Linear regression analysis of binary response data with mixed covariates - a simulation study

In a clinical trial with binary outcome, analyses are required for treatment or study group comparisons adjusted for covariate effects. A special problem arises with "mixed binary and Gaussian covariates", i.e., when some covariates are binary and some are continuous and may be assumed to be Gaussian. The correct model for such a data structure is of the logistic form. In the past, analyses of such data have been carried out by linear regression as well as by logistic regression methods. In this article, computer simulation was used to study the type I error level of linear regression analysis tests for treatment comparisons, when applied to a binary outcome variate obeying a logistic model with mixed binary and Gaussian covariates. It was found that the true type I error level depends on the distribution of covariates among treatment groups and on the magnitudes of the actual covariate effects, and can differ importantly from that assumed under Gaussian theory. Some recommendations are made for developing computer package programs for this problem.