Bayesian cost-effectiveness analysis of medical treatments / Elias Moreno, Francisco Jose Vazquez-Polo, Miguel Angel Negrin-Hernandez.

<OL><B><LI>Health economics evaluation </LI></B><P>Introduction </P><P>Conventional types of economic evaluation </P><P>The variables of cost-effectiveness analysis </P><P>Sources of uncertainty in cost-effectiveness analysis </P><P>Conventional tools for cost-effectiveness analysis </P><P>The incremental cost-effectiveness ratio </P><P>The incremental net benefit </P><P>Cost-effectiveness acceptability curve </P><P>Conventional subgroup analysis </P><P>An outline of Bayesian cost-effectiveness analysis </P><B><P></P><P><LI>Statistical inference in parametric models </LI><P></P></B><P>Introduction </P><P>Parametric sampling models </P><P>The likelihood function </P><P>Likelihood sets </P><P>The maximum likelihood estimator </P><P>Proving consistency and asymptotic normality </P><P>Reparametrization to a subparameter </P><P>Parametric Bayesian models </P><P>Subjective priors </P><P>Conjugate priors </P><P>Objective priors </P><P>The predictive distribution </P><P>Bayesian model selection </P><P>Intrinsic priors for model selection </P><P>The normal linear model </P><P>Maximum likelihood estimators </P><P>Bayesian estimators </P><P>An outline of variable selection </P><P></P><B><P><LI>Statistical decision theory </LI><P></P></B><P>Introduction </P><P>Elements of a decision problem </P><P>Ordering rewards </P><P>Lotteries </P><P>The Utility function </P><P>Axioms for the existence of the utility function </P><P>Criticisms to the utility function </P><P>Lotteries that depend on a parameter </P><P>The minimax strategy </P><P>The Bayesian strategy </P><P>Comparison </P><P>Optimal decisions in the presence of sampling information</P><P>The frequentist procedure </P><P>The Bayesian procedure </P><P></P><B><P><LI>Cost-effectiveness analysis. Optimal treatments </LI><P></P></B><P>Introduction </P><P>The net benefit of a treatment </P><P>Utility functions of the net benefit </P><P>The utility function U Optimal treatments </P><P>Interpretation of the expected utility </P><P>The utility function U Optimal treatments </P><P>Interpretation of the expected utility </P><P>Penalizing a new treatment </P><P>Parametric classes of probabilistic rewards </P><P>Frequentist predictive distribution of the net bene</P><P>Bayesian predictive distribution of the net benefit </P><P>Statistical models for cost and effectiveness </P><P>The normal-normal model </P><P>The lognormal-normal model </P><P>The lognormal-Bernoulli model </P><P>The bivariate normal model </P><P>The dependent lognormal-Bernoulli model </P><P>A case study </P><P>The cost-effectiveness acceptability curve for the utility</P><P>function U </P><P>The case of completely unknown rewards </P><P>The case of parametric rewards </P><P>The cost-effectiveness acceptability curve for the utility</P><P>function U </P><P>Comments on cost-effectiveness acceptability curve </P><P></P><B><P><LI>Cost-effectiveness analysis for heterogenous data </LI><P></P></B><P>Introduction </P><P>Clustering </P><P>Prior distributions </P><P>Posterior distribution of the cluster models </P><P>Examples </P><P>Bayesian meta-analysis </P><P>The Bayesian meta-model </P><P>The likelihood of the meta-parameter and the</P><P>linking distribution </P><P>Properties of the linking distribution </P><P>Examples </P><P>Contents</P><P>The predictive distribution of (c; e) conditional on a partition</P><P>The unconditional predictive distribution of (c; e) </P><P>The predictive distribution of the net benefit z </P><P>The case of independent c and e </P><P>Optimal treatments </P><P>Examples </P><P></P><B><P><LI>Subgroup cost-effectiveness</B> <B>analysis </LI><P></P></OL></B><P>Introduction </P><P>The data and the Bayesian model </P><P>The independent normal-normal model </P><P>The normal-normal model </P><P>The lognormal-normal model </P><P>The probit sampling model </P><P>Bayesian variable selection </P><P>Notation </P><P>Posterior model probability </P><P>The hierarchical uniform prior for models </P><P>Zellner's gpriors for model parameters </P><P>Intrinsic priors for model parameters </P><P>Bayes factors for normal linear models </P><P>Bayes factors for probit models </P><P>Bayesian predictive distribution of the net benefit </P><P>The normal-normal case </P><P>The case where c and e are independent </P><P>The lognormal-normal case </P><P>Optimal treatments for subgroups </P><P>Examples </P><P>Improving subgroup definition </P><P></P>

Cost-effectiveness analysis is becoming an increasingly important tool for decision making in the health systems. Cost-Effectiveness of Medical Treatments formulates the cost-effectiveness analysis as a statistical decision problem, identifies the sources of uncertainty of the problem, and gives an overview of the frequentist and Bayesian statistical approaches for decision making. Basic notions on decision theory such as space of decisions, space of nature, utility function of a decision and optimal decisions, are explained in detail using easy to read mathematics. Features Focuses on cost-effectiveness analysis as a statistical decision problem and applies the well-established optimal statistical decision methodology. Discusses utility functions for cost-effectiveness analysis. Enlarges the class of models typically used in cost-effectiveness analysis with the incorporation of linear models to account for covariates of the patients. This permits the formulation of the group (or subgroup) theory. Provides Bayesian procedures to account for model uncertainty in variable selection for linear models and in clustering for models for heterogeneous data. Model uncertainty in cost-effectiveness analysis has not been considered in the literature. Illustrates examples with real data. In order to facilitate the practical implementation of real datasets, provides the codes in Mathematica for the proposed methodology. The motivation for the book is to make the achievements in cost-effectiveness analysis accessible to health providers, who need to make optimal decisions, to the practitioners and to the students of health sciences. Elaias Moreno is Professor of Statistics and Operational Research at the University of Granada, Spain, Corresponding Member of the Royal Academy of Sciences of Spain, and elect member of ISI. Francisco Josae Vaazquez-Polo is Professor of Mathematics and Bayesian Methods at the University of Las Palmas de Gran Canaria, and Head of the Department of Quantitative Methods. Miguel aAngel Negrain is Senior Lecturer in the Department of Quantitative Methods at the ULPGC. His main research topics are Bayesian methods applied to Health Economics, economic evaluation and cost-effectiveness analysis, meta-analysis and equity in the provision of healthcare services.

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