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Bayesian Design of Discrete Choice Experiments for Valuing Health State Utilities

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Bayesian Design of Discrete Choice Experiments for Valuing Health State Utilities Bayesian Design of Discrete Choice Experiments for Valuing Health State Utilities by Fatimah Ali Aloef Thesis submitted to the University of Sheffield for the degree of Doctoral of Philosophy School of Mathematics and Statistics January 2015 To my parents and my little family. Acknowledgments First I mostly thank my PhD supervisors Prof. Jeremy Oakley and Dr. Eleanor Stillman for all their help and support. I really appreciate their valuable advices during my PhD that contributed to make this thesis possible. It is of my honor to be one of their students and benefit from their experiences. I wish to express my sincere thanks to Dr. Kevin Walters and Prof. Peter Goos for reading my thesis and providing me with significant and constructive suggestions in the oral examination. This thesis could not have been completed without their generous and professional assistances. I am also grateful to Prof. John Brazier at the ScHARR of the university of Sheffield for providing us with the data sets for asthma case study and making available for us to use their data. I would like also to thank the staff on the Mathematics department for being friendly and helpful all the time. I would like also thank all my friends (too many to present here but you know who you are) for being supportive, and providing me the friendship I needed during my studies and understanding my fluctuated mood during the PhD. I am really thankful to my friends Sujunya Boonpradit and Madina Hassan for supporting and encouraging me all the time. I specially thank my dad, mum, and my brothers and sisters for their support and prayers and for their entire love. Special thanks for my little family, my husband who support me all the time and has faith in me and my intellect even when I felt down. Also my kids Ali and the little angel Sarah where there is no words can describe how much I do love them. Abstract This thesis aims to develop an efficient methodology to construct efficient discrete choice experiments (DCEs) for health state utility estimation within the QALY framework. The use of the QALY measure in health economic evaluation together with meth- ods related to measuring the QALY weight/health state utilities are reviewed in order to establish the fundamental knowledge needed for valuing health. DCEs are used to value health state utilities, which is simpler than other direct valuation methods. Nev- ertheless, DCEs are still undergoing research to improve their uses in valuing utilities, in particular in designing experiments which are used to construct the DCEs The main issues with the current choice designs together with design considerations for valuing utilities are identified in this thesis. Advanced work for constructing choice designs, particularly Bayesian optimal design, is reviewed to construct more efficient de- signs for valuing utilities. Since constructing Bayesian optimal designs requires a prior distribution for the unknown choice model parameters, Bayesian analysis is performed for a real data to obtain appropriate prior distributions. Constructing Bayesian optimal choice designs for valuing utilities within QALY framework using the existing choice design software is investigated. We find there are limitations because of the design considerations for valuing health state utilities particularly in terms of anchoring utility values into the QALY scale (0-1 scale). We then develop a new algorithm based on modifying the latest advanced choice design algorithms such that they account for the design considerations which overcomes the limitations with the existing design software. Methods for simplifying the choice design questions are also provided. We demonstrate the use of our design algorithm by constructing Bayesian choice designs for asthma quality of life classification system (AQL-5D), and then investigate the effect of the choice of the prior distribution on the choice of Bayesian designs. Contents 1 Introduction 1 1.1 Introduction . .1 1.2 Economic Evaluation in Health Care . .2 1.3 Discrete Choice Experiments and Valuing Health . .6 1.4 Motivation for Better Choice Design . .9 1.5 Aim of the Thesis . 11 1.6 Thesis Outline . 12 2 Valuing Health and Discrete Choice Experiments 14 2.1 Introduction . 14 2.2 QALYs . 15 2.2.1 Illustrative Example . 16 2.3 Classification Systems . 17 ii 2.3.1 Generic Classification System . 18 2.3.2 Condition Specific Classification System . 20 2.3.3 Modelling Health State Classification System Valuation . 22 2.4 Measuring Preference . 24 2.4.1 Direct Valuation Techniques . 24 2.4.1.1 Time Trade-Off . 25 2.4.1.2 Standard Gamble . 27 2.4.1.3 Visual Analogue Scale . 29 2.4.2 Direct Valuation Method Issues . 30 2.4.3 Indirect Valuation Techniques . 31 2.4.3.1 Ranking . 31 2.4.3.2 Discrete Choice Experiments . 32 2.4.4 Advantages and Disadvantages of DCE Techniques . 34 2.5 Discrete Choice Models . 37 2.5.1 Modelling Discrete Choice Data . 37 2.5.2 Model Identification . 40 2.5.3 Multinomial Logit Model . 43 2.6 Summary . 47 3 Literature Review: DCEs and their Design in Health Economics 49 3.1 Introduction . 49 iii 3.2 DCEs in Health Economics . 51 3.2.1 DCEs in Health Economics: A Review . 51 3.2.2 Methods Used to Create Choice Sets . 54 3.2.3 Methodological Issues . 57 3.3 Context-specific Design Considerations . 62 3.4 Optimality Theory . 65 3.4.1 Optimality Criteria . 67 3.4.2 The General Equivalence Theorem . 71 3.4.3 Example: Deriving the D-optimal Design for the General Linear Model . 72 3.5 Nonlinear Optimal Design Problem . 76 3.5.1 Locally Optimal Designs . 77 3.5.2 Bayesian Optimal Designs . 78 3.6 Bayesian Experimental Design Criteria for Nonlinear Models . 80 3.6.1 Asymptotic Bayesian Criteria . 81 3.6.2 Exact Bayesian Criteria . 83 3.6.3 Bayesian Information Criteria . 85 3.7 Design Algorithms and Software . 87 3.7.1 Local and Utility-neutral Optimal Design Algorithms . 88 3.7.2 Bayesian Optimal Design Algorithms . 92 3.8 Summary . 98 iv 4 Analysis of the AQL-5D Data 102 4.1 Introduction . 102 4.2 Data Description . 104 4.2.1 TTO Data . 104 4.2.2 Discrete Choice Data . 106 4.3 Method for Modelling Health State Utilities . 108 4.4 Classical Inference for Health State Utilities . 110 4.4.1 Modelling TTO Data . 110 4.4.2 Modelling Discrete Choice Data . 116 4.4.3 Comparing Classical Inference for Health State Utilities . 122 4.5 Bayesian Inference for Health State Utility . 125 4.5.1 Prior Distribution . 126 4.5.2 Obtaining the Posterior Distribution . 128 4.5.3 MCMC Results for TTO Model . 131 4.5.4 MCMC Results for the DCE Model . 138 4.6 Summary and Discussion . 146 5 Bayesian Optimal Choice Designs for Valuing Health State Utilities 149 5.1 Introduction . 149 5.2 Deriving the Optimality Criterion for the MNL model . 150 5.3 Constructing Choice Design Using Available Software . 163 v 5.4 Bayesian Design Algorithm for Generating DCE for Valuing Health State Utilities . 168 5.4.1 Random Search Algorithm . 168 5.4.2 Coordinate-exchange Algorithm . 173 5.4.3 Updating the Information Matrix and the Cholesky Decomposition175 5.5 Simplifying the Choice Task . 180 5.5.1 Determining the Fixed Attributes in Each Choice Set . 181 5.5.2 Assigning Attribute levels for Fixed and Non-fixed Attributes . 182 5.6 Bayesian Optimal Choice Design for the AQL-5D Classification System 183 5.6.1 Constructing Bayesian Pairwise Experiments for the AQL-5D Classification System . 184 5.6.2 Comparing Bayesian Optimal Designs . 187 5.6.3 Comparing LBD and Bayesian Optimal Designs . 191 5.7 Summary and Discussion . 194 6 Sensitivity of the Bayesian Optimal Choice Design to the Prior Dis- tribution 197 6.1 Introduction . 197 6.2 Prior Distributions for Designing Optimal Choice Experiment for Valu- ing Health States Utilities . 198 6.3 Appropriate Choice Tasks and the Prior Distribution . 203 6.4 Sensitivity to the Prior Distribution: Illustrative Study . 207 vi 6.4.1 Comparing Design Efficiency for Non-identical Priors of the Pa- rameters . 209 6.4.2 Comparing Design Efficiency for i.i.d Priors of the Parameters . 216 6.4.3 The Sensitivity of Bayesian Choice Design to the Prior Distribu- tion of the Scale Parameter . 218 6.5 Summary and Discussion . 224 7 Conclusion 227 7.1 Summary of the Thesis . 228 7.2 Discussion of the Main Findings . 230 7.3 Limitation and Further Work . 234 7.4 Main Recommendations for Practical Applications . 237 Appendices 239 A.1 Posterior Distributions . 239 A.2 Discrete Choice Designs . 243 A.2.1 DCE for Asthma Health States Using Huber and Zwerina (1996) Approach . 243 A.2.2 DCE for Asthma Health States Using Bayesian Approach . 244 A.2.2.1 Bayesian Designs with Full Profiles . 244 A.2.2.2 Bayesian Designs with Partial Profiles . 245 Bibliography 249 vii List of Abbreviations AQL-5D Asthma Quality of Life classification with five dimensions/attributes. CEA Cost-effectiveness Analysis. CMA Cost-minimisation Analysis. CSPMs condition specific preference-based measures. CUA Cost-utility Analysis. DALY disability adjusted life-year. DCE discrete choice experiment. EQ-5D European qality of life with five dimen- sions/attributes. FIM Fisher information matrix. GFIM generalised Fisher information matrix. GPMs generic preference-based measures. HRQoL health related quality of life. HTA Health Technology Appraisal. HUI health utility index. HYE health years equivalent. ICER incremental cost effectiveness ratio. LBD level balanced design. MNL multinomial logit model. NICE National Institute for Health and Care Excel- lence. QALY quality-adjusted life-year.
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