Statistical inference for net benefit measures in biomarker validation studies

Referral strategies based on risk scores and medical tests are commonly proposed. Direct assessment of their clinical utility requires implementing the strategy and is not possible in the early phases of biomarker research. Prior to late-phase studies, net benefit measures can be used to assess the potential clinical impact of a proposed strategy. Validation studies, in which the biomarker defines a prespecified referral strategy, are a gold standard approach to evaluating biomarker potential. Uncertainty, quantified by a confidence interval, is important to consider when deciding whether a biomarker warrants an impact study, does not demonstrate clinical potential, or that more data are needed. We establish distribution theory for empirical estimators of net benefit and propose empirical estimators of variance. The primary results are for the most commonly employed estimators of net benefit: from cohort and unmatched case-control samples, and for point estimates and net benefit curves. Novel estimators of net benefit under stratified two-phase and categorically matched case-control sampling are proposed and distribution theory developed. Results for common variants of net benefit and for estimation from right-censored outcomes are also presented. We motivate and demonstrate the methodology with examples from lung cancer research and highlight its application to study design.