Extensions of Permutation Solutions to Test for Treatment Effects in Replicated Single-Case Alternation Experiments with Multivariate Response

Single-case experiments are frequently used to do research involving a clinical intervention, since large-n trials are often impractical in clinical research. In order to investigate a possible difference in the effect of the treatments considered in the study, nonparametric instruments are valid tools; in particular, permutation solutions work well when we wish to assess differences in treatment effects. We present an extension of a permutation solution to the multivariate response case and to the case of replicated single-case experiments. A simulation study shows that the approach is both reliable under the null hypothesis and powerful under the alternative. At the end, we present the results of an application to two real experiments.     

Blinded sample size re-estimation in clinical trials comparing several treatments

An important question that arises in clinical trials is how many additional observations, if any, are required beyond those originally planned. This has satisfactorily been answered in the case of two-treatment double-blind clinical experiments. However, one may be interested in comparing a new treatment with its competitors, which may be more than one. This problem is addressed in this investigation involving responses from arbitrary distributions, in which the mean and the variance are not functionally related. First, a solution in determining the initial sample size for specified level of significance and power at a specified alternative is obtained. Then it is shown that when the initial sample size is large, the nominal level of significance and the power at the pre-specified alternative are fairly robust for the proposed sample size re-estimation procedure. An application of the results is made to the blood coagulation functionality problem considered by Kropf et al. [Multiple comparisons of treatments with stable multivariate tests in a two-stage adaptive design, including a test for non-inferiority, Biom. J. 42(8) (2000), pp. 951–965].     

Efficient crossover designs in the presence of interactions between direct and carry-over treatment effects

Crossover designs, or repeated measurements designs, are used for experiments in which t treatments are applied to each of n experimental units successively over p time periods. Such experiments are widely used in areas such as clinical trials, experimental psychology and agricultural field trials. In addition to the direct effect on the response of the treatment in the period of application, there is also the possible presence of a residual, or carry-over, effect of a treatment from one or more previous periods. We use a model in which the residual effect from a treatment depends upon the treatment applied in the succeeding period; that is, a model which includes interactions between the treatment direct and residual effects. We assume that residual effects do not persist further than one succeeding period.A particular class of strongly balanced repeated measurements designs with n=t² units and which are uniform on the periods is examined. A lower bound for the A-efficiency of the designs for estimating the direct effects is derived and it is shown that such designs are highly efficient for any number of periods p=2,…,2t.     

Response‐adaptive designs for binary responses: How to offer patient benefit while being robust to time trends?

Response‐adaptive randomisation (RAR) can considerably improve the chances of a successful treatment outcome for patients in a clinical trial by skewing the allocation probability towards better performing treatments as data accumulates. There is considerable interest in using RAR designs in drug development for rare diseases, where traditional designs are not either feasible or ethically questionable. In this paper, we discuss and address a major criticism levelled at RAR: namely, type I error inflation due to an unknown time trend over the course of the trial. The most common cause of this phenomenon is changes in the characteristics of recruited patients—referred to as patient drift. This is a realistic concern for clinical trials in rare diseases due to their lengthly accrual rate. We compute the type I error inflation as a function of the time trend magnitude to determine in which contexts the problem is most exacerbated. We then assess the ability of different correction methods to preserve type I error in these contexts and their performance in terms of other operating characteristics, including patient benefit and power. We make recommendations as to which correction methods are most suitable in the rare disease context for several RAR rules, differentiating between the 2‐armed and the multi‐armed case. We further propose a RAR design for multi‐armed clinical trials, which is computationally efficient and robust to several time trends considered.     

Bayesian adaptive bandit-based designs using the Gittins index for multi-armed trials with normally distributed endpoints

Adaptive designs for multi-armed clinical trials have become increasingly popular recently because of their potential to shorten development times and to increase patient response. However, developing response-adaptive designs that offer patient-benefit while ensuring the resulting trial provides a statistically rigorous and unbiased comparison of the different treatments included is highly challenging. In this paper, the theory of Multi-Armed Bandit Problems is used to define near optimal adaptive designs in the context of a clinical trial with a normally distributed endpoint with known variance. We report the operating characteristics (type I error, power, bias) and patient-benefit of these approaches and alternative designs using simulation studies based on an ongoing trial. These results are then compared to those recently published in the context of Bernoulli endpoints. Many limitations and advantages are similar in both cases but there are also important differences, specially with respect to type I error control. This paper proposes a simulation-based testing procedure to correct for the observed type I error inflation that bandit-based and adaptive rules can induce.     

Assessing robustness of crossover designsto subjects dropping out

In some crossover experiments, particularly in medical applications, subjects may fail to complete their sequences of treatments for reasons unconnected with the treatments received. A method is described of assessing the robustness of a planned crossover design, with more than two periods, to subjects leaving the study prematurely. The method involves computing measures of efficiency for every possible design that can result, and is therefore very computationally intensive. Summaries of these measures are used to choose between competing designs. The computational problem is reduced to a manageable size by a software implementation of Polya theory. The method is applied to comparing designs for crossover studies involving four treatments and four periods. Designs are identified that are more robust to subjects dropping out in the final period than those currently favoured in medical and clinical trials.     

Adaptive designs for pivotal trials: discussion points from the PSI Adaptive Design Expert Group

The Committee for Medicinal Products for Human Use (CHMP) is currently preparing a guideline on 'methodological issues in confirmatory clinical trials with flexible design and analysis plan'. PSI (Statisticians in the Pharmaceutical Industry) sponsored a meeting of pharmaceutical statisticians with an interest in the area to share experiences and identify potential opportunities for adaptive designs in late-phase clinical drug development. This article outlines the issues raised, resulting discussions and consensus views reached. Adaptive designs have potential utility in late-phase clinical development. Sample size re-estimation seems to be valuable and widely accepted, but should be made independent of the observed treatment effect where possible. Where unblinding is necessary, careful consideration needs to be given to preserving the integrity of the trial. An area where adaptive designs can be particularly beneficial is to allow dose selection in pivotal trials via adding/dropping treatment arms; for example, combining phase II and III of the drug development program. The more adaptations made during a late-phase clinical trial, the less likely that the clinical trial would be considered as a confirmatory trial. In all cases it would be advisable to consult with regulatory agencies at the protocol design stage. All involved should remain open to scientifically valid opportunities to improve drug development.     

Optimal two treatment repeated measurement designs for three periods

Repeated Measurement Designs, with two treatments, n (experimental) units and p periods are examined, the two treatments are denoted A and B. The model with independent observations within and between treatment sequences is used. Optimal designs are derived for: (i) the difference of direct treatment effects and the difference of residual effects, (ii) the difference of direct treatment effects, and (iii) the difference of residual effects. We prove that for three periods when n is odd the optimal design in the three cases (i), (ii), and (iii) is determined by taking the sequences BAA and ABB in numbers differing by one. If n is even, the optimal design in cases (i), (ii), and (iii) is again the same, by taking the sequences ABB and BAA in equal numbers. In case (i), for n even or odd, in the optimal design there is no correlation between the two estimated parameters. For n even, case (i) was solved by Cheng and Wu in 1980. The above imply that with two treatments in practice are preferable to use three periods instead of two.     

Construction of more Flexible and Efficient P–rep Designs

Early generation variety trials are very important in plant and tree breeding programs. Typically many entries are tested, often with very few resources available. Unreplicated trials using control plots are popular and it is common to repeat the trials at a number of locations. An alternative is to use partially replicated (p–rep) designs, where a proportion of the test entries are replicated at each location. We extend a method for the generation of p–rep designs based on α–arrays to allow for a much broader class of designs to be constructed. Updating procedures for the average efficiency factor and its upper bound are developed for application to the computer generation of efficient p–rep designs.     

On the efficiency of adaptive designs for flexible interim decisions in clinical trials

It is shown that the optimal group sequential designs considered in Tsiatis and Mehta [2003. On the inefficiency of the adaptive design for monitoring clinical trials. Biometrika 90, 367–378] are special cases of the more general flexible designs which allow for a valid inference after adapting a predetermined way to spend the rejection and acceptance probabilities. An unforeseen safety issue in a clinical trial, for example, could make a change of the preplanned number of interim analyses and their sample sizes appropriate. We derive flexible designs which have equivalent rejection and acceptance regions if no adaptation is performed, but at the same time allow for an adaptation of the spending functions, and have a conditional optimality property.     

Non binary partially neighbor balanced designs for circular blocks

ABSTRACT

Neighbor designs are recommended for the cases where the performance of treatment is affected by the neighboring treatments as in biometrics and agriculture. In this paper we have constructed two new series of non binary partially neighbor balanced designs for v = 2n and v = 2n+1 number of treatments, respectively. The blocks in the design are non binary and circular but no treatment is ever a neighbor to itself. The designs proposed here are partially balanced in terms of nearest neighbors. No such series are known in the literature.     

An application of taguchi's methods reconsidered

Two aspects of Taguchi's methods for analyzing parameter design experiments that can be improved upon are considered. It is shown how using interaction graphs instead of marginal graphs, and how using the sample variance instead of a signal-to-noise ratio, can lead to product designs that are more robust to variation. The advantages of the alternative analysis will be illustrated by reanalyzing a case study considered by Barker (1986).     

PARTIALLY EQUINEIGHBOURED DESIGNS

This paper presents further results on a class of designs called equineighboured designs, ED. These designs are intended for field and related experiments, especially whenever there is evidence that observations in the same block are correlated. An ED has the property that every unordered pair of treatments occurs as nearest neighbours equally frequently at each level. Ipinyomi (1986) has defined and shown that ED are balanced designs when neighbouring observations are correlated. He has also presented ED as a continuation of the development of optimal block designs. An ED would often require many times the number of experimental materials needed for the construction of an ordinary balanced incomplete block, BIB, design for the same number of treatments and block sizes. Thus for a relatively large number of treatments and block sizes the required minimum number of blocks may be excessively large for practical use of ED. In this paper we shall define and examine partially equineighboured designs with n concurrences, PED (n), as alternatives where ED are practically unachievable. Particular attention will be given to designs with smaller numbers of blocks and for which only as little balance as possible may be lost.     

Practical approaches for design and analysis of clinical trials of infertility treatments: crossover designs and the Mantel–Haenszel method are recommended

Crossover designs have some advantages over standard clinical trial designs and they are often used in trials evaluating the efficacy of treatments for infertility. However, clinical trials of infertility treatments violate a fundamental condition of crossover designs, because women who become pregnant in the first treatment period are not treated in the second period. In previous research, to deal with this problem, some new designs, such as re‐randomization designs, and analysis methods including the logistic mixture model and the beta‐binomial mixture model were proposed. Although the performance of these designs and methods has previously been evaluated in large‐scale clinical trials with sample sizes of more than 1000 per group, the actual sample sizes of infertility treatment trials are usually around 100 per group. The most appropriate design and analysis for these moderate‐scale clinical trials are currently unclear. In this study, we conducted simulation studies to determine the appropriate design and analysis method of moderate‐scale clinical trials for irreversible endpoints by evaluating the statistical power and bias in the treatment effect estimates. The Mantel–Haenszel method had similar power and bias to the logistic mixture model. The crossover designs had the highest power and the smallest bias. We recommend using a combination of the crossover design and the Mantel–Haenszel method for two‐period, two‐treatment clinical trials with irreversible endpoints. Copyright © 2015 John Wiley & Sons, Ltd.     

Adaptative Designs for Multi-Arm Clinical Trials: The Play-the-Winner Rule Revisited

Adaptative designs for clinical trials that are based on a generalization of the “play-the-winner” rule are considered as an alternative to previously developed models. Theoretical and numerical results show that these designs perform better for the usual criteria. Bayesian methods are proposed for the statistical analysis of these designs.     

Convergence properties of sequential Bayesian D-optimal designs

We establish convergence properties of sequential Bayesian optimal designs. In particular, for sequential D-optimality under a general nonlinear location-scale model for binary experiments, we establish posterior consistency, consistency of the design measure, and the asymptotic normality of posterior following the design. We illustrate our results in the context of a particular application in the design of phase I clinical trials, namely a sequential design of Haines et al. [2003. Bayesian optimal designs for phase I clinical trials. Biometrics 59, 591–600] that incorporates an ethical constraint on overdosing.     

The Multivariate Randomized Complete Block Design: A Novel Permutation Solution in Case of Ordered Categorical Variables

In this article, multivariate extensions of the combination-based test statistics for the comparison of several treatments in the multivariate Randomized Complete Block designs are introduced in case of categorical response variables. Several tests for the multivariate Randomized Complete Block designs, including MANOVA procedure, are compared with the method proposed via a Monte Carlo simulation study. The method has also been applied to a real case study in the field of sensorial testing studies. Results suggest that in each experimental situation where normality of the supposed underlying continuous model is hard to justify and especially when errors have heavy-tailed distributions, the proposed nonparametric procedure can be considered as a valid solution.     

Asymptotics of adaptive design with two alternating generating matrices

In the application of generalized Pólya urn (GPU) model to designs of clinical trials, in contrast to the classical homogeneous models, it is more realistic to assume nonhomogeneous generating matrices. However, in literature, due to mathematical difficulties, the generating matrices are either assumed to be homogeneous or asymptotically homogeneous (see Bai and Hu, 1999). In the present paper, we consider a new model which uses two alternating generating matrices. The theoretical results show that the asymptotics still hold in this nonhomogeneous case. Moreover, the simulation results also support the theoretical conclusions. Furthermore, this model provides a starting point for the future study of adaptive designs with non-convergent generating matrices.     

Curtailed two-stage designs with two dependent binary endpoints

When phase I clinical trials were found to be unable to precisely estimate the frequency of toxicity, Brayan and Day proposed incorporating toxicity considerations into two-stage designs in phase II clinical trials. Conaway and Petroni further pointed out that it is important to evaluate the clinical activity and safety simultaneously in studying cancer treatments with more toxic chemotherapies in a phase II clinical trial. Therefore, they developed multi-stage designs with two dependent binary endpoints. However, the usual sample sizes in phase II trials make these designs difficult to control the type I error rate at a desired level over the entire null region and still have sufficient power against reasonable alternatives. Therefore, the curtailed sampling procedure summarized by Phatak and Bhatt will be applied to the two-stage designs with two dependent binary endpoints in this paper to reduce sample sizes and speed up the development process for drugs.