Simultaneous confidence bands for restricted logistic regression models

The hyperbolic 1 - alpha confidence bands for one logistic regression model with restricted predictors have been considered in the statistical literature. At times, one wishes to construct simultaneous confidence bands for comparing several logistic regression models. It seems that Liu's book [Simultaneous Inference in Regression, Chapman & Hall, 2010, Chapter 8] is the only published work that has addressed this problem. Liu suggested simulation-based methods for constructing simultaneous confidence bands for comparing several logistic models, but further research was warranted to assess the conservativeness of the bands. In this paper, we propose a dimension-wise partitioning method to construct a set of simultaneous confidence bands for the comparisons of several logistic regression functions with a pre-specified function in a stepwise fashion. In addition, simulation studies cast new light on the assumption of predetermined testing order for the stepwise procedures presented in this paper and by Hsu and Berger [Stepwise confidence intervals without multiplicity adjustment for dose-response and toxicity studies, J. Amer. Statist. Assoc. 94 (1999), pp. 468-482]. As an illustration, we include an example on the success rate of thrombolysis associated with patient characteristics regarding post-thrombotic syndrome.