Subgroup identification in dose-finding trials via model-based recursive partitioning

An important task in early phase drug development is to identify patients, which respond better or worse to an experimental treatment. While a variety of different subgroup identification methods have been developed for the situation of trials that study an experimental treatment and control, much less work has been done in the situation when patients are randomized to different dose groups. In this article we propose new strategies to perform subgroup analyses in dose-finding trials and discuss the challenges, which arise in this new setting. We consider model-based recursive partitioning, which has recently been applied to subgroup identification in two arm trials, as a promising method to tackle these challenges and assess its viability using a real trial example and simulations. Our results show that model-based recursive partitioning can be used to identify subgroups of patients with different dose-response curves and improves estimation of treatment effects and minimum effective doses, when heterogeneity among patients is present.Comment: 23 pages, 6 figure

Model Selection versus Model Averaging in Dose Finding Studies

Phase II dose finding studies in clinical drug development are typically conducted to adequately characterize the dose response relationship of a new drug. An important decision is then on the choice of a suitable dose response function to support dose selection for the subsequent Phase III studies. In this paper we compare different approaches for model selection and model averaging using mathematical properties as well as simulations. Accordingly, we review and illustrate asymptotic properties of model selection criteria and investigate their behavior when changing the sample size but keeping the effect size constant. In a large scale simulation study we investigate how the various approaches perform in realistically chosen settings. Finally, the different methods are illustrated with a recently conducted Phase II dosefinding study in patients with chronic obstructive pulmonary disease.Comment: Keywords and Phrases: Model selection; model averaging; clinical trials; simulation stud

Approximating Probability Densities by Iterated Laplace Approximations

The Laplace approximation is an old, but frequently used method to approximate integrals for Bayesian calculations. In this paper we develop an extension of the Laplace approximation, by applying it iteratively to the residual, i.e., the difference between the current approximation and the true function. The final approximation is thus a linear combination of multivariate normal densities, where the coefficients are chosen to achieve a good fit to the target distribution. We illustrate on real and artificial examples that the proposed procedure is a computationally efficient alternative to current approaches for approximation of multivariate probability densities. The R-package iterLap implementing the methods described in this article is available from the CRAN servers.Comment: to appear in Journal of Computational and Graphical Statistics, http://pubs.amstat.org/loi/jcg

Response-adaptive dose-finding under model uncertainty

Dose-finding studies are frequently conducted to evaluate the effect of different doses or concentration levels of a compound on a response of interest. Applications include the investigation of a new medicinal drug, a herbicide or fertilizer, a molecular entity, an environmental toxin, or an industrial chemical. In pharmaceutical drug development, dose-finding studies are of critical importance because of regulatory requirements that marketed doses are safe and provide clinically relevant efficacy. Motivated by a dose-finding study in moderate persistent asthma, we propose response-adaptive designs addressing two major challenges in dose-finding studies: uncertainty about the dose-response models and large variability in parameter estimates. To allocate new cohorts of patients in an ongoing study, we use optimal designs that are robust under model uncertainty. In addition, we use a Bayesian shrinkage approach to stabilize the parameter estimates over the successive interim analyses used in the adaptations. This approach allows us to calculate updated parameter estimates and model probabilities that can then be used to calculate the optimal design for subsequent cohorts. The resulting designs are hence robust with respect to model misspecification and additionally can efficiently adapt to the information accrued in an ongoing study. We focus on adaptive designs for estimating the minimum effective dose, although alternative optimality criteria or mixtures thereof could be used, enabling the design to address multiple objectives.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS445 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

MCPMod: An R Package for the Design and Analysis of Dose-Finding Studies

In this article the MCPMod package for the R programming environment will be introduced. It implements a recently developed methodology for the design and analysis of dose-response studies that combines aspects of multiple comparison procedures and modeling approaches (Bretz et al. 2005). The MCPMod package provides tools for the analysis of dose finding trials, as well as a variety of tools necessary to plan an experiment to be analyzed using the MCP-Mod methodology

Functional Uniform Priors for Nonlinear Modelling

This paper considers the topic of finding prior distributions when a major component of the statistical model depends on a nonlinear function. Using results on how to construct uniform distributions in general metric spaces, we propose a prior distribution that is uniform in the space of functional shapes of the underlying nonlinear function and then back-transform to obtain a prior distribution for the original model parameters. The primary application considered in this article is nonlinear regression, but the idea might be of interest beyond this case. For nonlinear regression the so constructed priors have the advantage that they are parametrization invariant and do not violate the likelihood principle, as opposed to uniform distributions on the parameters or the Jeffrey's prior, respectively. The utility of the proposed priors is demonstrated in the context of nonlinear regression modelling in clinical dose-finding trials, through a real data example and simulation. In addition the proposed priors are used for calculation of an optimal Bayesian design.Comment: submitted for publicatio