Bayesian nonparametric inference for the overlap coefficient: With an application to disease diagnosis

Abstract

Diagnostic tests play an important role in medical research and clinical practice. The ultimate goal of a diagnostic test is to distinguish between diseased and nondiseased individuals and before a test is routinely used in practice, it is a pivotal requirement that its ability to discriminate between these two states is thoroughly assessed. The overlap coefficient, which is defined as the proportion of overlap area between two probability density functions, has gained popularity as a summary measure of diagnostic accuracy. We propose two Bayesian nonparametric estimators, based on Dirichlet process mixtures, for estimating the overlap coefficient. We further introduce the covariate-specific overlap coefficient and develop a Bayesian nonparametric approach based on Dirichlet process mixtures of additive normal models for estimating it. A simulation study is conducted to assess the empirical performance of our proposed estimators. Two illustrations are provided: one concerned with the search for biomarkers of ovarian cancer and another one aimed to assess the age-specific accuracy of glucose as a biomarker of diabetes.

Keywords: Bayesian nonparametrics; Dirichlet process mixtures; covariate-adjustment; diagnostic test; overlap coefficient.