When Method Choice Changes Statistical Inference: A Comparison of a Baseline Two-Stage Approach and Bayesian Joint Modeling for Longitudinal and Survival Data in an HIV Clinical Trial

Abstract

The two-stage approach and Bayesian joint modeling are commonly used to analyze longitudinal biomarker measurements together with time-to-event outcomes. Using data from an HIV clinical trial of 467 patients with repeated CD4 measurements and all-cause mortality as the survival outcome, we compared a baseline two-stage approach with a Bayesian joint model. The two-stage analysis fitted a linear mixed-effects model and included each patient's predicted baseline CD4 value as a fixed covariate in a Cox proportional hazards model. The joint model simultaneously modeled the longitudinal CD4 process and survival while linking mortality risk to the current underlying CD4 value. The estimated association between ddI and mortality was similar in direction and magnitude across the two approaches. The two-stage estimate was HR = 1.342 (95% CI: 1.006-1.789), whereas the joint-model estimate was HR = 1.383 (95% CrI: 0.952-2.010). The estimated protective association of CD4 was stronger under the joint model (HR = 0.776) than under the two-stage approach (HR = 0.826). Because the approaches used different summaries of the longitudinal CD4 process, the observed differences cannot be attributed solely to measurement error or informative dropout. The findings demonstrate that the treatment of longitudinal biomarker information can materially affect statistical inference.