Bayesian models for subgroup analysis in clinical trials.

BACKGROUND: In a pharmaceutical drug development setting, possible interactions between the treatment and particular baseline clinical or demographic factors are often of interest. However, the subgroup analysis required to investigate such associations remains controversial. Concerns with classical hypothesis testing approaches to the problem include low power, multiple testing, and the possibility of data dredging. PURPOSE: As an alternative to hypothesis testing, the use of shrinkage estimation techniques is investigated in the context of an exploratory post hoc subgroup analysis. A range of models that have been suggested in the literature are reviewed. Building on this, we explore a general modeling strategy, considering various options for shrinkage of effect estimates. This is applied to a case-study, in which evidence was available from seven-phase II-III clinical trials examining a novel therapy, and also to two artificial datasets with the same structure. METHODS: Emphasis is placed on hierarchical modeling techniques, adopted within a Bayesian framework using freely available software. A range of possible subgroup model structures are applied, each incorporating shrinkage estimation techniques. RESULTS: The investigation of the case-study showed little evidence of subgroup effects. Because inferences appeared to be consistent across a range of well-supported models, and model diagnostic checks showed no obvious problems, it seemed this conclusion was robust. It is reassuring that the structured shrinkage techniques appeared to work well in a situation where deeper inspection of the data suggested little evidence of subgroup effects. LIMITATIONS: The post hoc examination of subgroups should be seen as an exploratory analysis, used to help make better informed decisions regarding potential future studies examining specific subgroups. To a certain extent, the degree of understanding provided by such assessments will be limited by the quality and quantity of available data. CONCLUSIONS: In light of recent interest by health authorities into the use of subgroup analysis in the context of drug development, it appears that Bayesian approaches involving shrinkage techniques could play an important role in this area. Hopefully, the developments outlined here provide useful methodology for tackling such a problem, in-turn leading to better informed decisions regarding subgroups.

A proof of concept phase II non-inferiority criterion.

Traditional phase III non-inferiority trials require compelling evidence that the treatment vs control effect bfθ is better than a pre-specified non-inferiority margin θ(NI) . The standard approach compares this margin to the 95 per cent confidence interval of the effect parameter. In the phase II setting, in order to declare Proof of Concept (PoC) for non-inferiority and proceed in the development of the drug, different criteria that are specifically tailored toward company internal decision making may be more appropriate. For example, less evidence may be needed as long as the effect estimate is reasonably convincing. We propose a non-inferiority design that addresses the specifics of the phase II setting. The requirements are that (1) the effect estimate be better than a critical threshold θ(C), and (2) the type I error with regard to θ(NI) is controlled at a pre-specified level. This design is compared with the traditional design from a frequentist as well as a Bayesian perspective, where the latter relies on the Level of Proof (LoP) metric, i.e. the probability that the true effect is better than effect values of interest. Clinical input is required to establish the value θ(C), which makes the design transparent and improves interactions within clinical teams. The proposed design is illustrated for a non-inferiority trial for a time-to-event endpoint in oncology.

Summarizing historical information on controls in clinical trials.

BACKGROUND: Historical information is always relevant when designing clinical trials, but it might also be incorporated in the analysis. It seems appropriate to exploit past information on comparable control groups. PURPOSE: Phase IV and proof-of-concept trials are used to discuss aspects of summarizing historical control data as prior information in a new trial. The importance of a fair assessment of the similarity of control parameters is emphasized. METHODS: The methodology is meta-analytic-predictive. Heterogeneity of control parameters is expressed via the between-trial variation, which is the key parameter determining the prior effective sample size and its upper bound (prior maximum sample size). RESULTS: For a Phase IV trial (930 control patients in 11 historical trials) between-trial heterogeneity was fairly small, resulting in a prior effective sample size of approximately 90 patients. For a proof-of-concept trial (363 patients in four historical trials) heterogeneity was moderate to substantial, resulting in a prior effective sample size of approximately 20. For another proof-of-concept trial (14 patients in one historical trial), assuming substantial heterogeneity implied a prior effective sample size of 7. The prior effective sample size can only be large if the amount of historical data is large and between-trial heterogeneity is small. The prior effective sample size is bounded by the prior maximum sample size (ratio of within- to between-trial variance), irrespective of the amount of historical data. LIMITATIONS: The meta-analytic-predictive approach assumes exchangeability of control parameters across trials. Due to the difficulty to quantify between-trial variability, sensitivity of conclusions regarding assumptions and type of inference should be assessed. CONCLUSIONS: The use of historical control information is a valuable option and may lead to more efficient clinical trials. The proposed approach is attractive for nonconfirmatory trials, but under certain circumstances extensions to the confirmatory setting could be envisaged as well.

A combined score test for binary and ordinal endpoints from clinical trials.

There is growing interest, especially for trials in stroke, in combining multiple endpoints in a single clinical evaluation of an experimental treatment. The endpoints might be repeated evaluations of the same characteristic or alternative measures of progress on different scales. Often they will be binary or ordinal, and those are the cases studied here. In this paper we take a direct approach to combining the univariate score statistics for comparing treatments with respect to each endpoint. The correlations between the score statistics are derived and used to allow a valid combined score test to be applied. A sample size formula is deduced and application in sequential designs is discussed. The method is compared with an alternative approach based on generalized estimating equations in an illustrative analysis and replicated simulations, and the advantages and disadvantages of the two approaches are discussed.

The future of drug development: advancing clinical trial design.

Declining pharmaceutical industry productivity is well recognized by drug developers, regulatory authorities and patient groups. A key part of the problem is that clinical studies are increasingly expensive, driven by the rising costs of conducting Phase II and III trials. It is therefore crucial to ensure that these phases of drug development are conducted more efficiently and cost-effectively, and that attrition rates are reduced. In this article, we argue that moving from the traditional clinical development approach based on sequential, distinct phases towards a more integrated view that uses adaptive design tools to increase flexibility and maximize the use of accumulated knowledge could have an important role in achieving these goals. Applications and examples of the use of these tools--such as Bayesian methodologies--in early- and late-stage drug development are discussed, as well as the advantages, challenges and barriers to their more widespread implementation.

A note on the power prior.

The power prior by Ibrahim and Chen (Statist. Sci. 2000; 15:46-60) is one of several methods to incorporate historical data in the analysis of a clinical trial. The power prior raises the likelihood of the historical data to the power parameter a(0) which quantifies the discounting of the historical data due to heterogeneity between trials. It is shown that the standard method of estimating the power parameter from the historical and current data is inappropriate, and we therefore suggest to use a modified power prior approach or to consider alternative methods instead.

A Bayesian case study in oncology Phase I combination dose-finding using logistic regression with covariates.

A Bayesian approach to finding the maximum tolerated dose (MTD) is presented. The approach is flexible, allowing inclusion of covariates, and enables transparent dose recommendations based on comprehensive inferential summaries on the probability of dose-limiting toxicities (DLT). A case study is presented for a Phase I combination of two oncology drugs, nilotinib and imatinib. Data obtained and decisions made during the study are described. Final determination of the MTD pair is outlined, along with discussion regarding the use and interpretability of within- and end-of-study data.

Confirmatory adaptive designs with Bayesian decision tools for a targeted therapy in oncology.

The ability to select a sensitive patient population may be crucial for the development of a targeted therapy. Identifying such a population with an acceptable level of confidence may lead to an inflation in development time and cost. We present an approach that allows to decrease these costs and to increase the reliability of the population selection. It is based on an actual adaptive phase II/III design and uses Bayesian decision tools to select the population of interest at an interim analysis. The primary endpoint is assumed to be the time to some event like e.g. progression. It is shown that the use of appropriately stratified logrank tests in the adaptive test procedure guarantees overall type I error control also when using information on patients that are censored at the adaptive interim analysis. The use of Bayesian decision tools for the population selection decision making is discussed. Simulations are presented to illustrate the operating characteristics of the study design relative to a more traditional development approach. Estimation of treatment effects is considered as well.

Critical aspects of the Bayesian approach to phase I cancer trials.

The Bayesian approach to finding the maximum-tolerated dose in phase I cancer trials is discussed. The suggested approach relies on a realistic dose-toxicity model, allows one to include prior information, and supports clinical decision making by presenting within-trial information in a transparent way. The modeling and decision-making components are flexible enough to be extendable to more complex settings. Critical aspects are emphasized and a comparison with the continual reassessment method (CRM) is performed with data from an actual trial and a simulation study. The comparison revealed similar operating characteristics while avoiding some of the difficulties encountered in the actual trial when applying the CRM.

Testing and estimation in flexible group sequential designs with adaptive treatment selection.

Integrating selection and confirmation phases into a single trial can expedite the development of new treatments and allows to use all accumulated data in the decision process. In this paper we review adaptive treatment selection based on combination tests and propose overall adjusted p-values and simultaneous confidence intervals. Also point estimation in adaptive trials is considered. The methodology is illustrated in a detailed example based on an actual planned study.

Modeling missingness for time-to-event data: a case study in osteoporosis.

Clinical trials of long duration are often hampered by high dropout rates, making statistical inference and interpretation of results difficult. Statistical inference should be based on models selected according to whether missingness is independent of response [missing completely at random (MCAR)], or depends on response either through observed responses only [missing at random (MAR)] or through unobserved responses [nonignorable missing (NIM)]. If the dropout rate is high and little is known about the dropout mechanism, plausible nonignorable missing scenarios should be investigated as a sensitivity tool, offering the data analyst an understanding of the robustness of conclusions. Modeling missingness is illustrated by an analysis of an interval censored time-to-event outcome from a 5-year clinical trial on fracture response in osteoporosis in which the overall dropout rate was substantial. In this article, we provide an overview of a reanalysis accounting for possible nonignorable missingness, emphasize the importance of modeling the dropout and response mechanisms jointly, and highlight critical points arising in missing data problems.

A score test for binary data with patient non-compliance.

A score test is developed for binary clinical trial data, which incorporates patient non-compliance while respecting randomization. It is assumed in this paper that compliance is 'all-or-nothing', in the sense that a patient either accepts all of the treatment assigned as specified in the protocol, or none of it. Direct analytic comparisons of the adjusted test statistic for both the score test and the likelihood ratio test are made with the corresponding test statistics that adhere to the intention-to-treat principle. It is shown that no gain in power is possible over the intention-to-treat analysis, by adjusting for patient non-compliance. Sample size formulae are derived and simulation studies are used to demonstrate that the sample size approximation holds.

Estimating a treatment effect in survival studies in which patients switch treatment.

For disease indications such as Acquired Immune Deficiency Syndrome (AIDS) and various cancers, randomization to a pure control treatment may be scientifically desirable but not ethically acceptable. Clinicians may insist that the experimental treatment be made available, at least as a rescue medication, for all patients in the control arm. A method for estimating a treatment effect in survival data from randomized clinical trials of this type is developed under an accelerated failure time model. This approach retains all patients in the groups to which they were randomized and is not based on an ad hoc subgroup analysis. By conditioning on having observed patient switch times, this method avoids the need to model patient switching patterns in the analysis. This new approach is evaluated using simulation studies, and is illustrated through analysing data from a Medical Research Council lung cancer trial.