Article

# Two Criteria for Evaluating Risk Prediction Models

Biostatistics Branch, National Cancer Institute, 6120 Executive Boulevard, Bethesda, Maryland 20892, USA.

Biometrics (Impact Factor: 1.57). 12/2010; 67(3):1057-65. DOI: 10.1111/j.1541-0420.2010.01523.x Source: PubMed

**ABSTRACT**

We propose and study two criteria to assess the usefulness of models that predict risk of disease incidence for screening and prevention, or the usefulness of prognostic models for management following disease diagnosis. The first criterion, the proportion of cases followed PCF (q), is the proportion of individuals who will develop disease who are included in the proportion q of individuals in the population at highest risk. The second criterion is the proportion needed to follow-up, PNF (p), namely the proportion of the general population at highest risk that one needs to follow in order that a proportion p of those destined to become cases will be followed. PCF (q) assesses the effectiveness of a program that follows 100q% of the population at highest risk. PNF (p) assess the feasibility of covering 100p% of cases by indicating how much of the population at highest risk must be followed. We show the relationship of those two criteria to the Lorenz curve and its inverse, and present distribution theory for estimates of PCF and PNF. We develop new methods, based on influence functions, for inference for a single risk model, and also for comparing the PCFs and PNFs of two risk models, both of which were evaluated in the same validation data.

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##### Article: Extensions of criteria for evaluating risk prediction models for public health applications

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**ABSTRACT:**We recently proposed two novel criteria to assess the usefulness of risk prediction models for public health applications. The proportion of cases followed, PCF(p), is the proportion of individuals who will develop disease who are included in the proportion p of individuals in the population at highest risk. The proportion needed to follow-up, PNF(q), is the proportion of the general population at highest risk that one needs to follow in order that a proportion q of those destined to become cases will be followed (Pfeiffer, R. M. and Gail, M. H., 2011. Two criteria for evaluating risk prediction models. Biometrics 67, 1057-1065). Here, we extend these criteria in two ways. First, we introduce two new criteria by integrating PCF and PNF over a range of values of q or p to obtain iPCF, the integrated PCF, and iPNF, the integrated PNF. A key assumption in the previous work was that the risk model is well calibrated. This assumption also underlies novel estimates of iPCF and iPNF based on observed risks in a population alone. The second extension is to propose and study estimates of PCF, PNF, iPCF, and iPNF that are consistent even if the risk models are not well calibrated. These new estimates are obtained from case-control data when the outcome prevalence in the population is known, and from cohort data, with baseline covariates and observed health outcomes. We study the efficiency of the various estimates and propose and compare tests for comparing two risk models, both of which were evaluated in the same validation data.