David Ohlssen

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.

Guidance on the implementation and reporting of a drug safety Bayesian network meta-analysis

The Drug Information Association Bayesian Scientific Working Group (BSWG) was formed in 2011 with a vision to ensure that Bayesian methods are well understood and broadly utilized for design and analysis and throughout the medical product development process, and to improve industrial, regulatory, and economic decision making. The group, composed of individuals from academia, industry, and regulatory, has as its mission to facilitate the appropriate use and contribute to the progress of Bayesian methodology. In this paper, the safety sub-team of the BSWG explores the use of Bayesian methods when applied to drug safety meta-analysis and network meta-analysis. Guidance is presented on the conduct and reporting of such analyses. We also discuss different structural model assumptions and provide discussion on prior specification. The work is illustrated through a case study involving a network meta-analysis related to the cardiovascular safety of non-steroidal anti-inflammatory drugs.

Estimands and Their Role in Clinical Trials

ABSTRACT The National Research Council (NRC) highlighted the need to more clearly distinguish between the target of estimation (“estimand”) and the method of estimation (“estimator”) in clinical trials. While the NRC report on “The Prevention and Treatment of Missing Data in Clinical Trials” focuses on issues arising due to missing data, a framework to coherently align trial objectives and corresponding estimands is valuable in a broader sense. The International Council for Harmonization of Technical Requirements for Pharmaceuticals for Human Use (ICH) has reinforced this by tasking a working group to develop an addendum to the ICH-E9 guideline “Statistical Principles for Clinical Trials.” In this article, we motivate the need for change, propose a structured framework to bridge trial objectives with proper inference tools, and discuss how it may impact the role of statisticians involved in clinical trial design and analysis.

Safety of formoterol in adults and children with asthma: a meta-analysis

BACKGROUND The safety of long-acting β2 agonists (LABA) for the treatment of persistent asthma remains a topic of ongoing debate. OBJECTIVE To evaluate the risk of serious asthma-related events among patients treated with formoterol, a meta-analysis of all Novartis-sponsored controlled clinical trials was conducted. METHODS Forty-five randomized, placebo- and active-controlled, parallel-group or crossover studies with formoterol were included. Background inhaled corticosteroid (ICS) use was permitted in all studies; however, in only 2 studies was ICS randomized as study medication. Sub-analyses of the pooled data were performed according to age (5-12; 13-18; >18 years), baseline ICS use, and lung function. Odds ratios (OR) and 95% confidence intervals (CIs) were calculated between formoterol (twice-daily), albuterol (salbutamol) 4 times per day (active control), and placebo. RESULTS Patients were randomized to formoterol (n = 5,367), placebo (n = 2,026), and albuterol (n = 976). Two deaths were reported, 1 each in the formoterol (asthma exacerbation) and the placebo (hemorrhagic pancreatitis) groups. No statistically significant differences in serious asthma exacerbations were observed compared with placebo in adolescents and adults. In children, a higher frequency of hospitalizations was observed among patients treated with formoterol compared with placebo (OR 8.4; 95% CI: 1.1-65.3). A trend toward fewer exacerbations was observed among subjects reporting concomitant ICS use at baseline. CONCLUSIONS This analysis supports current guideline recommendations for the use of LABAs only as add-on therapy to ICS.

The current state of Bayesian methods in medical product development: survey results and recommendations from the DIA Bayesian Scientific Working Group.

Bayesian applications in medical product development have recently gained popularity. Despite many advances in Bayesian methodology and computations, increase in application across the various areas of medical product development has been modest. The DIA Bayesian Scientific Working Group (BSWG), which includes representatives from industry, regulatory agencies, and academia, has adopted the vision to ensure Bayesian methods are well understood, accepted more broadly, and appropriately utilized to improve decision making and enhance patient outcomes. As Bayesian applications in medical product development are wide ranging, several sub-teams were formed to focus on various topics such as patient safety, non-inferiority, prior specification, comparative effectiveness, joint modeling, program-wide decision making, analytical tools, and education. The focus of this paper is on the recent effort of the BSWG Education sub-team to administer a Bayesian survey to statisticians across 17 organizations involved in medical product development. We summarize results of this survey, from which we provide recommendations on how to accelerate progress in Bayesian applications throughout medical product development. The survey results support findings from the literature and provide additional insight on regulatory acceptance of Bayesian methods and information on the need for a Bayesian infrastructure within an organization. The survey findings support the claim that only modest progress in areas of education and implementation has been made recently, despite substantial progress in Bayesian statistical research and software availability.

Strategies on Using Prior Information When Assessing Adverse Events

Assessing safety in drug development naturally incorporates an accumulation of knowledge as we progress from one study to another in a clinical development program. Ideally, it is the early clinical trial data that give us the greatest opportunity to leverage relevant historical information into the design and analysis of later phase clinical trials. While Bayesian methods would appear to provide an ideal framework for assessing safety in this context, concerns regarding the formulation and prespecification of a prior have limited their use in practice. More specifically, when information from previous studies is used to form a prior, an implicit assumption of exchangeability is made. However, the possibility of nonexchangeability, which could lead to conflict between prior and the data, cannot be ruled out. Based on these challenges, in this article we outline a number of strategies based on using simple Bayesian methods to assess safety concerns related to a prespecified adverse event. Three approaches to forming a prior distribution will be examined: (i) a single informative conjugate prior; (ii) a meta-analytic-predictive prior (MAP), which comprises of a mixture of conjugate priors; and (iii) a robust mixture prior, involving a combination of either the single conjugate prior or MAP with a noninformative prior. In the final case, when prior-data conflict arises between the historical informative prior and the data collected from the concurrent study, the addition of a noninformative prior serves as an automatic corrective feature. These methods will be illustrated with a motivating example involving the development of a new drug/delivery device for the treatment of agitation in schizophrenia. In addition, a simulation study will examine the performance of each approach to prior specification.

Bayesian modeling and inference for clinical trials with partial retrieved data following dropout

In randomized clinical trials, it is common that patients may stop taking their assigned treatments and then switch to a standard treatment (standard of care available to the patient) but not the treatments under investigation. Although the availability of limited retrieved data on patients who switch to standard treatment, called off-protocol data, could be highly valuable in assessing the associated treatment effect with the experimental therapy, it leads to a complex data structure requiring the development of models that link the information of per-protocol data with the off-protocol data. In this paper, we develop a novel Bayesian method to jointly model longitudinal treatment measurements under various dropout scenarios. Specifically, we propose a multivariate normal mixed-effects model for repeated measurements from the assigned treatments and the standard treatment, a multivariate logistic regression model for those stopping the assigned treatments, logistic regression models for those starting a standard treatment off protocol, and a conditional multivariate logistic regression model for completely withdrawing from the study. We assume that withdrawing from the study is non-ignorable, but intermittent missingness is assumed to be at random. We examine various properties of the proposed model. We develop an efficient Markov chain Monte Carlo sampling algorithm. We analyze in detail via the proposed method a real dataset from a clinical trial.

A flexible Bayesian approach for modeling monotonic dose-response relationships in drug development trials.

Clinical trials often involve comparing 2–4 doses or regimens of an experimental therapy with a control treatment. These studies might occur early in a drug development process, where the aim might be to demonstrate a basic level of proof (the so-called proof of concept (PoC) studies), at a later stage, to help establish a dose or doses that should be used in phase III trials (dose-finding), or even in confirmatory studies, where the registration of several doses might be considered. When a small number of doses are examined, the ability to implement parametric modeling is somewhat limited. As an alternative, in this paper, a flexible Bayesian model is suggested. In particular, we draw on the idea of using Bayesian model averaging (BMA) to exploit an assumed monotonic dose–response relationship, without using strong parametric assumptions. The approach is exemplified by assessing operating characteristics in the design of a PoC study examining a new treatment for psoriatic arthritis and a post hoc data analysis involving three confirmatory clinical trials, which examined an adjunctive treatment for partial epilepsy. Key difficulties, such as prior specification and computation, are discussed. A further extension, based on combining the flexible modeling with a classical multiple comparisons procedure, known as MCP–MOD, is examined. The benefit of this extension is a potential reduction in the number of simulations that might be needed to investigate operating characteristics of the statistical analysis.

A Review of: “Clinical Prediction Models: A Practical Approach to Development, Validation, and Updating, by E. W. Steyerberg”

When thinking about statistical developments in prognostic modeling, my thoughts immediately turn to the excellent work of Harrell (2001), who emphasized the need to use good statistical practice in all aspects of empirical modeling: for example, avoiding dichotomizing of continuous variables, using appropriate strategies to handle missing data, adopting modern estimation techniques that incorporate shrinkage, and the need for proper model validation using simulationbased techniques. Steyerberg, who cites Harrell’s work as an important inspiration for his book, uses all of these ideas to form a principled strategy for the development of clinical prediction models. The introductory chapter presents an overview of this strategy, consisting of seven themes, which can be described as: (1) the definition of the prediction problem and research question; (2) the coding of the outcome of interest and predictors; (3) model specification; (4) estimation and inference; (5) examination of model performance in terms of model fit; (6) examination of predictive properties and dealing with overfitting; and (7) the presentation of results. While Harrell’s earlier work also focused on developing a strategy, Steyerberg’s book is aimed at a much more applied audience. The book is filled with many practical examples, and as possible statistical techniques are explained using text rather than mathematical notation, the material should be accessible to epidemiologists, public health researchers, and applied biostatisticians. The remainder of the book is divided into four parts, the first of which (Chapters 2–6) considers motivating examples, an overview of study design, and a review of basic statistical modeling techniques that could be used in prediction modeling. The second part of the book (Chapters 7–18), focuses on providing a series of modern regression techniques, illustrated by various examples, which form the basis of the seven-part strategy. Part III (Chapters 19–21) examines generalizability or the external validity of prediction models. Finally, Chapters 22–24 consider a series of case studies. The application areas and motivating examples described in Chapter 2 provide a good idea about the overall scope of problems that are addressed in the book. Examples include public health interventions in breast cancer; therapeutic decision making (replacement of risky heart valves); adjustment for covariates in randomized control trials; propensity score adjustment to examine the effect of statins on mortality rates; and the use of case-mix adjustment when comparing health care providers. Chapter 3 addresses design, rightly focusing on the need

Functional Mixed Effects Model for the Analysis of Dose-Titration Studies

ABSTRACT Functional data analysis, which analyzes data that can be represented by curves or images, has many potential applications in clinical trials. Motivated by a real example, this study constructs a functional mixed effects model for analyzing a clinical outcome that is observed continuously over a long period of time. A penalized spline (P-spline)-based method is applied to obtain the estimators of the mean function and the time-varying coefficients. Simulation studies are conducted to investigate the consistency, efficiency, and robustness of the method. To illustrate the use of the method, a real data analysis is performed and produces interpretable results.