Abstract
Cost-effective yet efficient designs are critical to the success of biomarker evaluation research. Two-phase sampling designs, under which expensive markers are only measured on a subsample of cases and non-cases within a prospective cohort, are useful in novel biomarker studies for preserving study samples and minimizing cost of biomarker assaying. Statistical methods for quantifying the predictiveness of biomarkers under two-phase studies have been proposed (Cai and Zheng, 2012; Liu, Cai and Zheng, 2012). These methods are based on a class of inverse probability weighted (IPW) estimators where weights are 'true' sampling weights that simply reflect the sampling strategy of the study. While simple to implement, existing IPW estimators are limited by lack of practicality and efficiency. In this manuscript, we investigate a variety of two-phase design options and provide statistical approaches aimed at improving the efficiency of simple IPW estimators by incorporating auxiliary information available for the entire cohort. We consider accuracy summary estimators that accommodate auxiliary information in the context of evaluating the incremental values of novel biomarkers over existing prediction tools. In addition, we evaluate the relative efficiency of a variety of sampling and estimation options under two-phase studies, shedding light on issues pertaining to both the design and analysis of biomarker validation studies. We apply our methods to the evaluation of a novel biomarker for liver cancer risk conducted with a two-phase nested case control design (Lok et al., 2010).