Some Surprising Results About Covariate Adjustment in Logistic Regression Models

Laurence D. Robinson, Division of Biostatistics, School of Public Health, University of California, Berkeley
Nicholas P. Jewell, Division of Biostatistics, School of Public Health, University of California, Berkeley

Abstract

Results from classic linear regression regarding the effect of adjusting for covariates upon the precision of an estimator of exposure effect are often assumed to apply more generally to other types of regression models. In this paper we show that such an assumption is not justified in the case of logistic regression, where the effect of adjusting for covariates upon precision is quite different. For example, in classic linear regression the adjustment for a non-confounding predictive covariate results in improved precision, whereas such adjustment in logistic regression results in a loss of precision. However, when testing for a treatment effect in randomized studies, it is always more efficient to adjust for predictive covariates when logistic models are used, and thus in this regard the behavior of logistic regression is the same as that of classic linear regression.