals Sustaining a Complete

362

Anterior Cruciate Ligament Tear in Early Adulthood. Arthritis Care & Research 2017; 69: 201-208. 4.

Holt HL, Katz JN, Reichmann WM, Gerlovin H, Wright EA, Hunter DJ, et al. Forecasting the burden of

RI PT

363 364

advanced knee osteoarthritis over a 10-year period in a cohort of 60–64 year-old US adults. Osteoarthritis

365

and Cartilage 2011; 19: 44-50.

366

5.

Kopec JA, Sayre EC, Fines P, Flanagan WM, Nadeau C, Okhmatovskaia A, et al. Effects of Reductions in Body Mass Index on the Future Osteoarthritis Burden in Canada: A Population-Based Microsimulation

368

Study. Arthritis Care & Research 2016; 68: 1098-1105. 6.

370 371

Wellington, New Zealand 2007. 7.

372 373

Robson B, Harris R. Hauora: Māori Standards of Health IV. Te Rōpū Rangahau Hauora a Eru Pōmare,

Ministry of Health. Annual Update of Key Results 2013/14: New Zealand Health Survey. Wellington, New Zealand: Ministry of Health 2014.

8.

M AN U

369

SC

367

Roberts M, Russell LB, Paltiel AD, Chambers M, McEwan P, Krahn M. Conceptualizing a Model: A

374

Report of the ISPOR-SMDM Modeling Good Research Practices Task Force-2. Value in Health 2012; 15:

375

804-811. 9.

Siebert U, Alagoz O, Bayoumi AM, Jahn B, Owens DK, Cohen DJ, et al. State-Transition Modeling: A

TE D

376 377

Report of the ISPOR-SMDM Modeling Good Research Practices Task Force-3. Value in Health 2012; 15:

378

812-820.

380

10. Losina E, Walensky RP, Kessler CL, Emrani PS, Reichmann WM, Wright EA, et al. Cost-effectiveness of Total Knee Arthroplasty in the United States. Archives of Internal Medicine 2009; 169: 1113-1121.

EP

379

11. Losina E, Walensky RP, Reichmann WM, Holt HL, Gerlovin H, Solomon DH, et al. Impact of Obesity and

382

Knee Osteoarthritis on Morbidity and Mortality in Older Americans. Annals of Internal Medicine 2011;

383

154: 217-226.

384 385 386 387 388 389 390

AC C

381

12. Kopec JA, Sayre EC, Flanagan WM, Fines P, Cibere J, Rahman MM, et al. Development of a populationbased microsimulation model of osteoarthritis in Canada. Osteoarthritis and Cartilage 2010; 18: 303-311. 13. Kellgren JH, Lawrence JS. Radiological assessment of osteo-arthrosis. Annals of the Rheumatic Diseases 1957; 16: 494-502. 14. Brazier JE, Roberts J. The Estimation of a Preference-Based Measure of Health From the SF-12. Medical Care 2004; 42: 851-859. 15. Statistics New Zealand. 2013 Census. Wellington, New Zealand: Statistics New Zealand 2014.

11

ACCEPTED MANUSCRIPT 391 392 393 394

16. Statistics New Zealand. Understanding and Working with Ethnicity Data. Wellington, New Zealand: Statistics New Zealand 2005. 17. Ministry of Health. New Zealand Health Survey 2013/14. Wellington, New Zealand: Statistics New Zealand 2015. 18. Annual Update of Key Results 2015/16: New Zealand Health Survey [online database]. Available at

396

minhealthnz.shinyapps.io/nz-health-survey-2015-16-annual-update/ [Accessed 9 May 2017]. Wellington,

397

NZ: Ministry of Health.

398 399

RI PT

395

19. Statistics New Zealand. New Zealand Period Life Tables. Wellington, New Zealand: Statistics New Zealand 2015.

20. Berrington de Gonzalez A, Hartge P, Cerhan JR, Flint AJ, Hannan L, MacInnis RJ, et al. Body-Mass Index

401

and Mortality among 1.46 Million White Adults. New England Journal of Medicine 2010; 363: 2211-2219.

402

21. Blakely T, Foster R, Wilson N. Burden of Disease Epidemiology, Equity and Cost-Effectiveness (BODE3)

SC

400

Study Protocol, Version 2.1.

Public Health Monograph Series, vol. 30. Wellington, New Zealand:

404

Department of Public Health, University of Otago, Wellington 2012.

M AN U

403

405

22. GBD 2015 Disease and Injury Incidence and Prevalence Collaborators. Global, regional, and national

406

incidence, prevalence, and years lived with disability for 310 diseases and injuries, 1990-2015: a

407

systematic analysis for the Global Burden of Disease Study 2015. Lancet 2016; 388: 1545-1602.

409

23. Abbott JH, Usiskin IM, Wilson R, Hansen P, Losina E. The quality-of-life burden of knee osteoarthritis in New Zealand adults: a model-based evaluation. PLoS ONE 2017; 12: e0185676.

TE D

408

410

24. Jordan JM, Helmick CG, Renner JB, Luta G, Dragomir AD, Woodard J, et al. Prevalence of knee

411

symptoms and radiographic and symptomatic knee osteoarthritis in African Americans and Caucasians: the

412

Johnson County Osteoarthritis Project. Journal of Rheumatology 2007; 34: 172-180.

414

25. Cooper C, Snow S, McAlindon TE, Kellingray S, Stuart B, Coggon D, et al. Risk factors for the incidence

EP

413

and progression of radiographic knee osteoarthritis. Arthritis & Rheumatism 2000; 43: 995-1000. 26. Gwynne-Jones DP, Iosua EE, Stout KM. Rationing for Total Hip and Knee Arthroplasty Using the New

416

Zealand Orthopaedic Association Score: Effectiveness and Comparison With Patient-Reported Scores.

417

Journal of Arthroplasty 2016; 31: 957-962.

418 419

AC C

415

27. New Zealand Joint Registry. The New Zealand Joint Registry Sixteen Year Report. New Zealand Orthopaedic Association 2015.

420

28. Abbott JH, Usiskin I, Wilson R, Losina E. Health-loss burden of osteoarthritis in New Zealand: computer-

421

simulation estimate and between-model cross-validation [conference abstract]. Osteoarthritis and Cartilage

422

2016; 24: S426.

423

29. Devlin NJ, Hansen P, Kind P, Williams A. Logical inconsistencies in survey respondents' health state

424

valuations – a methodological challenge for estimating social tariffs. Health Economics 2003; 12: 529-544.

12

ACCEPTED MANUSCRIPT 425 426 427 428

30. Torrance GW, Feeny D, Furlong W. Visual Analog Scales: Do They Have a Role in the Measurement of Preferences for Health States. Medical Decision Making 2001; 21: 329-334. 31. GHDx: GBD Results Tool [online database]. Available at ghdx.healthdata.org/gbd-results-tool [Accessed 3 April 2017]. Seattle, WA: Institute for Health Metrics and Evaluation. 32. Centers for Disease Control and Prevention. National Health and Nutrition Examination Survey:

430

NHANES-III - data files. http://www.cdc.gov/nchs/nhanes/nhanes3/data_files.htm. [Accessed 12

431

September 2016].

432 433

RI PT

429

33. Sullivan PW, Ghushchyan V. Preference-based EQ-5D index scores for chronic conditions in the United States. Medical Decision Making 2006; 26: 410-420.

34. Cross M, Smith E, Hoy D, Nolte S, Ackerman I, Fransen M, et al. The global burden of hip and knee

435

osteoarthritis: estimates from the Global Burden of Disease 2010 study. Annals of the Rheumatic Diseases

436

2014; 73: 1323-1330.

438

35. Salomon JA, Haagsma JA, Davis A, Maertens de Noordhout C, Polinder S, Havelaar AH, et al. Disability

M AN U

437

SC

434

weights for the Global Burden of Disease 2013 study. Lancet 2015; 3: e712-723.

439

AC C

EP

TE D

440

13

ACCEPTED MANUSCRIPT 441

FIGURE LEGENDS

442

Figure 1: Structure of the NZ-MOA model

443 Figure 2: Predicted and actual provision of total knee replacements, by age group and sex Bars indicate observed provision rates. Dashed lines indicate modelled provision rates without adjustment for age-varying offer/acceptance rates. Solid lines indicate calibrated modelled provision rates. Source: NZ-MOA model; New Zealand Joint Registry [27]. NZ-MOA results estimated using a simulation run of 5,000,000 trials for each age group-by-sex point.

RI PT

444 445 446 447 448 449 450 451 452 453 454

Figure 3: Lifetime per-capita undiscounted QALY losses due to knee OA, by age at baseline, sex, and ethnicity, 2006 population Source: NZ-MOA model; Abbott et al. (2017) [23]. NZ-MOA results estimated using a simulation run of 5,000,000 trials for each age group-by-sex-by-ethnicity point.

Figure 4: Population lifetime QALY losses, one-way sensitivity analysis

Red vertical line indicates the benchmark model estimate. Horizontal bars indicate estimates obtained at the lower and upper bounds of the 95% CI for each input parameter. Source: NZ-MOA model. Results estimated using a simulation run of 5,000,000 trials for each bar.

M AN U

456 457 458 459

SC

455

AC C

EP

TE D

460

14

ACCEPTED MANUSCRIPT TABLES

462

Table 1: Prevalence of total knee replacement at baseline

463 464

Age 35–44 45–54 55–64 65–74 75–84 85+ Male Non-Māori Non-obese 0.0% 0.1% 1.0% 3.8% 8.3% 11.4% Obese 0.0% 0.4% 2.5% 7.9% 15.0% 19.4% Māori Non-obese 0.0% 0.1% 1.0% 3.8% 8.0% 11.3% Obese 0.0% 0.4% 2.7% 8.4% 15.1% 19.3% Female Non-Māori Non-obese 0.0% 0.1% 0.9% 3.2% 7.3% 10.1% Obese 0.0% 0.4% 2.6% 7.6% 14.7% 18.7% Māori Non-obese 0.0% 0.1% 0.9% 3.2% 7.1% 10.1% Obese 0.0% 0.5% 2.7% 7.9% 14.7% 18.6% Source: NZ-MOA model. Each age group-by-sex-by-ethnicity cell estimated using a simulation run of 5,000,000 trials. Annual TKR provision rates calibrated to data sourced from the New Zealand Joint Registry.[27]

RI PT

461

AC C

EP

TE D

M AN U

SC

465 466

15

ACCEPTED MANUSCRIPT Table 2: Distribution of radiographic knee OA at baseline (excluding those with existing total knee replacement)

468

Age 35–44 45–54 55–64 65–74 75–84 85+ Male Non-obese No radiographic knee OA 98.7% 96.1% 91.8% 87.5% 84.9% 84.3% K-L grade 2 1.0% 2.8% 5.9% 9.0% 10.3% 8.8% K-L grade 3 0.3% 1.0% 2.2% 3.3% 4.5% 6.3% K-L grade 4 0.0% 0.1% 0.1% 0.2% 0.3% 0.6% Obese No radiographic knee OA 97.9% 94.4% 89.5% 85.6% 84.4% 84.5% K-L grade 2 1.2% 3.2% 6.0% 8.3% 8.3% 6.1% K-L grade 3 0.8% 2.1% 3.9% 5.3% 6.2% 7.5% K-L grade 4 0.1% 0.4% 0.6% 0.8% 1.1% 1.9% Female Non-obese No radiographic knee OA 97.8% 93.7% 86.8% 79.6% 75.0% 73.5% K-L grade 2 1.8% 4.9% 9.8% 14.5% 16.5% 14.6% K-L grade 3 0.4% 1.3% 3.0% 5.3% 7.5% 9.8% K-L grade 4 0.0% 0.1% 0.3% 0.6% 1.0% 2.1% Obese No radiographic knee OA 96.5% 90.7% 82.7% 76.0% 73.5% 73.0% K-L grade 2 2.3% 5.8% 10.3% 13.4% 13.3% 10.1% K-L grade 3 1.0% 2.8% 5.6% 8.3% 10.0% 11.1% K-L grade 4 0.2% 0.7% 1.5% 2.3% 3.3% 5.8% Source: NZ-MOA model. Each age group-by-sex-by K-L grade cell estimated using a simulation run of 5,000,000 trials.

SC

RI PT

467

AC C

EP

TE D

M AN U

469 470

16

ACCEPTED MANUSCRIPT 471 472

Table 3: Average health-related quality of life detriment attributable to radiographic knee OA at baseline (excluding those with existing total knee replacement)

473

Age 35–44 45–54 55–64 65–74 75–84 85+ Male Non-obese 0.026 0.028 0.028 0.028 0.029 0.032 Obese 0.037 0.037 0.036 0.035 0.035 0.038 Female Non-obese 0.027 0.028 0.030 0.031 0.033 0.035 Obese 0.036 0.038 0.039 0.039 0.040 0.044 Source: NZ-MOA model. Each age group-by-sex cell estimated using a simulation run of 5,000,000 trials.

AC C

EP

TE D

M AN U

SC

RI PT

474 475

17

ACCEPTED MANUSCRIPT Table 4: QALY losses due to knee osteoarthritis, 2006 population, prevalence cohort only

Male

477 478 479

Lifetime, initial population aged 40–84 OAPol OAPol NZ-MOA (VAS) (transformed) 122,382 177,585 83,936

Female

185,083

289,655

140,427

Total

307,466

467,240

224,364

Single-year, population aged 35–99 NZ-MOA† 2,110 3,595 5,706

NZBD/GBD (2005) 1,720 2,770 4,490

Source: NZ-MOA model; Abbott et al. (2017) [23]; Global Burden of Disease study [31]. NZ-MOA results estimated using a simulation run of 5,000,000 trials for each cell. † Adjusted for population growth from 2005 to 2006

RI PT

476

480 481

AC C

EP

TE D

M AN U

SC

482

18

ACCEPTED MANUSCRIPT Appendix B, of Wilson R, Abbott JH. Development and validation of a new population-based simulation model of osteoarthritis in New Zealand.

RI PT

This appendix provides further details on the modelling approach and the estimation of input parameters for the derivation of SF-6D outcomes associated with radiographic knee osteoarthritis in the NZ-MOA model. Model structure

SC

The SF-6D instrument consists of five ordinal dimensions of health-related quality of life (Physical Functioning, Social Functioning, Pain, Mental Health, and Vitality) and one dimension without a clear ordinal representation (Role Limitations, consisting of Rolephysical and Role-emotional sub-dimensions).[Brazier & Roberts 2004] In order to treat all dimensions equivalently, we split Role Limitations into its two subcomponents, providing seven ordinal dimensions of HRQoL to be modelled.

∗ , =   + , ,

M AN U

Each dimension is modelled as an unobserved normally distributed latent variable, which is then compartmentalised into discrete intervals to provide the observable SF-6D profiles. That is, we view each observed dimension
as the (stochastic) outcome of a latent variable where , ~(0, 1),  is a vector of explanatory variables observed for individual  at time , and  is the vector of coefficients on the elements of ; the observed outcome is , =

1 2

∗ if , < , ∗ if , ≤ , < ,! . ⋮ ∗ if , ≥ ,%& '

TE D

⋮ #  This characterization implies that the parameters and  determining observed outcomes can be estimated by ordinal probit regression for each dimension.

EP

Derivation of input parameters

AC C

To model the incremental HRQoL detriments associated with radiographic knee OA, we require information on both the general population distribution of SF-6D outcomes within the New Zealand population and the progression of SF-6D outcomes among those with radiographic OA. New Zealand population data on the distribution of SF-6D outcomes are available from the New Zealand Health Survey 2013/14, but no comparable data are available for the radiographic OA population in New Zealand. To obtain data on the SF-6D outcomes of those with confirmed radiographic knee OA, we have used the public datasets available from the Osteoarthritis Initiative, a large longitudinal cohort study of those with, or at high risk of, radiographic knee OA in several sites in the US (see www.oai.ucsf.edu). As has been widely discussed in the literature on discrete choice analysis, particularly in the application to preference analysis, discrete choice models such as logit/probit regression (and their variants including multinomial and ordinal models) identify the parameters of interest ( ) only up to a scaling constant, leading to difficulties in comparing or combining estimates obtained from different populations or using different preference elicitation methods.[Swait & Louviere 1993; Bradley & Daly 1994; Hensher et al. 1999] If the unobserved sources of variation in HRQoL outcomes differ between data sources, the estimates derived from each

ACCEPTED MANUSCRIPT of these sources will not be directly comparable. In the case considered here, unobserved variation is likely to be smaller in the OAI than the population data, as the OAI sample all have the same health condition (radiographic knee OA) whereas the general population sample can have a much broader range of health; in this case, the estimated coefficients from the OAI will overstate the true effect size relative to the estimates derived from the general population. In other words, the problem becomes ∗ , =   + , ,

RI PT

*,-./0 if  ∈ NZHS where , ~N)0, *, +, with *, = , . If *-./0 ≠ *567 , the estimated

*,567 if  ∈ OAI parameters from the two samples will not be equivalent. The implied probabilities of the discrete observed levels of  are

Pr), = >+ = Φ)),@ −   +B*, + − Φ)),@' −   +B*, +,

SC

where ,C = −∞, ,%& = ∞. Without loss of generality, we can normalize *-./0 = 1.

M AN U

This problem can be solved, however, by pooling the data from both sources, and estimating a non-linear model in which the coefficient estimates arising from the OAI data are adjusted proportionately by a (constant) scaling factor.[Swait & Louviere 1993] The pooled model, with scaling parameter E, = 1⁄*, > 0, can be estimated by maximum likelihood with the log-likelihood function lnJ = ∑ ∑@ I,@ ln LΦ M),@ −   +E, N − Φ M),@' −   +E, NO, where P,@ is an indicator variable equal to 1 if  = >, 0 otherwise.

AC C

EP

TE D

The  terms include an indicator dummy for data drawn from the OAI sample, and can include variables not observed in one of the samples (e.g. variables measuring OA status which are observed in the OAI but not NZHS data); these variables are set to zero in the nonobserved sample. Since all variables are adjusted by the scaling parameter E , the corresponding elements of  , which describe the effects of OA progression on health status, can be directly combined with the estimates for the general population to generate the predicted distribution of SF-6D outcomes for those with radiographic knee OA in the NZ population. We include as such variables the number of years since the incidence of radiographic knee OA, to capture the annual progression of symptoms among those with OA, and dummies for structural progression to each of K-L grade 3 and K-L grade 4, to capture the additional development of symptoms associated with further structural disease progression. Control variables common to both samples include age, sex, and obesity status; Māori ethnicity is included for the NZHS sample only. Those receiving total knee replacement (TKR) surgery are excluded from the estimation sample, as outcomes following TKR are modelled separately (see the main article text for details). The effects associated with radiographic knee OA (on the latent variable scale) are reported in Table B1 below. The latent variables  ∗ (including the random component ), along with the cutpoints , are directly implemented in the NZ-MOA model, indirectly generating individual utility scores through the algorithm of Brazier & Roberts (2004). The resulting average health utility values, stratified by sex, ethnicity, obesity, and K-L grade, are reported in Table A5 in Appendix A.

ACCEPTED MANUSCRIPT Table B1: Effects of Radiographic Knee OA on SF-6D dimensions, latent variable (ordinal probit) model RL-emotional 0.051 −0.008 0.031

SF 0.010 0.024 0.076

PAIN 0.013 0.073 0.239

MH −0.001 0.000 0.078

VIT −0.001 0.018 0.102

RI PT

Annual increment Progression K-L grade 2 to 3 Progression K-L grade 3 to 4

Dimension PF RL-physical 0.010 0.039 0.007 0.294 0.452 0.504

References

Bradley M, Daly A. Use of the logit scaling approach to test for rank-order and fatigue effects in stated preference data. Transportation 1994; 21: 167-184.

SC

Brazier JE, Roberts J. The estimation of a preference-based measure of health from the SF12. Medical Care 2004; 42: 851-859.

M AN U

Hensher D, Louviere J, Swait J. Combining sources of preference data. Journal of Econometrics 1999; 89: 197-221.

AC C

EP

TE D

Swait J, Louviere J. The Role of the Scaling Parameter in the Estimation and Comparison of Multinomial Logit Models. Journal of Marketing Research 1993; 30: 305-314.

ACCEPTED MANUSCRIPT Appendix A, of Wilson R, Abbott JH. Development and validation of a new population-based simulation model of osteoarthritis in New Zealand.

Table A1: Baseline population distribution 65-74 6.9% 0.5% 7.3% 0.5% 15.2%

75-84 3.6% 0.2% 4.3% 0.2% 8.2%

85+ 1.1% 0.0% 2.0% 0.0% 3.2%

Total 43.0% 4.4% 47.5% 5.1% 100%

SC

55-64 9.6% 0.9% 10.1% 1.0% 21.7%

M AN U

Population share Age: 35-44 45-54 Male Non-Māori 10.4% 11.3% Māori 1.5% 1.4% Female Non-Māori 11.6% 12.2% Māori 1.7% 1.6% Total 25.2% 26.4%

RI PT

This appendix presents further tables summarising the distribution of input parameters used in the NZ-MOA model of radiographic knee osteoarthritis. The values reported in Tables A1A5 are average values (proportions and/or means) of the underlying distributions implemented in the model, grouped by age, sex, ethnicity, obesity, and K-L grade as labelled.

Mean age (SD) 56.0 (13.6) 51.4 (11.5) 56.6 (14.4) 51.5 (11.9) 55.8 (13.9)

Source: Drawn from the discrete joint probability distribution of age (in years), ethnicity (Māori/non-Māori), and sex (Male/Female) from the NZ Census 2013 (Statistics New Zealand, 2014).

Table A2: Baseline distribution of obesity

TE D

Population share (within sex/ethnicity groups) Overweight Obese I Obese II Underweight Normal weight (BMI (BMI (BMI (BMI < 18.5) (BMI 18.5–25) 25–30) 30–35) 35–40) Male Non-Māori 0.6% 23.0% 40.8% 25.7% 8.0% Māori 0.5% 13.5% 29.1% 29.2% 17.2% Female Non-Māori 2.9% 29.3% 33.8% 21.4% 8.8% Māori 1.0% 14.9% 26.6% 26.3% 17.1% Total 1.7% 25.2% 36.3% 23.8% 9.3%

Obese III (BMI 40+) 1.8% 10.5% 3.8% 14.1% 3.8%

Mean BMI (SD) 28.6 (4.8) 31.7 (6.5) 28.2 (6.0) 32.2 (7.4) 28.7 (5.7)

AC C

EP

Source: NZ Health Survey 2013/14 (Ministry of Health, 2015). Continuous BMI modelled following a log-normal distribution with sex-, ethnicity- and age-specific mean and standard deviation: ߤBMI = expሺ2.994 + 0.013 × Age − 0.0001 × Ageଶ + ሺ0.060 − 0.004 × Age + 0.00003 × Ageଶ ሻ × Female + ሺ0.014 + 0.004 × Age − 0.00004 × Ageଶ ሻ × Maori + ሺ0.028 + 0.0003 × Age − 0.000003 × Ageଶ ሻ × Female × Maoriሻ ଶ ߪBMI = expሺ0.044 − 0.0004 × Age + 0.000002 × Ageଶ + ሺ−0.005 + 0.001 × Age − 0.00001 × Ageଶ ሻ × Female + ሺ−0.008 + 0.001 × Age − 0.00001 × Ageଶ ሻ × Maori + ሺ0.015 − 0.001 × Age + 0.00001 × Ageଶ ሻ × Female × Maoriሻ

ACCEPTED MANUSCRIPT Table A3: Prevalence of radiographic knee osteoarthritis

Male

Total

Total† 8.4% 11.1% 11.7% 15.3% 12.4% 15.8% 16.5% 20.9% 11.8%

RI PT

Female

Prevalence of radiographic knee osteoarthritis (K-L grade ≥ 2) 45-54 55-64 65-74 75-84 85+ Age: 35-44 Non-obese 1.4% 4.0% 9.1% 15.8% 22.1% 25.3% Obese I 1.9% 5.6% 12.3% 20.8% 28.1% 31.6% Obese II 2.0% 6.0% 13.1% 21.6% 29.1% 32.7% Obese III 2.9% 8.2% 17.7% 28.2% 36.3% 40.3% Non-obese 2.3% 6.5% 14.0% 22.9% 30.3% 33.9% Obese I 3.2% 8.9% 18.4% 28.7% 36.7% 40.3% Obese II 3.4% 9.5% 19.3% 29.8% 37.9% 41.6% Obese III 4.8% 13.0% 25.1% 36.7% 44.8% 47.2% 2.2% 6.3% 13.5% 21.7% 28.6% 32.0%

†

M AN U

SC

Age-standardised to the total NZ adult population Source: Prevalence of self-reported doctor-diagnosed all-site OA estimated using logistic regression, conditional on age, sex, ethnicity, and obesity, using data from the NZ Health Survey 2013/14 (Ministry of Health, 2015): Log Odds OA = −11.274 + 0.594 × Female + 0.036 × Overweight + 0.376 × Obese I + 0.440 × Obese II + 0.824 × Obese III + 0.224 × Age − 0.001 × Age , where Overweight: 25 ≤ BMI < 30; Obese I: 30 ≤ BMI < 35; Obese II: 35 ≤ BMI < 40; Obese III: BMI ≥ 40. Ratio of knee OA to all-site OA derived from US population data, following Abbott et al. (2017): Men: 0.713; Women: 0.665. Ratio of radiographic knee OA to self-reported doctor-diagnosed knee OA sourced from GBD 2015 Methods Appendix (GBD 2015 Disease and Injury Incidence and Prevalence Collaborators, 2016): Odds ratio: 1.30.

Table A4: Severity distribution and annual progression of radiographic knee osteoarthritis

†

TE D

Non-Maori Non-obese Obese Maori Non-obese Obese Female Non-Maori Non-obese Obese Maori Non-obese Obese Total

EP

Male

Distribution of OA severity† K-L grade 2 K-L grade 3 K-L grade 4 64.4% 31.8% 3.8% 46.1% 43.6% 10.3% 64.4% 31.6% 4.0% 45.3% 43.7% 10.9% 71.4% 24.0% 4.6% 53.1% 34.1% 12.9% 71.0% 24.2% 4.8% 52.3% 34.4% 13.3% 60.6% 31.9% 7.5%

Annual progression rate Grade 2 to 3 Grade 3 to 4 5.58% 1.29% 12.26% 2.94% 5.58% 1.29% 12.26% 2.94% 4.00% 1.95% 8.95% 4.27% 4.00% 1.95% 8.95% 4.27%

AC C

Age-standardised to the total NZ adult population with OA Source: Annual progression rates from Holt et al. (2011); baseline distribution estimated using NZ-MOA model, based on progression rates as reported and incidence rates derived from prevalence rates reported in Table A3 (assuming zero case fatality, zero remission).

ACCEPTED MANUSCRIPT Table A5: Average HRQoL values

RI PT

K-L grade 4 0.763 0.745 0.724 0.694 0.755 0.736 0.717 0.684 0.743 0.722 0.703 0.677 0.732 0.714 0.694 0.663

SC

Non-Māori Non-obese Obese I Obese II Obese III Māori Non-obese Obese I Obese II Obese III Female Non-Māori Non-obese Obese I Obese II Obese III Māori Non-obese Obese I Obese II Obese III Total

0.837

†

M AN U

Male

Mean HRQoL value, age-standardised† K-L grade 0/1 K-L grade 2 K-L grade 3 0.856 0.837 0.807 0.840 0.821 0.791 0.820 0.795 0.765 0.791 0.770 0.739 0.849 0.829 0.798 0.834 0.812 0.782 0.813 0.791 0.762 0.783 0.761 0.734 0.838 0.818 0.786 0.823 0.802 0.771 0.802 0.779 0.749 0.771 0.750 0.720 0.831 0.808 0.778 0.815 0.792 0.762 0.794 0.770 0.740 0.763 0.739 0.710 0.812

0.778

0.722

Age-standardised to the total NZ adult population Source: Estimated using NZ-MOA model, based on HRQoL progression model and parameters as described in Appendix B.

EP

Annual probability of TKR, conditional on eligibility criteria Male Female 0.03 0.06 0.09 0.08 0.26 0.13 0.41 0.26 0.68 0.30 0.79 0.33 0.90 0.30 0.89 0.33 0.63 0.24 0.34 0.14 0.17 0.06 0.02 0.01

AC C

Age 35-39 40-44 45-49 50-54 55-59 60-64 65-69 70-74 75-79 80-84 85-89 90-99

TE D

Table A6: Acceptance/offer rates for total knee replacement

Source: Calibrated using NZ-MOA model to match NZ Joint Registry provision data (New Zealand Joint Registry, 2015).

References Abbott JH, Usiskin IM, Wilson R, Hansen P, Losina E. The quality-of-life burden of knee osteoarthritis in New Zealand adults: a model-based evaluation. PloS ONE 12: e0185676. 2017. GBD 2015 Disease and Injury Incidence and Prevalence Collaborators. Global, regional, and national incidence, prevalence, and years lived with disability for 310 diseases and injuries, 1990-2015: a systematic analysis for the Global Burden of Disease Study 2015. Lancet 388: 1545-1602. 2016.

ACCEPTED MANUSCRIPT Holt HL, Katz JN, Reichmann WM, Gerlovin H, Wright EA, Hunter DJ, et al. Forecasting the burden of advanced knee osteoarthritis over a 10-year period in a cohort of 60-64 year-old US adults. Osteoarthritis and Cartilage 19: 44-50. 2011. Ministry of Health. New Zealand Health Survey 2013/14. Wellington, NZ: Statistics New Zealand. 2015. New Zealand Joint Registry. The New Zealand Joint Registry Sixteen Year Report. New Zealand Orthopaedic Association. 2015.

AC C

EP

TE D

M AN U

SC

RI PT

Statistics New Zealand. 2013 Census. Wellington, NZ: Statistics New Zealand. 2014.

ACCEPTED MANUSCRIPT

New Trial

t=0

RI PT

No

Yes

SC

Survive?

M AN U

Initial Characteristics (age, sex, ethnicity, BMI)

Update Characteristics

1. Structural progression

TE D

t=t+1

Update K-L Grade

EP

Initial K-L Grade

Initial HRQoL and Costs

Initialization

AC C

Evaluate treatment strategy Update HRQoL and Costs Annual Transition

2. HRQoL valuation

ACCEPTED MANUSCRIPT

RI PT SC M AN U

Female Male

TE D

500

EP

250

AC C

TKR (rate per 100,000 population, 2015)

750

0 35

40

45

50

55

60

65 70 Age

75

80

85

90

95

100

ACCEPTED MANUSCRIPT

Non−Maori Men

Non−Maori Women

0.6

RI PT

0.5 0.4 0.3

0.0 50

55

60

65

Maori Men 0.6

75

80

45

50

55

60

65

70

75

80

0.4 0.3 0.2

OAPol (VAS)

0.1 0.0 45

50

55

60

65

70 75 80 45 50 55 Cohort age at baseline (2006)

60

65

NZ−MOA OAPol (transformed)

Maori Women

EP

0.5

70

TE D

45

AC C

QALYs per capita

0.1

M AN U

SC

0.2

70

75

80

ACCEPTED MANUSCRIPT

SC

RI PT

HRQoL detriments

M AN U

OA structural progression

AC C

EP

TE D

OA prevalence

BMI distribution

0

100

200

300 400 500 600 700 Population lifetime QALY losses (000s), assuming conservative care only

800

900

100