The effect of omitted covariates on confidence interval and study power in binary outcome analysis: A simulation study

Background/objectives: The consequence of omitted but balanced covariates on odds ratio point estimation is well-known in the literature. When exposure or intervention has a non-null effect on disease outcome, omitted covariates lead to underestimation of the effect of exposure or intervention. However, the effect of omitted covariates on confidence interval and study power is unknown. Study design and setting: A simulation study is carried out to assess the effect of omitted covariates on confidence interval and study power for a plausible range of scenarios. Coverage probability and study power are assessed systematically over a range of study size, type of omitted covariate and magnitude of effect. A real-life example using a randomised experiment on flies' sexuality is provided. Results: When a balanced covariate is omitted, coverage probability was lowered by 2.9-80%. Likewise study power was reduced by as much as 58%. The impact becomes substantial when the covariate is continuous, has large variability and has a larger effect than the effect of exposure or intervention. The result from a real-life example concurs with the simulation finding. Conclusion: Omitting an important balanced covariate lowers both coverage probability and study power. This implies the need for thoughtful consideration of important covariates at the design as well as the analysis stages of a study.