Dose-Response Modeling for Ordinal Outcome Data

We consider the characterization of a dose-response relationship when the response variable is ordinal in nature. Initially, we review the existing models for describing such a relationship, and propose an extension that allows for the possibility of non-zero probabilities of response for the different categories of the ordinal outcome variable associated with the control group. We illustrate via a simulation study the difficulties that can be encountered in model fitting when significant background responses are not acknowledged. In order to further enlarge the spectrum of dose-response relationships that can be accurately modeled, we introduce splines into the existing models for ordinal outcome data; demonstrating in a simulation that such models can provide a superior fit relative to existing ones. We also propose an alternative reference dose measure for ordinal responses. Specifically, we propose an alternative method for defining the benchmark dose, BMD, for ordinal outcome data. The approach yields an estimator that is robust to the number of ordinal categories into which we divide the response. In addition, the estimator is consistent with currently accepted definitions of the BMD for quantal and continuous data when the number of categories for the ordinal response is two, or become extremely large, respectively. We suggest two methods for determining an interval reflecting the lower confidence limit of the BMD; one based on the delta method, the other on a likelihood ratio approach. We show via a simulation study that intervals based on the latter approach are able to achieve the nominal level of coverage.