Estimating the capacity for improvement in risk prediction with a marker

Consider a set of baseline predictors X to predict a binary outcome D and let Y be a novel marker or predictor. This paper is concerned with evaluating the performance of the augmented risk model P(D = 1 vertical bar Y,X) compared with the baseline model P(D = 1 vertical bar X). The diagnostic likelihood ratio, DLRX(y), quantifies the change in risk obtained with knowledge of Y = y for a subject with baseline risk factors X. The notion is commonly used in clinical medicine to quantify the increment in risk prediction due to Y. It is contrasted here with the notion of covariate-adjusted effect of Y in the augmented risk model. We also propose methods for making inference about DLRX(y). Case-control study designs are accommodated. The methods provide a mechanism to investigate if the predictive information in Y varies with baseline covariates. In addition, we show that when combined with a baseline risk model and information about the population distribution of Y given X, covariate-specific predictiveness curves can be estimated. These curves are useful to an individual in deciding if ascertainment of Y is likely to be informative or not for him. We illustrate with data from 2 studies: one is a study of the performance of hearing screening tests for infants, and the other concerns the value of serum creatinine in diagnosing renal artery stenosis.