Model-based dose finding under model uncertainty using general parametric models

The statistical methodology for the design and analysis of clinical Phase II dose-response studies, with related software implementation, is well developed for the case of a normally distributed, homoscedastic response considered for a single timepoint in parallel group study designs. In practice, however, binary, count, or time-to-event endpoints are encountered, typically measured repeatedly over time and sometimes in more complex settings like crossover study designs. In this paper, we develop an overarching methodology to perform efficient multiple comparisons and modeling for dose finding, under uncertainty about the dose-response shape, using general parametric models. The framework described here is quite broad and can be utilized in situations involving for example generalized nonlinear models, linear and nonlinear mixed effects models, Cox proportional hazards models, with the main restriction being that a univariate dose-response relationship is modeled, that is, both dose and response correspond to univariate measurements. In addition to the core framework, we also develop a general purpose methodology to fit dose-response data in a computationally and statistically efficient way. Several examples illustrate the breadth of applicability of the results. For the analyses, we developed the R add-on package DoseFinding, which provides a convenient interface to the general approach adopted here.