Decreased Susceptibility of Marginal Odds Ratios to Finite-sample Bias

Parameters representing adjusted treatment effects may be defined marginally or conditionally on covariates. The choice between a marginal or covariate-conditional parameter should be driven by the study question. However, an unappreciated benefit of marginal estimators is a reduction in susceptibility to finite-sample bias relative to the unpenalized maximum likelihood estimator of the covariate-conditional odds ratio (OR). Using simulation, we compare the finite-sample bias of different marginal and conditional estimators of the OR. We simulated a logistic model to have 15 events per parameter and two events per parameter. We estimated the covariate-conditional OR by maximum likelihood with and without Firth's penalization. We used three estimators of the marginal OR: g-computation, inverse probability of treatment weighting, and augmented inverse probability of treatment weighting. At 15 events per parameter, as expected, all estimators were effectively unbiased. At two events per parameter, the unpenalized covariate-conditional estimator was notably biased but penalized covariate-conditional and marginal estimators exhibited minimal bias.