Model-based approaches for time-dependent dose finding with repeated binary data.

The goal of a clinical Phase II dose finding study is to describe the dose response relationship and to find a target dose (TD) or dose range that ensures a certain efficacy. In many applications, however, it is useful to consider combinations of dose and time under treatment instead of the dose only. The estimation of a minimum effective dose as a function of time allows, e.g. for a decision on an optimal initial treatment duration, if this initial treatment is followed by a maintenance therapy or aftercare which is supposed to start when a certain response rate is achieved. Bretz et al. (Biometrics 2005; 61:738-748) proposed a methodology that combines formal hypothesis testing for dose response with flexible modeling of the dose response relationship and estimating a target dose. In this paper a framework is proposed that allows for an extension of this methodology to a procedure that takes into account both, dose and time under treatment based on repeated binary data. A set of nonlinear mixed effects models is considered. The primary goal of such a study is the estimation of a minimum effective dose defined by the marginal probability, either in absolute terms or relative to placebo, as a function of time.Examples for the TD as a function of time are given under specific model assumptions using a response function which depends on a cumulated dose response over time. The proposed models are illustrated by a case study on the treatment of psoriasis. The precision of the TD estimation as given by its standard error and bias are presented under different dose-response models and scenarios. The precision conditioned on the correct underlying model shape is contrasted with the precision of a procedure that incorporates a model selection step after which the TD is estimated using the selected model, and with the precision obtained under a misspecified model.