Meta-analysis of clinical trials with competing time-to-event endpoints

Recommendations for the analysis of competing risks in the context of randomized clinical trials are well established. Meta-analysis of individual patient data (IPD) is the gold standard for synthesizing evidence for clinical interpretation based on multiple studies. Surprisingly, no formal guidelines have been yet proposed to conduct an IPD meta-analysis with competing risk endpoints. To fill this gap, this work details (i) how to handle the heterogeneity between trials via a stratified regression model for competing risks and (ii) that the usual metrics of inconsistency to assess heterogeneity can readily be employed. Our proposal is illustrated by the re-analysis of a recently published meta-analysis in nasopharyngeal carcinoma, aiming at quantifying the benefit of the addition of chemotherapy to radiotherapy on each competing endpoint.     

Designs for group sequential phase II clinical trials

The main goal of Phase II cancer clinical trials is to identify the therapeutic efficacy of new treatments. For ethical reasons, group sequential procedures, which allow for early stopping when a treatment is either extremely effective or extremely ineffective, have been widely employed in these trials. Although several useful design methods have been discussed in the literature (Fleming, 1982, Biometrics 38, 143-152; Lee, 1979, Cancer Treatment Reports 63, No. 11-12), we are unaware of any results addressing the problem of finding an optimal rule easily by computer. In this paper, using an idea based on the Neyman-Pearson lemma, we propose a method to search over a restricted set of designs and to select the optimal one in this set according to optimality criteria. In all the combinations we have investigated (more than 100) the optimal design produced by our method is the true global optimum. Other applications are discussed.     

Study duration for clinical trials with survival response and early stopping rule

A comparative clinical trial with built-in sequential stopping rules allows earlier-than-scheduled stopping, should there be a significant indication of treatment difference. In a clinical trial where the major outcome is time (survival time or response) to a certain event such as failure, the design of the study should determine how long one needs to accrue patients and follow through until there is a sufficient number of events observed during the entire study duration. This paper proposes a unified design procedure for group sequential clinical trials with survival response. The time to event is assumed to be exponentially distributed, but the arguments extend naturally to the proportional hazards model after suitable transformation on the time scale. An example from the Eastern Cooperative Oncology Group (ECOG) is given to illustrate how this procedure can be implemented. The same example is used to explore the overall operating characteristics and the robustness of the proposed group sequential design.     

Response-adaptive randomization for clinical trials with continuous outcomes

We provide an explicit asymptotic method to evaluate the performance of different response-adaptive randomization procedures in clinical trials with continuous outcomes. We use this method to investigate four different response-adaptive randomization procedures. Their performance, especially in power and treatment assignment skewing to the better treatment, is thoroughly evaluated theoretically. These results are then verified by simulation. Our analysis concludes that the doubly adaptive biased coin design procedure targeting optimal allocation is the best one for practical use. We also consider the effect of delay in responses and nonstandard responses, for example, Cauchy distributed response. We illustrate our procedure by redesigning a real clinical trial.     

One-sided sequential stopping boundaries for clinical trials: a decision-theoretic approach

We address one-sided stopping rules for clinical trials, or more generally, drug development programs, from a decision-theoretic point of view. If efficacy results are sufficiently negative then the trial will be stopped. But regardless of how positive the efficacy results are, the trial will continue in order to demonstrate safety. We show how sequential decisions should be made by a pharmaceutical company attempting to maximize its expected profits.     

Designs for phase I clinical trials with multiple courses of subjects at different doses

Summary .   The goal of this article is to provide a new design framework and its corresponding estimation for phase I trials. Existing phase I designs assign each subject to one dose level based on responses from previous subjects. Yet it is possible that subjects with neither toxicity nor efficacy responses can be treated at higher dose levels, and their subsequent responses to higher doses will provide more information. In addition, for some trials, it might be possible to obtain multiple responses (repeated measures) from a subject at different dose levels. In this article, a nonparametric estimation method is developed for such studies. We also explore how the designs of multiple doses per subject can be implemented to improve design efficiency. The gain of efficiency from "single dose per subject" to "multiple doses per subject" is evaluated for several scenarios. Our numerical study shows that using "multiple doses per subject" and the proposed estimation method together increases the efficiency substantially.     

Decision theoretic designs for phase II clinical trials with multiple outcomes

In many phase II clinical trials, it is essential to assess both efficacy and safety. Although several phase II designs that accommodate multiple outcomes have been proposed recently, none are derived using decision theory. This paper describes a Bayesian decision theoretic strategy for constructing phase II designs based on both efficacy and adverse events. The gain function includes utilities assigned to patient outcomes, a reward for declaring the new treatment promising, and costs associated with the conduct of the phase II trial and future phase III testing. A method for eliciting gain function parameters from medical collaborators and for evaluating the design's frequentist operating characteristics is described. The strategy is illustrated by application to a clinical trial of peripheral blood stem cell transplantation for multiple myeloma.     

A response-adaptive randomization procedure for multi-armed clinical trials with normally distributed outcomes

We propose a novel response-adaptive randomization procedure for multi-armed trials with continuous outcomes that are assumed to be normally distributed. Our proposed rule is non-myopic, and oriented toward a patient benefit objective, yet maintains computational feasibility. We derive our response-adaptive algorithm based on the Gittins index for the multi-armed bandit problem, as a modification of the method first introduced in Villar et al. (Biometrics, 71, pp. 969-978). The resulting procedure can be implemented under the assumption of both known or unknown variance. We illustrate the proposed procedure by simulations in the context of phase II cancer trials. Our results show that, in a multi-armed setting, there are efficiency and patient benefit gains of using a response-adaptive allocation procedure with a continuous endpoint instead of a binary one. These gains persist even if an anticipated low rate of missing data due to deaths, dropouts, or complete responses is imputed online through a procedure first introduced in this paper. Additionally, we discuss how there are response-adaptive designs that outperform the traditional equal randomized design both in terms of efficiency and patient benefit measures in the multi-armed trial context.     

The impact of stopping rules on heterogeneity of results in overviews of clinical trials.

This paper explores the extent to which application of statistical stopping rules in clinical trials can create an artificial heterogeneity of treatment effects in overviews (meta-analyses) of related trials. For illustration, we concentrate on overviews of identically designed group sequential trials, using either fixed nominal or O'Brien and Fleming two-sided boundaries. Some analytic results are obtained for two-group designs and simulation studies are otherwise used, with the following overall findings. The use of stopping rules leads to biased estimates of treatment effect so that the assessment of heterogeneity of results in an overview of trials, some of which have used stopping rules, is confounded by this bias. If the true treatment effect being studied is small, as is often the case, then artificial heterogeneity is introduced, thus increasing the Type I error rate in the test of homogeneity. This could lead to erroneous use of a random effects model, producing exaggerated estimates and confidence intervals. However, if the true mean effect is large, then between-trial heterogeneity may be underestimated. When undertaking or interpreting overviews, one should ascertain whether stopping rules have been used (either formally or informally) and should consider whether their use might account for any heterogeneity found.     

Interim analyses in randomized clinical trials: ramifications and guidelines for practitioners

Recent developments in group sequential methods have had a great impact on the design and analysis of randomized clinical trials. The consequences for both planned and unplanned interim analyses are discussed using several real trials as illustrations. Guidelines for the conduct of interim analysis are given, including tables of nominal significance levels and required sample sizes for several group sequential plans. Areas in need of further theoretical advance include multiple endpoints, estimation of treatment differences, stratification, and design of multiple-armed trials.     

Assessing treatment effect heterogeneity in clinical trials with blocked binary outcomes

This paper addresses treatment effect heterogeneity (also referred to, more compactly, as 'treatment heterogeneity') in the context of a controlled clinical trial with binary endpoints. Treatment heterogeneity, variation in the true (causal) individual treatment effects, is explored using the concept of the potential outcome. This framework supposes the existance of latent responses for each subject corresponding to each possible treatment. In the context of a binary endpoint, treatment heterogeniety may be represented by the parameter, pi2, the probability that an individual would have a failure on the experimental treatment, if received, and would have a success on control, if received. Previous research derived bounds for pi2 based on matched pairs data. The present research extends this method to the blocked data context. Estimates (and their variances) and confidence intervals for the bounds are derived. We apply the new method to data from a renal disease clinical trial. In this example, bounds based on the blocked data are narrower than the corresponding bounds based only on the marginal success proportions. Some remaining challenges (including the possibility of further reducing bound widths) are discussed.     

Bayesian hierarchical classification and information sharing for clinical trials with subgroups and binary outcomes

Bayesian hierarchical models have been applied in clinical trials to allow for information sharing across subgroups. Traditional Bayesian hierarchical models do not have subgroup classifications; thus, information is shared across all subgroups. When the difference between subgroups is large, it suggests that the subgroups belong to different clusters. In that case, placing all subgroups in one pool and borrowing information across all subgroups can result in substantial bias for the subgroups with strong borrowing, or a lack of efficiency gain with weak borrowing. To resolve this difficulty, we propose a hierarchical Bayesian classification and information sharing (BaCIS) model for the design of multigroup phase II clinical trials with binary outcomes. We introduce subgroup classification into the hierarchical model. Subgroups are classified into two clusters on the basis of their outcomes mimicking the hypothesis testing framework. Subsequently, information sharing takes place within subgroups in the same cluster, rather than across all subgroups. This method can be applied to the design and analysis of multigroup clinical trials with binary outcomes. Compared to the traditional hierarchical models, better operating characteristics are obtained with the BaCIS model under various scenarios.     

Monitoring clinical trials based on predictive probability of significance

At a given point in a clinical trial, investigators may ask the question: "What is the likelihood of a significant result if the trial were continued?" One possible answer to this question is to examine a predictive probability of the significant difference with further patient accrual. [See, for example, Choi, Smith, and Becker (1985, Controlled Clinical Trials 6, 280-288).] This paper proposes and investigates the approach in trials for comparing the means of two normal populations. Two methods for calculating the predictive probability are examined. The results indicate that the predictive probability can be a useful conservative measure in monitoring trials.     

Designing and analyzing clinical trials with composite outcomes: consideration of possible treatment differences between the individual outcomes

When the individual outcomes within a composite outcome appear to have different treatment effects, either in magnitude or direction, researchers may question the validity or appropriateness of using this composite outcome as a basis for measuring overall treatment effect in a randomized controlled trial. The question remains as to how to distinguish random variation in estimated treatment effects from important heterogeneity within a composite outcome. This paper suggests there may be some utility in directly testing the assumption of homogeneity of treatment effect across the individual outcomes within a composite outcome. We describe a treatment heterogeneity test for composite outcomes based on a class of models used for the analysis of correlated data arising from the measurement of multiple outcomes for the same individuals. Such a test may be useful in planning a trial with a primary composite outcome and at trial end with final analysis and presentation. We demonstrate how to determine the statistical power to detect composite outcome treatment heterogeneity using the POISE Trial data. Then we describe how this test may be incorporated into a presentation of trial results with composite outcomes. We conclude that it may be informative for trialists to assess the consistency of treatment effects across the individual outcomes within a composite outcome using a formalized methodology and the suggested test represents one option.     

A sample size adjustment procedure for clinical trials based on conditional power

When designing clinical trials, researchers often encounter the uncertainty in the treatment effect or variability assumptions. Hence the sample size calculation at the planning stage of a clinical trial may also be questionable. Adjustment of the sample size during the mid-course of a clinical trial has become a popular strategy lately. In this paper we propose a procedure for calculating additional sample size needed based on conditional power, and adjusting the final-stage critical value to protect the overall type-I error rate. Compared to other previous procedures, the proposed procedure uses the definition of the conditional type-I error directly without appealing to an extra special function for it. It has better flexibility in setting up interim decision rules and the final-stage test is a likelihood ratio test.