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|Y,X) compared with the baseline model P(D = 1|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 two studies: one is a study of the performance of hearing screening tests for infants; the other concerns the value of serum creatinine in diagnosing renal artery stenosis.