1. Health economics evaluation

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

2. Statistical inference in parametric models

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

3. Statistical decision theory

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

4. Cost-effectiveness analysis. Optimal treatments

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

5. Cost-effectiveness analysis for heterogenous data

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

6. 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 gpriors 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

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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