Construction of simultaneous confidence bands for multiple logistic regression models over restricted regions

This article presents methods for constructing an asymptotic hyperbolic band under the multiple logistic regression model when the predictor variables are restricted to a specific region. Scheffe's method yields unnecessarily wide, and hence conservative, bands if the predictor variables can be restricted to a certain region. Piegorsch and Casella [Confidence bands for logistic regression with restricted predictor variables. Biometrics. 1988;44:739-750] developed a procedure to build an asymptotic confidence band for the multiple logistic regression model over particular regions. Those regions are shown to be special cases of the region, which was first investigated by Seppanen and Uusipaikka [Confidence bands for linear regression over restricted regions. Scand J Stat. 1992;19:73-81] in the multiple linear regression context. This article also provides methods for constructing conservative confidence bands when the restricted region is not of the specified form. Particularly, rectangular restricted regions, which are commonly encountered in practice, are considered. Two examples are given to illustrate the proposed methodology, and one example shows that the proposed procedure outperforms the method given by Piegorsch and Casella (1988).