Robust Medical Test Evaluation Using Flexible Bayesian Semiparametric Regression Models

Adam J Branscum,Wesley O Johnson,Andre T Baron

doi:10.1155/2013/131232

Abstract

The application of Bayesian methods is increasing in modern epidemiology. Although parametric Bayesian analysis has penetrated the population health sciences, flexible nonparametric Bayesian methods have received less attention. A goal in nonparametric Bayesian analysis is to estimate unknown functions (e.g., density or distribution functions) rather than scalar parameters (e.g., means or proportions). For instance, ROC curves are obtained from the distribution functions corresponding to continuous biomarker data taken from healthy and diseased populations. Standard parametric approaches to Bayesian analysis involve distributions with a small number of parameters, where the prior specification is relatively straight forward. In the nonparametric Bayesian case, the prior is placed on an infinite dimensional space of all distributions, which requires special methods. A popular approach to nonparametric Bayesian analysis that involves Polya tree prior distributions is described. We provide example code to illustrate how models that contain Polya tree priors can be fit using SAS software. The methods are used to evaluate the covariate-specific accuracy of the biomarker, soluble epidermal growth factor receptor, for discerning lung cancer cases from controls using a flexible ROC regression modeling framework. The application highlights the usefulness of flexible models over a standard parametric method for estimating ROC curves.

Highlights

Bayesian analysis is often used in the support of epidemiologic research [1,2,3,4,5,6,7]
Statistical methods focus on estimating sensitivity and specificity, while with quantitative data, standard objects of interest are the receiver operating characteristic (ROC) curve and area under the curve (AUC)
The main goals of this paper are (i) to use flexible Bayesian models and ROC curves to evaluate the accuracy of a biomarker that may depend on patient characteristics and (ii) to provide a nontechnical description of Polya tree priors and show how they can be implemented in epidemiological research using standard statistical software

Summary

Introduction

Bayesian analysis is often used in the support of epidemiologic research [1,2,3,4,5,6,7]. A contemporary area of research in the population health sciences involves the development and application of statistical methods for evaluating the accuracy of medical tests. Statistical methods focus on estimating sensitivity and specificity, while with quantitative data, standard objects of interest are the receiver operating characteristic (ROC) curve and area under the curve (AUC). The ROC curve can be regarded as a graphical portrayal of the degree of separation between the distributions of test outcomes for “diseased” and nondiseased populations. The formula for an ROC curve depends on Se(k) and Sp(k), the sensitivity and specificity of the test at classification threshold k. Y can be any continuously measured classifier that varies according to a cumulative distribution function G0 for nondiseased individuals and varies according to G1 for diseased individuals.

Objectives

Methods

Results

Conclusion