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Biostatistics Advance Access originally published online on August 19, 2008
Biostatistics 2009 10(1):172-186; doi:10.1093/biostatistics/kxn025
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© The Author 2008. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org.

Estimating the capacity for improvement in risk prediction with a marker

Wen Gu and Margaret Sullivan Pepe*

Department of Biostatistics, University of Washington, Box 357232, 1705 Northeast Pacific Street, Seattle, WA 98195, USA and Fred Hutchinson Cancer Research Center, Division of Public Health Science, M2-B500, 1100 Fairview Avenue North, Seattle, WA 98109, USA mspepe{at}u.washington.edu

* To whom correspondence should be addressed.

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 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.

Keywords: Biomarker; Classification; Diagnostic likelihood ratio; Diagnostic test; Logistic regression; Posterior probability

Received November 29, 2007; revised May 29, 2008; accepted for publication June 27, 2008.


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