How Cox models react to a study-specific confounder in a patient-level pooled dataset: Random-effects better cope with an imbalanced covariate across trials unless baseline hazards differ

Abstract

Combining patient-level data from clinical trials can connect rare phenomena with clinical endpoints, but statistical techniques applied to a single trial may become problematical when trials are pooled. Estimating the hazard of a binary variable unevenly distributed across trials showcases a common pooled database issue. We studied how an unevenly distributed binary variable can compromise the integrity of fixed and random effects Cox proportional hazards models. We compared fixed effect and random effects Cox proportional hazards models on a set of simulated datasets inspired by a 17-trial pooled database of patients presenting with ST-segment elevation myocardial infarction (STEMI) and non-STEMI undergoing percutaneous coronary intervention. An unevenly distributed covariate can bias hazard ratio estimates, inflate standard errors, raise type I error, and reduce power. While uneveness causes problems for all Cox proportional hazards models, random effects suffer least. Compared to fixed effect models, random effects suffer lower bias and trade inflated type I errors for improved power. Contrasting hazard rates between trials prevent accurate estimates from both fixed and random effects models. When modeling a covariate unevenly distributed across pooled trials with similar baseline hazard rates, Cox proportional hazards models with a random trial effect more accurately estimate hazard ratios than fixed effects. Differing between-trial baseline hazard rates bias both random and fixed effect models. With an unevenly-distributed covariate and similar baseline hazard rates across trials, a random effects Cox proportional hazards model outperforms a fixed effect model, but cannot overcome contrasting baseline hazard rates.