Variance-penalized response-adaptive randomization with mismeasurement

We consider response-adaptive design of clinical trials under a variance-penalized criterion in the presence of mismeasurement. An explicit expression for the variance-penalized criterion with misclassified dichotomous responses is derived for response-adaptive designs and some properties are discussed. A new target proportion of treatment allocation is proposed under the criterion and related simulation results are presented.     

A natural lead-in approach to response-adaptive allocation for continuous outcomes

Response-adaptive (RA) allocation designs can skew the allocation of incoming subjects toward the better performing treatment group based on the previously accrued responses. While unstable estimators and increased variability can adversely affect adaptation in early trial stages, Bayesian methods can be implemented with decreasingly informative priors (DIP) to overcome these difficulties. DIPs have been previously used for binary outcomes to constrain adaptation early in the trial, yet gradually increase adaptation as subjects accrue. We extend the DIP approach to RA designs for continuous outcomes, primarily in the normal conjugate family by functionalizing the prior effective sample size to equal the unobserved sample size. We compare this effective sample size DIP approach to other DIP formulations. Further, we considered various allocation equations and assessed their behavior utilizing DIPs. Simulated clinical trials comparing the behavior of these approaches with traditional Frequentist and Bayesian RA as well as balanced designs show that the natural lead-in approaches maintain improved treatment with lower variability and greater power.     

Block response-adaptive randomization in clinical trials with binary endpoints

In a clinical trial, response-adaptive randomization (RAR) uses accumulating data to weigh the randomization of remaining patients in favour of the better performing treatment. The aim is to reduce the number of failures within the trial. However, many well-known RAR designs, in particular, the randomized play-the-winner-rule (RPWR), have a highly myopic structure which has sometimes led to unfortunate randomization sequences when used in practice. This paper introduces random permuted blocks into two RAR designs, the RPWR and sequential maximum likelihood estimation, for trials with a binary endpoint. Allocation ratios within each block are restricted to be one of 1:1, 2:1 or 3:1, preventing unfortunate randomization sequences. Exact calculations are performed to determine error rates and expected number of failures across a range of trial scenarios. The results presented show that when compared with equal allocation, block RAR designs give similar reductions in the expected number of failures to their unmodified counterparts. The reductions are typically modest under the alternative hypothesis but become more impressive if the treatment effect exceeds the clinically relevant difference.     

A numerical study for comparing two response-adaptive designs for continuous treatment effects

We study two sequential, response-adaptive randomized designs for clinical trials; one has been proposed in Bandyopadhyay and Biswas (Biometrika 88: 409–419, 2001) and in Biswas and Basu (Sankhya Ser B 63:27–42, 2001), the other stems from the randomly reinforced urn introduced and studied in Muliere et al. (J Stat Plan Inference 136:1853–1874, 2006a). Both designs can be used in clinical trials where the response from each patient is a continuous variable. Comparison is conducted through numerical studies and along a new guideline for the evaluation of a response-adaptive design.     

Comparison of response adaptive randomization features in multiarm clinical trials with control

We investigate multiple features of response adaptive randomization (RAR) in the context of a multiple arm randomized trial with control, where the primary goal is the identification of the best arm for use in a broader patient population. We maintain constant control allocation and vary the length of time until RAR is started, interim frequency, the underlying quantity used to calculate the randomization probabilities, and a threshold resulting in temporary arm dropping. We evaluate the designs on five metrics measuring benefit to the internal trial population, the future external population, and statistical estimation. Our results indicate these features have minimal interaction within the space explored, with preference for earlier activation of RAR, more frequent interim analyses, randomizing in proportion to the probability each arm is the best, and aggressive thresholding for temporarily dropping arms. The results illustrate useful principles for maximizing the benefit of RAR in practice.     

Weighted re‐randomization tests for minimization with unbalanced allocation

Re‐randomization test has been considered as a robust alternative to the traditional population model‐based methods for analyzing randomized clinical trials. This is especially so when the clinical trials are randomized according to minimization, which is a popular covariate‐adaptive randomization method for ensuring balance among prognostic factors. Among various re‐randomization tests, fixed‐entry‐order re‐randomization is advocated as an effective strategy when a temporal trend is suspected. Yet when the minimization is applied to trials with unequal allocation, fixed‐entry‐order re‐randomization test is biased and thus compromised in power. We find that the bias is due to non‐uniform re‐allocation probabilities incurred by the re‐randomization in this case. We therefore propose a weighted fixed‐entry‐order re‐randomization test to overcome the bias. The performance of the new test was investigated in simulation studies that mimic the settings of a real clinical trial. The weighted re‐randomization test was found to work well in the scenarios investigated including the presence of a strong temporal trend. Copyright © 2013 John Wiley & Sons, Ltd.     

A design for testing clinical strategies: biased adaptive within-subject randomization

We propose a method for assigning treatment in clinical trials, called the 'biased coin adaptive within-subject' (BCAWS) design: during the course of follow-up, the subject's response to a treatment is used to influence the future treatment, through a 'biased coin' algorithm. This design results in treatment patterns that are closer to actual clinical practice and may be more acceptable to patients with chronic disease than the usual fixed trial regimens, which often suffer from drop-out and non-adherence. In this work, we show how to use the BCAWS design to compare treatment strategies, and we provide a simple example to illustrate the method.     

Randomization tests for multiple regression

Four generic means of conducting randomization tests in the context of multiple regression are analysed. Based on their performance in traditional repeated samples, three of these are shown to be inappropriate or applicable only in special circumstances; their shortcomings are illustrated via Monte Carlo studies     

A Bayesian sequential design with adaptive randomization for 2‐sided hypothesis test

Bayesian sequential and adaptive randomization designs are gaining popularity in clinical trials thanks to their potentials to reduce the number of required participants and save resources. We propose a Bayesian sequential design with adaptive randomization rates so as to more efficiently attribute newly recruited patients to different treatment arms. In this paper, we consider 2‐arm clinical trials. Patients are allocated to the 2 arms with a randomization rate to achieve minimum variance for the test statistic. Algorithms are presented to calculate the optimal randomization rate, critical values, and power for the proposed design. Sensitivity analysis is implemented to check the influence on design by changing the prior distributions. Simulation studies are applied to compare the proposed method and traditional methods in terms of power and actual sample sizes. Simulations show that, when total sample size is fixed, the proposed design can obtain greater power and/or cost smaller actual sample size than the traditional Bayesian sequential design. Finally, we apply the proposed method to a real data set and compare the results with the Bayesian sequential design without adaptive randomization in terms of sample sizes. The proposed method can further reduce required sample size.     

Balanced covariates with response adaptive randomization

Response adaptive randomization (RAR) methods for clinical trials are susceptible to imbalance in the distribution of influential covariates across treatment arms. This can make the interpretation of trial results difficult, because observed differences between treatment groups may be a function of the covariates and not necessarily because of the treatments themselves. We propose a method for balancing the distribution of covariate strata across treatment arms within RAR. The method uses odds ratios to modify global RAR probabilities to obtain stratum‐specific modified RAR probabilities. We provide illustrative examples and a simple simulation study to demonstrate the effectiveness of the strategy for maintaining covariate balance. The proposed method is straightforward to implement and applicable to any type of RAR method or outcome.     

Bayesian response adaptive randomization using longitudinal outcomes

The response adaptive randomization (RAR) method is used to increase the number of patients assigned to more efficacious treatment arms in clinical trials. In many trials evaluating longitudinal patient outcomes, RAR methods based only on the final measurement may not benefit significantly from RAR because of its delayed initiation. We propose a Bayesian RAR method to improve RAR performance by accounting for longitudinal patient outcomes (longitudinal RAR). We use a Bayesian linear mixed effects model to analyze longitudinal continuous patient outcomes for calculating a patient allocation probability. In addition, we aim to mitigate the loss of statistical power because of large patient allocation imbalances by embedding adjusters into the patient allocation probability calculation. Using extensive simulation we compared the operating characteristics of our proposed longitudinal RAR method with those of the RAR method based only on the final measurement and with an equal randomization method. Simulation results showed that our proposed longitudinal RAR method assigned more patients to the presumably superior treatment arm compared with the other two methods. In addition, the embedded adjuster effectively worked to prevent extreme patient allocation imbalances. However, our proposed method may not function adequately when the treatment effect difference is moderate or less, and still needs to be modified to deal with unexpectedly large departures from the presumed longitudinal data model. Copyright © 2015 John Wiley & Sons, Ltd.     

Evaluation of the statistical power for multiple tests: a case study

It is challenging to estimate the statistical power when a complicated testing strategy is used to adjust for the type-I error for multiple comparisons in a clinical trial. In this paper, we use the Bonferroni Inequality to estimate the lower bound of the statistical power assuming that test statistics are approximately normally distributed and the correlation structure among test statistics is unknown or only partially known. The method was applied to the design of a clinical study for sample size and statistical power estimation.     

Shift in re‐randomization distribution with conditional randomization test

Proschan, Brittain, and Kammerman made a very interesting observation that for some examples of the unequal allocation minimization, the mean of the unconditional randomization distribution is shifted away from 0. Kuznetsova and Tymofyeyev linked this phenomenon to the variations in the allocation ratio from allocation to allocation in the examples considered in the paper by Proschan et al. and advocated the use of unequal allocation procedures that preserve the allocation ratio at every step. In this paper, we show that the shift phenomenon extends to very common settings: using conditional randomization test in a study with equal allocation. This phenomenon has the same cause: variations in the allocation ratio among the allocation sequences in the conditional reference set, not previously noted. We consider two kinds of conditional randomization tests. The first kind is the often used randomization test that conditions on the treatment group totals; we describe the variations in the conditional allocation ratio with this test on examples of permuted block randomization and biased coin randomization. The second kind is the randomization test proposed by Zheng and Zelen for a multicenter trial with permuted block central allocation that conditions on the within‐center treatment totals. On the basis of the sequence of conditional allocation ratios, we derive the value of the shift in the conditional randomization distribution for specific vector of responses and the expected value of the shift when responses are independent identically distributed random variables. We discuss the asymptotic behavior of the shift for the two types of tests. Copyright © 2013 John Wiley & Sons, Ltd.     

Dynamic allocation as a balancing act

The CPMP Points to Consider on Adjustment for Baseline Covariates recently came into operation. As well as providing sound guidance, this document states a strong position against dynamic allocation. This paper reviews the most important issues involved and aims to stimulate interest in further investigating alternative allocation methods in clinical trials. Copyright © 2004 John Wiley & Sons, Ltd.     

Use of simulation to compare the performance of minimization with stratified blocked randomization

Minimization is an alternative method to stratified permuted block randomization, which may be more effective at balancing treatments when there are many strata. However, its use in the regulatory setting for industry trials remains controversial, primarily due to the difficulty in interpreting conventional asymptotic statistical tests under restricted methods of treatment allocation. We argue that the use of minimization should be critically evaluated when designing the study for which it is proposed. We demonstrate by example how simulation can be used to investigate whether minimization improves treatment balance compared with stratified randomization, and how much randomness can be incorporated into the minimization before any balance advantage is no longer retained. We also illustrate by example how the performance of the traditional model-based analysis can be assessed, by comparing the nominal test size with the observed test size over a large number of simulations. We recommend that the assignment probability for the minimization be selected using such simulations.     

Permuting incomplete paired data: a novel exact and asymptotic correct randomization test

Various statistical tests have been developed for testing the equality of means in matched pairs with missing values. However, most existing methods are commonly based on certain distributional assumptions such as normality, 0-symmetry or homoscedasticity of the data. The aim of this paper is to develop a statistical test that is robust against deviations from such assumptions and also leads to valid inference in case of heteroscedasticity or skewed distributions. This is achieved by applying a clever randomization approach to handle missing data. The resulting test procedure is not only shown to be asymptotically correct but is also finitely exact if the distribution of the data is invariant with respect to the considered randomization group. Its small sample performance is further studied in an extensive simulation study and compared to existing methods. Finally, an illustrative data example is analysed.     

Almost most powerful tests against composite alternatives

Likelihood ratio considerations are used to derive uniform bounds on the acceptance and rejection regions of the family of locally most powerful randomization tests for a two-sample comparison of censored data, When applied to radioimmunoassay data, these bounds are close enough to permit effective decision making. The methodology extends to a wide class of testing problems.     

Adaptive sequential procedures for comparing new treatments with a standard

In this paper we propose and study two sequential elimination procedures for selecting all new treatments better than a standard or control treatment. These procedures differ from those previously proposed in that we assume variances are unequal and unknown. Expressions for asymptotic expected sample sizes are given. Confidence intervals associated with the procedures are also discussed.     

Effects of unstratified and centre‐stratified randomization in multi‐centre clinical trials

This paper deals with the analysis of randomization effects in multi‐centre clinical trials. The two randomization schemes most often used in clinical trials are considered: unstratified and centre‐stratified block‐permuted randomization. The prediction of the number of patients randomized to different treatment arms in different regions during the recruitment period accounting for the stochastic nature of the recruitment and effects of multiple centres is investigated. A new analytic approach using a Poisson‐gamma patient recruitment model (patients arrive at different centres according to Poisson processes with rates sampled from a gamma distributed population) and its further extensions is proposed. Closed‐form expressions for corresponding distributions of the predicted number of the patients randomized in different regions are derived. In the case of two treatments, the properties of the total imbalance in the number of patients on treatment arms caused by using centre‐stratified randomization are investigated and for a large number of centres a normal approximation of imbalance is proved. The impact of imbalance on the power of the study is considered. It is shown that the loss of statistical power is practically negligible and can be compensated by a minor increase in sample size. The influence of patient dropout is also investigated. The impact of randomization on predicted drug supply overage is discussed. Copyright © 2010 John Wiley & Sons, Ltd.     

Two-stage k-sample designs for the ordered alternative problem

In preclinical studies and clinical dose-ranging trials, the Jonckheere-Terpstra test is widely used in the assessment of dose-response relationships. Hewett and Spurrier (1979) presented a two-stage analog of the test in the context of large sample sizes. In this paper, we propose an exact test based on Simon's minimax and optimal design criteria originally used in one-arm phase II designs based on binary endpoints. The convergence rate of the joint distribution of the first and second stage test statistics to the limiting distribution is studied, and design parameters are provided for a variety of assumed alternatives. The behavior of the test is also examined in the presence of ties, and the proposed designs are illustrated through application in the planning of a hypercholesterolemia clinical trial. The minimax and optimal two-stage procedures are shown to be preferable as compared with the one-stage procedure because of the associated reduction in expected sample size for given error constraints.