  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.
