Sample size calculations for ROC studies: parametric robustness and Bayesian nonparametrics

Abstract

Methods for sample size calculations in ROC studies often assume independent normal distributions for test scores among the diseased and nondiseased populations. We consider sample size requirements under the default two-group normal model when the data distribution for the diseased population is either skewed or multimodal. For these two common scenarios we investigate the potential for robustness of calculated sample sizes under the mis-specified normal model and we compare to sample sizes calculated under a more flexible nonparametric Dirichlet process mixture model. We also highlight the utility of flexible models for ROC data analysis and their importance to study design. When nonstandard distributional shapes are anticipated, our Bayesian nonparametric approach allows investigators to determine a sample size based on the use of more appropriate distributional assumptions than are generally applied. The method also provides researchers a tool to conduct a sensitivity analysis to sample size calculations that are based on a two-group normal model. We extend the proposed approach to comparative studies involving two continuous tests. Our simulation-based procedure is implemented using the WinBUGS and R software packages and example code is made available.