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. Copyright © 2010 John Wiley & Sons, Ltd.