Semiparametric methods for evaluating the covariate-specific predictiveness of continuous markers in matched case-control studies

To assess the value of a continuous marker in predicting the risk of a disease, a graphical tool called the predictiveness curve has been proposed. It characterizes the marker's predictiveness, or capacity to stratify risk for the population, by displaying the distribution of risk endowed by the marker. Methods for making inference about the curve and for comparing curves in a general population have been developed. However, knowledge about a marker's performance in the general population only is not enough. Since a marker's effect on the risk model and its distribution can both differ across subpopulations, its predictiveness may vary when applied to different subpopulations. Moreover, information about the predictiveness of a marker conditional on baseline covariates is valuable for individual decision-making about having the marker measured or not. Therefore, to realize the usefulness of a risk prediction marker fully, it is important to study its performance conditional on covariates. We propose semiparametric methods for estimating covariate-specific predictiveness curves for a continuous marker. Unmatched and matched case-control study designs are accommodated. We illustrate application of the methodology by evaluating serum creatinine as a predictor of risk of renal artery stenosis.