Analysis of the effects of adjusting for binary non-confounders in a logistic regression model after all true confounders have been accounted for : a simulation study

In observational studies, confounding variables that affect both the exposure and an outcome of interest are a general concern. It is well known that failure to control for confounding variables adequately can worsen inference on an exposure's effect on outcome. In this paper, we explore how exposure effect inference changes when non-confounding covariates are added to the assumed logistic regression model, after the set of all true confounders are included. This is done via an exhaustive simulation study with thousands of randomly generated scenarios to make general statements about over-adjusting in logistic regression. Our results show that in general, adding non-confounders to the regression model decreases the mean squared error for non-null exposure effects. The probability of both type I and type II errors also decrease with addition of more covariates given that all true confounders are controlled for.