Uncovering hidden influences : impact of omitted covariates on the estimation of treatment effects using Cox regression in randomized and propensity score matched trials

Abstract

Hazard ratios (HRs) are commonly used to describe treatment effects in trials focusing on time-to-event outcomes, but have faced growing criticism, particularly regarding non-collapsibility and causal interpretation. This work highlights another concern: unobserved or omitted covariates that induce bias in both randomized and propensity score matched trials. To address this, a new approach, “Dynamic Landmarking”, is introduced. It visually detects biased estimates by iteratively removing sorted observations and refitting Cox models. It also evaluates the balance of observed but omitted covariates using the sum of squared z-differences. Simulations confirm its effectiveness in identifying biased estimates and relevant omitted covariates that cause them. An application to 27 large RCTs found no empirical evidence of built-in selection bias, likely due to small treatment effects and strict inclusion criteria. Thus, HRs remain generally valid, at least regarding this type of bias.