Comparison to control in logistic regression

We are interested in comparing logistic regressions for several test treatments or populations with a logistic regression for a standard treatment or population. The research was motivated by some real life problems, which are discussed as data examples. We propose a step-down likelihood ratio method for declaring differences between the test treatments or populations and the standard treatment or population. Competitors based on the sequentially rejective Bonferroni Wald statistic, sequentially rejective exact Wald statistic and Reiersol's statistic are also discussed. It is shown that the proposed method asymptotically controls the probability of type I error. A Monte Carlo Simulation shows that the proposed method performs well for relatively small sample sizes, outperforming its competitors.