Estimating the receiver operating characteristic curve in matched case control studies

The matched case-control design is frequently used in the study of complex disorders and can result in significant gains in efficiency, especially in the context of measuring biomarkers; however, risk prediction in this setting is not straightforward. We propose an inverse-probability weighting approach to estimate the predictive ability associated with a set of covariates. In particular, we propose an algorithm for estimating the summary index, area under the curve corresponding to the Receiver Operating Characteristic curve associated with a set of pre-defined covariates for predicting a binary outcome. By combining data from the parent cohort with that generated in a matched case control study, we describe methods for estimation of the population parameters of interest and the corresponding area under the curve. We evaluate the bias associated with the proposed methods in simulations by considering a range of parameter settings. We illustrate the methods in two data applications: (1) a prospective cohort study of cardiovascular disease in women, the Women's Health Study, and (2) a matched case-control study nested within the Nurses' Health Study aimed at risk prediction of invasive breast cancer.