Evaluating longitudinal markers under two-phase study designs.

Little attention has been given to the design of efficient studies to evaluate longitudinal biomarkers. Measuring longitudinal markers on an entire cohort is cost prohibitive and, especially for rare outcomes such as cancer, may be infeasible. Thus, methods for evaluation of longitudinal biomarkers using efficient and cost-effective study designs are needed. Case cohort (CCH) and nested case-control (NCC) studies allow investigators to evaluate biomarkers rigorously and at reduced cost, with only a small loss in precision. In this article, we develop estimators of several measures to evaluate the accuracy and discrimination of predicted risk under CCH and NCC study designs. We use double inverse probability weighting (DIPW) to account for censoring and sampling bias in estimation and inference procedures. We study the asymptotic properties of the proposed estimators. To facilitate inference using two-phase longitudinal data, we develop valid resampling-based variance estimation procedures under CCH and NCC. We evaluate the performance of our estimators under CCH and NCC using simulation studies and illustrate them on a NCC study within the hepatitis C antiviral long-term treatment against cirrhosis (HALT-C) clinical trial. Our estimators and inference procedures perform well under CCH and NCC, provided that the sample size at the time of prediction (effective sample size) is reasonable. These methods are widely applicable, efficient, and cost-effective and can be easily adapted to other study designs used to evaluate prediction rules in a longitudinal setting.