Implementing Optimal Allocation in Sequential Binary Response Experiments

Generalized multidimensional dynamic allocation method

Dynamic allocation has received considerable attention since it was first proposed in the 1970s as an alternative means of allocating treatments in clinical trials which helps to secure the balance of prognostic factors across treatment groups. The purpose of this paper is to present a generalized multidimensional dynamic allocation method that simultaneously balances treatment assignments at three key levels: within the overall study, within each level of each prognostic factor, and within each stratum, that is, combination of levels of different factors Further it offers capabilities for unbalanced and adaptive designs for trials. The treatment balancing performance of the proposed method is investigated through simulations which compare multidimensional dynamic allocation with traditional stratified block randomization and the Pocock-Simon method. On the basis of these results, we conclude that this generalized multidimensional dynamic allocation method is an improvement over conventional dynamic allocation methods and is flexible enough to be applied for most trial settings including Phases I, II and III trials.

Response-adaptive designs for continuous treatment responses in phase III clinical trials: A review

A variety of response-adaptive randomization procedures have been proposed in literature assuming binary outcomes. However, the list is not so long for continuous outcomes though many real clinical trials deal with continuous treatment responses. In this paper, we attempt to explore the available procedures together with a comparison of their performances. Some real-life adaptive trial is also reviewed.

Compound adaptive GPU design for clinical trials

In clinical trials, several competing treatments are often carried out in the same trial period. The goal is to assess the performances of these different treatments according to some optimality criterion and minimize risks to the patients in the entire process of the study. For this, each coming patient is allocated sequentially to one of the treatments according to a mechanism defined by the optimality criterion. In practice, sometimes different optimality criteria, or the same criterion with different regimes, need to be considered to assess the treatments in the same study, so that each mechanism is also evaluated through the trail study. In this case, the question is how to allocate the treatments to the incoming patients so that the criteria/mechanisms of interest are assessed during the trail process, and the overall performance of the trial is optimized under the combined criteria or regimes. In this paper, we consider this problem by investigating a compound adaptive generalized Pólya urn design. Basic asymptotic properties of this design are also studied.

A simulation study for comparing testing statistics in response-adaptive randomization

Background

Response-adaptive randomizations are able to assign more patients in a comparative clinical trial to the tentatively better treatment. However, due to the adaptation in patient allocation, the samples to be compared are no longer independent. At large sample sizes, many asymptotic properties of test statistics derived for independent sample comparison are still applicable in adaptive randomization provided that the patient allocation ratio converges to an appropriate target asymptotically. However, the small sample properties of commonly used test statistics in response-adaptive randomization are not fully studied.

Methods

Simulations are systematically conducted to characterize the statistical properties of eight test statistics in six response-adaptive randomization methods at six allocation targets with sample sizes ranging from 20 to 200. Since adaptive randomization is usually not recommended for sample size less than 30, the present paper focuses on the case with a sample of 30 to give general recommendations with regard to test statistics for contingency tables in response-adaptive randomization at small sample sizes.

Results

Among all asymptotic test statistics, the Cook's correction to chi-square test (T_MC) is the best in attaining the nominal size of hypothesis test. The William's correction to log-likelihood ratio test (T_ML) gives slightly inflated type I error and higher power as compared with T_MC, but it is more robust against the unbalance in patient allocation. T_MC and T_ML are usually the two test statistics with the highest power in different simulation scenarios. When focusing on T_MC and T_ML, the generalized drop-the-loser urn (GDL) and sequential estimation-adjusted urn (SEU) have the best ability to attain the correct size of hypothesis test respectively. Among all sequential methods that can target different allocation ratios, GDL has the lowest variation and the highest overall power at all allocation ratios. The performance of different adaptive randomization methods and test statistics also depends on allocation targets. At the limiting allocation ratio of drop-the-loser (DL) and randomized play-the-winner (RPW) urn, DL outperforms all other methods including GDL. When comparing the power of test statistics in the same randomization method but at different allocation targets, the powers of log-likelihood-ratio, log-relative-risk, log-odds-ratio, Wald-type Z, and chi-square test statistics are maximized at their corresponding optimal allocation ratios for power. Except for the optimal allocation target for log-relative-risk, the other four optimal targets could assign more patients to the worse arm in some simulation scenarios. Another optimal allocation target, R_RSIHR, proposed by Rosenberger and Sriram (Journal of Statistical Planning and Inference, 1997) is aimed at minimizing the number of failures at fixed power using Wald-type Z test statistics. Among allocation ratios that always assign more patients to the better treatment, R_RSIHR usually has less variation in patient allocation, and the values of variation are consistent across all simulation scenarios. Additionally, the patient allocation at R_RSIHR is not too extreme. Therefore, R_RSIHR provides a good balance between assigning more patients to the better treatment and maintaining the overall power.

Conclusion

The Cook's correction to chi-square test and Williams' correction to log-likelihood-ratio test are generally recommended for hypothesis test in response-adaptive randomization, especially when sample sizes are small. The generalized drop-the-loser urn design is the recommended method for its good overall properties. Also recommended is the use of the R_RSIHR allocation target.

An urn model for odds-ratio-based response-adaptive phase III clinical trials for two or more treatments

Adaptive data-dependent allocation designs are used in phase III clinical trials having two or more competing treatments with sequential entrance of patients, in order to allocate a larger number of patients to the better treatment. The odds ratio is a popular concept for biomedical practitioners; hence, odds-ratio-based adaptive designs could be very useful in practice. Rosenberger et al. (2001) introduced an odds-ratio-based two-treatment response-adaptive design; however, they did not study the properties in details. In this article, we describe these designs by means of urn models and provide limiting results for them. Some properties of the design are also studied numerically. We compare the performance of the proposed design with some possible competitors with respect to a few criteria. A real dataset is used to illustrate the applicability of the proposed design. Thus, we provide a base for using odds-ratio-based response-adaptive designs in practice. We extend our design for covariates and also for more than two treatments. In particular, we study the three-treatment design in this article.

Optimum treatment allocation rules under a variance heterogeneity model

We provide optimal treatment allocation schemes when the outcome variance varies across the treatment groups and our objectives are to estimate treatment effects with equal or unequal interest. Unlike other optimal designs, such as A-optimal designs, the proposed designs can be found without an iterative scheme. We evaluate robustness properties of the optimal designs to mis-specification in the expected variance from each group and identify situations when popular allocation schemes have poor efficiencies. An application to design a randomized rheumatoid arthritis trial is discussed, along with a potential application to design a cancer screening trial when the main outcome is a continuous variable.