The concept of residual confounding in regression models and some applications

In this paper the concept of residual confounding is generalized to various types of regression models such as logistic regression or Cox regression. Residual confounding and a newly suggested parameter, the relative residual confounding, are defined on the regression parameters of the models. The estimator gives the proportion of confounding which has been removed by incomplete adjustment. The concept quantifies the effects of categorizing continuous covariables and of model misspecification. These are investigated by a simulation study and with data from an epidemiological investigation. A case-control study of laryngeal cancer is used to illustrate the residual confounding effect of arbitrary transformation of a continuous confounder, smoking, on the effect of alcohol consumption on laryngeal cancer risk. The data also showed that categorization into two levels can yield high residual confounding. The parameters described in this paper are of some use in quantifying the effect of inadequate adjustment for confounding variables.