LOSS IN EFFICIENCY CAUSED BY OMITTING COVARIATES AND MISSPECIFYING EXPOSURE IN LOGISTIC-REGRESSION MODELS

We examine the effects of omitting covariates and misspecifying the explanatory variable of interest on tests of association between the explanatory variable and response based on logistic regression models. We assume throughout that the covariates are statistically independent of the explanatory variable, as under simple randomization. A general expression for the asymptotic loss in efficiency from omitting covariates and misspecifying the explanatory variable is derived. The expression for the asymptotic efficiency of the misspecified test statistic relative to the correctly specified test can be factored into two parts, each of which is less than or equal to 1. The first part reflects the consequences of misspecifying exposure, whereas the other part captures the effect of omitting needed covariates. This result permits numerical evaluation of the approximate loss in efficiency and can be useful in developing guidelines for study design and model-fitting procedures. We discuss applications of the result for several special cases.