Björn Bornkamp

Innovative Approaches for Designing and Analyzing Adaptive Dose-Ranging Trials

Inadequate selection of the dose to bring forward in confirmatory trials has been identified as one of the key drivers of the decreasing success rates observed in drug development programs across the pharmaceutical industry. In recognition of this problem, the Pharmaceutical Research and Manufacturers of America (PhRMA), formed a working group to evaluate and develop alternative approaches to dose finding, including adaptive dose-ranging designs. This paper summarizes the work of the group, including the results and conclusions of a comprehensive simulation study, and puts forward recommendations on how to improve dose ranging in clinical development, including, but not limited to, the use of adaptive dose-ranging methods.

A Simulation Study to Compare New Adaptive Dose–Ranging Designs

The main goals in an adaptive dose-ranging study are to detect dose response, to determine if any doses(s) meets clinical relevance, to estimate the dose-response, and then to decide on the dose(s) (if any) to take into the confirmatory Phase III. Adaptive dose-ranging study designs may result in power gains to detect dose response and higher precision in estimating the target dose and the dose response curve. In this article, we complement the library of available methods with five new adaptive dose-ranging designs. Due to their inherent complexity, the operating characteristics can be assessed only through intensive simulations. We present here results of a comprehensive simulation study that compares and contrasts these designs for a variety of different scenarios.

Design and Analysis of Dose-Finding Studies Combining Multiple Comparisons and Modeling Procedures

The search for an adequate dose involves some of the most complex series of decisions to be made in developing a clinically viable product. Typically decisions based on such dose-finding studies reside in two domains: (i) “proof” of evidence that the treatment is effective and (ii) the need to choose dose(s) for further development. We consider a unified strategy for designing and analyzing dose-finding studies, including the testing of proof-of-concept and the selection of one or more doses to take into further development. The methodology combines the advantages of multiple comparisons and modeling approaches, consisting of a multi-stage procedure. Proof-of-concept is tested in the first stage, using multiple comparison methods to identify statistically significant contrasts corresponding to a set of candidate models. If proof-of-concept is established in the first stage, the best model is then used for dose selection in subsequent stages. This article describes and illustrates practical considerations related to the implementation of this methodology. We discuss how to determine sample sizes and perform power calculations based on the proof-of-concept step. A relevant topic in this context is how to obtain good prior values for the model parameters: different methods to translate prior clinical knowledge into parameter values are presented and discussed. In addition, different possibilities of performing sensitivity analyses to assess the consequences of misspecifying the true parameter values are introduced. All methods are illustrated by a real dose-response phase II study for an anti-anxiety compound.

Bayesian Nonparametric Estimation of Continuous Monotone Functions with Applications to Dose–Response Analysis

In this article, we consider monotone nonparametric regression in a Bayesian framework. The monotone function is modeled as a mixture of shifted and scaled parametric probability distribution functions, and a general random probability measure is assumed as the prior for the mixing distribution. We investigate the choice of the underlying parametric distribution function and find that the two-sided power distribution function is well suited both from a computational and mathematical point of view. The model is motivated by traditional nonlinear models for dose-response analysis, and provides possibilities to elicitate informative prior distributions on different aspects of the curve. The method is compared with other recent approaches to monotone nonparametric regression in a simulation study and is illustrated on a data set from dose-response analysis.

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.

Adaptive and Model-Based Dose-Ranging Trials: Quantitative Evaluation and Recommendations. White Paper of the PhRMA Working Group on Adaptive Dose-Ranging Studies

Poor dose-regimen selection remains a key cause of the high attrition rate of investigational drugs in confirmatory trials, being directly related to the escalating costs of drug development. This article is a follow-up to the first white paper put forward by the PhRMA Working Group (WG) on Adaptive Dose-Ranging Studies (Bornkamp et al. 2007). It presents results and conclusions from a new round of simulation-based evaluations conducted by the WG, proposing a new set of recommendations to improve the accuracy and efficiency of dose-finding in clinical drug development.

Response-adaptive dose-finding under model uncertainty

Dose-finding studies are frequently conducted to evaluate the ef-fect of different doses or concentration levels of a compound on a re-sponse of interest. Applications include the investigation of a newmedicinal drug, a herbicide or fertilizer, a molecular entity, an envi-ronmental toxin, or an industrial chemical. In pharmaceutical drugdevelopment, dose-finding studies are of critical importance becauseof regulatory requirements that marketed doses are safe and pro-vide clinically relevant efficacy. Motivated by a dose-finding study inmoderate persistent asthma, we propose response-adaptive designsaddressing two major challenges in dose-finding studies: uncertaintyabout the dose-response models and large variability in parameterestimates. To allocate new cohorts of patients in an ongoing study,we use optimal designs that are robust under model uncertainty. Inaddition, we use a Bayesian shrinkage approach to stabilize the pa-rameter estimates over the successive interim analyses used in theadaptations. This approach allows us to calculate updated parameterestimates and model probabilities that can then be used to calculatethe optimal design for subsequent cohorts. The resulting designs arehence robust with respect to model misspecification and addition-ally can efficiently adapt to the information accrued in an ongoingstudy. We focus on adaptive designs for estimating the minimumeffective dose, although alternative optimality criteria or mixturesthereof could be used, enabling the design to address multiple objec-tives. In an extensive simulation study, we investigate the operatingcharacteristics of the proposed methods under a variety of scenariosdiscussed by the clinical team to design the aforementioned clinicalstudy.Received April 2010; revised November 2010.

A practical guide to Bayesian group sequential designs

Bayesian approaches to the monitoring of group sequential designs have two main advantages compared with classical group sequential designs: first, they facilitate implementation of interim success and futility criteria that are tailored to the subsequent decision making, and second, they allow inclusion of prior information on the treatment difference and on the control group. A general class of Bayesian group sequential designs is presented, where multiple criteria based on the posterior distribution can be defined to reflect clinically meaningful decision criteria on whether to stop or continue the trial at the interim analyses. To evaluate the frequentist operating characteristics of these designs, both simulation methods and numerical integration methods are proposed, as implemented in the corresponding R package gsbDesign. Normal approximations are used to allow fast calculation of these characteristics for various endpoints. The practical implementation of the approach is illustrated with several clinical trial examples from different phases of drug development, with various endpoints, and informative priors.

Functional Uniform Priors for Nonlinear Modeling

This article 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 Jeffreys prior, respectively. The utility of the proposed priors is demonstrated in the context of design and analysis of nonlinear regression modeling in clinical dose-finding trials, through a real data example and simulation.

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 article we develop an extension of the Laplace approximation, by applying it iteratively to the residual, that is, 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. This article has supplementary material online.