Bayesian Cost-Effectiveness Analysis of Medical Treatments: 1st Edition (Hardback) book cover

Bayesian Cost-Effectiveness Analysis of Medical Treatments

1st Edition

By Elias Moreno, Francisco Jose Vazquez-Polo, Miguel Angel Negrín-Hernández

Chapman and Hall/CRC

284 pages | 60 B/W Illus.

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Description

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.

Elías 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 José Vázquez-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 Ángel Negrín 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.

Table of Contents

  1. Health economics evaluation
  2. Introduction

    Conventional types of economic evaluation

    The variables of cost-effectiveness analysis

    Sources of uncertainty in cost-effectiveness analysis

    Conventional tools for cost-effectiveness analysis

    The incremental cost-effectiveness ratio

    The incremental net benefit

    Cost-effectiveness acceptability curve

    Conventional subgroup analysis

    An outline of Bayesian cost-effectiveness analysis

  3. Statistical inference in parametric models
  4. Introduction

    Parametric sampling models

    The likelihood function

    Likelihood sets

    The maximum likelihood estimator

    Proving consistency and asymptotic normality

    Reparametrization to a subparameter

    Parametric Bayesian models

    Subjective priors

    Conjugate priors

    Objective priors

    The predictive distribution

    Bayesian model selection

    Intrinsic priors for model selection

    The normal linear model

    Maximum likelihood estimators

    Bayesian estimators

    An outline of variable selection

  5. Statistical decision theory
  6. Introduction

    Elements of a decision problem

    Ordering rewards

    Lotteries

    The Utility function

    Axioms for the existence of the utility function

    Criticisms to the utility function

    Lotteries that depend on a parameter

    The minimax strategy

    The Bayesian strategy

    Comparison

    Optimal decisions in the presence of sampling information

    The frequentist procedure

    The Bayesian procedure

  7. Cost-effectiveness analysis. Optimal treatments
  8. Introduction

    The net benefit of a treatment

    Utility functions of the net benefit

    The utility function U Optimal treatments

    Interpretation of the expected utility

    The utility function U Optimal treatments

    Interpretation of the expected utility

    Penalizing a new treatment

    Parametric classes of probabilistic rewards

    Frequentist predictive distribution of the net bene

    Bayesian predictive distribution of the net benefit

    Statistical models for cost and effectiveness

    The normal-normal model

    The lognormal-normal model

    The lognormal-Bernoulli model

    The bivariate normal model

    The dependent lognormal-Bernoulli model

    A case study

    The cost-effectiveness acceptability curve for the utility

    function U

    The case of completely unknown rewards

    The case of parametric rewards

    The cost-effectiveness acceptability curve for the utility

    function U

    Comments on cost-effectiveness acceptability curve

  9. Cost-effectiveness analysis for heterogenous data
  10. Introduction

    Clustering

    Prior distributions

    Posterior distribution of the cluster models

    Examples

    Bayesian meta-analysis

    The Bayesian meta-model

    The likelihood of the meta-parameter and the

    linking distribution

    Properties of the linking distribution

    Examples

    Contents

    The predictive distribution of (c; e) conditional on a partition

    The unconditional predictive distribution of (c; e)

    The predictive distribution of the net benefit z

    The case of independent c and e

    Optimal treatments

    Examples

  11. Subgroup cost-effectiveness analysis

Introduction

The data and the Bayesian model

The independent normal-normal model

The normal-normal model

The lognormal-normal model

The probit sampling model

Bayesian variable selection

Notation

Posterior model probability

The hierarchical uniform prior for models

Zellner's g□□priors for model parameters

Intrinsic priors for model parameters

Bayes factors for normal linear models

Bayes factors for probit models

Bayesian predictive distribution of the net benefit

The normal-normal case

The case where c and e are independent

The lognormal-normal case

Optimal treatments for subgroups

Examples

Improving subgroup definition

About the Authors

Elías 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. He served as a President of the Spanish Statistical and Operational Research Society, 1992-1996, and Head of the Department of Statistics and Operational Research, 1986-1990, and he is in the editorial board of RACSAM, Test, ESTADISTICA and Global & Local Economic Review. He is co-editor of Bayesian Robustness, Vol. 29, Institute of Mathematical Statistics, Bayesian Statistics 6, Oxford University Press, and Topics on Methodological and Applied Statistical Inference, Springer-Verlag. He published around 120 papers on Statistical Inference in Statistical Journal including Journal of the Royal Statistical Society Series B, Journal of the American Statistical Association, The Annals of Statistics, Statistical Science, European Journal of Operational Research and Statistical Methods in Medical Research. Francisco José Vázquez-Polo is Professor of Mathematics and Bayesian Methods at the University of Las Palmas de Gran Canaria, and Head of the Department of Quantitative Method. He published twelve chapters of books and around 70 papers in Economics Journals including Journal of Business Economics & Statistics, European Journal of Health Economics, Health Economics, Journal of Health Economics, and in Statistical Journals including Journal of the Royal Statistical Society (Series B, C & D), European Journal of Operational Research, Computational Statistics and Data Analysis, Statistics in Medicine and Statistical Methods in Medical Research. Miguel Ángel Negrín 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. Part of his research has been published in Journals of reference in Health Economics and Statistics, such as Health Economics, Journal of Health Economics, European Journal of Health Economics, Value in Health, Statistics in Medicine, Medical Decision Making, European Journal of Operational Research and Statistical Methods in Medical Research. He serves in the editorial board of Gaceta Sanitaria (IF 2017: 1,58).

About the Series

Chapman & Hall/CRC Biostatistics Series

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
MAT029000
MATHEMATICS / Probability & Statistics / General
MED090000
MEDICAL / Biostatistics