Effect of Covariate Omission in Randomised Controlled Trials: A Review and Simulation Study

In randomised controlled trials (RCTs), the allocated treatment group and covariates are expected to be independent. In the framework of the normal model, omitting covariates affects precision of the treatment effect estimator but does not yield bias in the estimator. However, when covariates are omitted, the treatment effect estimator has a bias in non‐normal models such as logistic and Cox models even in RCTs. Additionally, covariate omission in the accelerated failure time model and Poisson model causes a bias in the standard error (SE) estimator and yields an inflation of Type‐I error rate for the treatment effect. In this study, we reviewed the literature regarding the effect of covariate omission from the aspect of the bias and precision of treatment effect estimator, bias of SE estimator, and Type‐I error rate for these models assumed in RCTs. Furthermore, we conducted a simulation study in a wide variety of scenarios to evaluate the effect of covariate omission. Our literature review and simulation study provide a simple guide for consideration of covariate adjustment in RCTs. We recommend that all important and measurement covariates be included in analysis models to reduce bias for the treatment effect and SE estimators and control the Type‐I error rate.