Restricted randomization designs in clinical trials.

Though therapeutic clinical trials are often categorized as using either "randomization" or "historical controls" as a basis for treatment evaluation, pure random assignment of treatments is rarely employed. Instead various restricted randomization designs are used. The restrictions include the balancing of treatment assignments over time and the stratification of the assignment with regard to covariates that may affect response. Restricted randomization designs for clinical trials differ from those of other experimental areas because patients arrive sequentially and a balanced design cannot be ensured. The major restricted randomization designs and arguments concerning the proper role of stratification are reviewed here. The effect of randomization restrictions on the validity of significance tests is discussed.     

Conditional Markov Chain Design for Accrual Clinical Trials

Randomization in a comparative experiment has, as one aim, the control of bias in the initial selection of experimental units. When the experiment is a clinical trial employing the accrual of patients, two additional aims are the control of admission bias and control of chronologic bias. This can be accomplished by using a method of randomization, such as the “biased coin design” of Efron, which sequentially forces balance. As an extension of Efron's design, this paper develops a class of conditional Markov chain designs. The detailed randomization employed utilizes the sequential imbalances in the treatment allocation as states in a Markov process. Through the use of appropriate transition probabilities, a range of possible designs can be attained. An additional objective of physical randomization is to provide a model for data analysis. Such a randomization theoretic analysis is presented for the current designs. In addition, Monte Carlo sampling results are given to support the proposed normal theory approximation to the exact randomization distribution.     

Bayesian Adaptive Randomization and Trial Monitoring with Predictive Probability for Time-to-Event Endpoint

There has been much development in Bayesian adaptive designs in clinical trials. In the Bayesian paradigm, the posterior predictive distribution characterizes the future possible outcomes given the currently observed data. Based on the interim time-to-event data, we develop a new phase II trial design by combining the strength of both Bayesian adaptive randomization and the predictive probability. By comparing the mean survival times between patients assigned to two treatment arms, more patients are assigned to the better treatment on the basis of adaptive randomization. We continuously monitor the trial using the predictive probability for early termination in the case of superiority or futility. We conduct extensive simulation studies to examine the operating characteristics of four designs: the proposed predictive probability adaptive randomization design, the predictive probability equal randomization design, the posterior probability adaptive randomization design, and the group sequential design. Adaptive randomization designs using predictive probability and posterior probability yield a longer overall median survival time than the group sequential design, but at the cost of a slightly larger sample size. The average sample size using the predictive probability method is generally smaller than that of the posterior probability design.     

On randomization testing in vegetation science: multifactor comparisons of relevé groups

Abstract. Hypothesis testing in phytocoenological applications is likely to be hindered when based on conventional statistical methods. The problem created by unrealistic assumptions can, however, be overcome by randomization. This paper discusses the general idea of randomization testing, describes a method and interprets its application in group comparisons. Two sets of variables are involved, the vegetation set on the basis of which the groups are compared and the environmental factors which delimit the groups under different analytical designs. Although simple partitioning of sum of squares is at the core of the test, the method has versatility of testing uni- or multifactor designs, which is novel in phytocoenological applications. The algorithm has been implemented in programs SYNCSA and MULTIV by V.P. Data from the Campos of southern Brazil are used for illustration.     

Conditional analysis of mixed Poisson processes with baseline counts: implications for trial design and analysis

The design of clinical trials is typically based on marginal comparisons of a primary response under two or more treatments. The considerable gains in efficiency afforded by models conditional on one or more baseline responses has been extensively studied for Gaussian models. The purpose of this article is to present methods for the design and analysis of clinical trials in which the response is a count or a point process, and a corresponding baseline count is available prior to randomization. The methods are based on a conditional negative binomial model for the response given the baseline count and can be used to examine the effect of introducing selection criteria on power and sample size requirements. We show that designs based on this approach are more efficient than those proposed by McMahon et al. (1994).     

Cox regression methods for two-stage randomization designs

Two-stage randomization designs (TSRD) are becoming increasingly common in oncology and AIDS clinical trials as they make more efficient use of study participants to examine therapeutic regimens. In these designs patients are initially randomized to an induction treatment, followed by randomization to a maintenance treatment conditional on their induction response and consent to further study treatment. Broader acceptance of TSRDs in drug development may hinge on the ability to make appropriate intent-to-treat type inference within this design framework as to whether an experimental induction regimen is better than a standard induction regimen when maintenance treatment is fixed. Recently Lunceford, Davidian, and Tsiatis (2002, Biometrics 58, 48-57) introduced an inverse probability weighting based analytical framework for estimating survival distributions and mean restricted survival times, as well as for comparing treatment policies at landmarks in the TSRD setting. In practice Cox regression is widely used and in this article we extend the analytical framework of Lunceford et al. (2002) to derive a consistent estimator for the log hazard in the Cox model and a robust score test to compare treatment policies. Large sample properties of these methods are derived, illustrated via a simulation study, and applied to a TSRD clinical trial.     

Sensitivity analyses comparing time-to-event outcomes only existing in a subset selected postrandomization and relaxing monotonicity

In randomized studies researchers may be interested in the effect of treatment assignment on a time-to-event outcome that only exists in a subset selected after randomization. For example, in preventative HIV vaccine trials, it is of interest to determine whether randomization to vaccine affects the time from infection diagnosis until initiation of antiretroviral therapy. Earlier work assessed the effect of treatment on outcome among the principal stratum of individuals who would have been selected regardless of treatment assignment. These studies assumed monotonicity, that one of the principal strata was empty (e.g., every person infected in the vaccine arm would have been infected if randomized to placebo). Here, we present a sensitivity analysis approach for relaxing monotonicity with a time-to-event outcome. We also consider scenarios where selection is unknown for some subjects because of noninformative censoring (e.g., infection status k years after randomization is unknown for some because of staggered study entry). We illustrate our method using data from an HIV vaccine trial.     

Clustered encouragement designs with individual noncompliance: bayesian inference with randomization,and application to advance directive forms

In many studies comparing a new 'target treatment' with a control target treatment, the received treatment does not always agree with assigned treatment-that is, the compliance is imperfect. An obvious example arises when ethical or practical constraints prevent even the randomized assignment of receipt of the new target treatment but allow the randomized assignment of the encouragement to receive this treatment. In fact, many randomized experiments where compliance is not enforced by the experimenter (e.g. with non-blinded assignment) may be more accurately thought of as randomized encouragement designs. Moreover, often the assignment of encouragement is at the level of clusters (e.g. doctors) where the compliance with the assignment varies across the units (e.g. patients) within clusters. We refer to such studies as 'clustered encouragement designs' (CEDs) and they arise relatively frequently (e.g. Sommer and Zeger, 1991; McDonald et al., 1992; Dexter et al., 1998) Here, we propose Bayesian methodology for causal inference for the effect of the new target treatment versus the control target treatment in the randomized CED with all-or-none compliance at the unit level, which generalizes the approach of Hirano et al. (2000) in important and surprisingly subtle ways, to account for the clustering, which is necessary for statistical validity. We illustrate our methods using data from a recent study exploring the role of physician consulting in increasing patients' completion of Advance Directive forms.     

Maximum entropy constrained balance randomization for clinical trials.

A specialization of the biased coin clinical trial randomization schemes of Pocock and Simon (1975) and Efron (1971) is proposed which gives guidelines for the coin biasing probabilities of assignment to treatment. The scheme parameterizes the often conflicting goals of random treatment assignment and allocation for stratum balance in terms of a single trade-off parameter specifying a desired degree of determinism. Treatment radomization probabilities are obtained iteratively in an exponential form which maximizes randomization entropy subject to a specified balance constraint.     

Treatment allocation for nonlinear models in clinical trials: the logistic model

Many clinical trials have a binary outcome variable. If covariate adjustment is necessary in the analysis, the logistic-regression model is frequently used. Optimal designs for allocating treatments for this model, or for any nonlinear or heteroscedastic model, are generally unbalanced with regard to overall treatment totals and totals within strata. However, all treatment-allocation methods that have been recommended for clinical trials in the literature are designed to balance treatments within strata, either directly or asymptotically. In this paper, the efficiencies of balanced sequential allocation schemes are measured relative to sequential Ds-optimal designs for the logistic model, using as examples completed trials conducted by the Eastern Cooperative Oncology Group and systematic simulations. The results demonstrate that stratified, balanced designs are quite efficient, in general. However, complete randomization is frequently inefficient, and will occasionally result in a trial that is very inefficient.     

Importance of randomization in microarray experimental designs with Illumina platforms

Measurements of gene expression from microarray experiments are highly dependent on experimental design. Systematic noise can be introduced into the data at numerous steps. On Illumina BeadChips, multiple samples are assayed in an ordered series of arrays. Two experiments were performed using the same samples but different hybridization designs. An experiment confounding genotype with BeadChip and treatment with array position was compared to another experiment in which these factors were randomized to BeadChip and array position. An ordinal effect of array position on intensity values was observed in both experiments. We demonstrate that there is increased rate of false-positive results in the confounded design and that attempts to correct for confounded effects by statistical modeling reduce power of detection for true differential expression. Simple analysis models without post hoc corrections provide the best results possible for a given experimental design. Normalization improved differential expression testing in both experiments but randomization was the most important factor for establishing accurate results. We conclude that lack of randomization cannot be corrected by normalization or by analytical methods. Proper randomization is essential for successful microarray experiments.     

An empirical verification of population assignment methods by marking and parentage data: hatchery and wild steelhead (Oncorhynchus mykiss) in Forks Creek, Washington, USA

Assignment tests are increasingly applied in ecology and conservation, although empirical comparisons of methods are still rare or are restricted to few of the available approaches. Furthermore, the performance of assignment tests in cases with low population differentiation, violations of Hardy-Weinberg equilibrium and unbalanced sampling designs has not been verified. The release of adult hatchery steelhead to spawn in Forks Creek in 1996 and 1997 provided an opportunity to compare the power of different assignment methods to distinguish their offspring from those of sympatric wild steelhead. We compared standard assignment methods requiring baseline samples (frequency, distance and Bayesian) and clustering approaches with and without baseline information, using six freely available computer programs. Assignments were verified by parentage data obtained for a subset of returning offspring. All methods provided similar assignment success, despite low differentiation between wild and hatchery fish (F(ST) = 0.02). Bayesian approaches with baseline data performed best, whereas the results of clustering methods were variable and depended on the samples included in the analysis and the availability of baseline information. Removal of a locus with null alleles and equalizing sample sizes had little effect on assignments. Our results demonstrate the robustness of most assignment tests to low differentiation and violations of assumptions, as well as their utility for ecological studies that require correct classification of different groups.     

Propensity Score Matching in Randomized Clinical Trials

Summary Cluster randomization trials with relatively few clusters have been widely used in recent years for evaluation of health‐care strategies. On average, randomized treatment assignment achieves balance in both known and unknown confounding factors between treatment groups, however, in practice investigators can only introduce a small amount of stratification and cannot balance on all the important variables simultaneously. The limitation arises especially when there are many confounding variables in small studies. Such is the case in the INSTINCT trial designed to investigate the effectiveness of an education program in enhancing the tPA use in stroke patients. In this article, we introduce a new randomization design, the balance match weighted (BMW) design, which applies the optimal matching with constraints technique to a prospective randomized design and aims to minimize the mean squared error (MSE) of the treatment effect estimator. A simulation study shows that, under various confounding scenarios, the BMW design can yield substantial reductions in the MSE for the treatment effect estimator compared to a completely randomized or matched‐pair design. The BMW design is also compared with a model‐based approach adjusting for the estimated propensity score and Robins‐Mark‐Newey E‐estimation procedure in terms of efficiency and robustness of the treatment effect estimator. These investigations suggest that the BMW design is more robust and usually, although not always, more efficient than either of the approaches. The design is also seen to be robust against heterogeneous error. We illustrate these methods in proposing a design for the INSTINCT trial.     

Design and Analysis of Crossover Trials for Absorbing Binary Endpoints

Summary The crossover is a popular and efficient trial design used in the context of patient heterogeneity to assess the effect of treatments that act relatively quickly and whose benefit disappears with discontinuation. Each patient can serve as her own control as within‐individual treatment and placebo responses are compared. Conventional wisdom is that these designs are not appropriate for absorbing binary endpoints, such as death or HIV infection. We explore the use of crossover designs in the context of these absorbing binary endpoints and show that they can be more efficient than the standard parallel group design when there is heterogeneity in individuals' risks. We also introduce a new two‐period design where first period “survivors” are rerandomized for the second period. This design combines the crossover design with the parallel design and achieves some of the efficiency advantages of the crossover design while ensuring that the second period groups are comparable by randomization. We discuss the validity of the new designs and evaluate both a mixture model and a modified Mantel–Haenszel test for inference. The mixture model assumes no carryover or period effects while the Mantel–Haenszel approach conditions out period effects. Simulations are used to compare the different designs and an example is provided to explore practical issues in implementation.     

Maximum likelihood estimation of generalized linear models for adaptive designs: Applications and asymptotics

Due to increasing discoveries of biomarkers and observed diversity among patients, there is growing interest in personalized medicine for the purpose of increasing the well‐being of patients (ethics) and extending human life. In fact, these biomarkers and observed heterogeneity among patients are useful covariates that can be used to achieve the ethical goals of clinical trials and improving the efficiency of statistical inference. Covariate‐adjusted response‐adaptive (CARA) design was developed to use information in such covariates in randomization to maximize the well‐being of participating patients as well as increase the efficiency of statistical inference at the end of a clinical trial. In this paper, we establish conditions for consistency and asymptotic normality of maximum likelihood (ML) estimators of generalized linear models (GLM) for a general class of adaptive designs. We prove that the ML estimators are consistent and asymptotically follow a multivariate Gaussian distribution. The efficiency of the estimators and the performance of response‐adaptive (RA), CARA, and completely randomized (CR) designs are examined based on the well‐being of patients under a logit model with categorical covariates. Results from our simulation studies and application to data from a clinical trial on stroke prevention in atrial fibrillation (SPAF) show that RA designs lead to ethically desirable outcomes as well as higher statistical efficiency compared to CARA designs if there is no treatment by covariate interaction in an ideal model. CARA designs were however more ethical than RA designs when there was significant interaction.     

Simultaneous Randomization Tests

Randomization analyses have been developed for testing main effects and interactions in standard experimental designs. However, exact multiple comparisons procedures for these randomization analyses have received little attention. This article proposes a general procedure for constructing simultaneous randomization tests that have prescribed type I error rates. An application of the procedure does provide for multiple comparisons in the randomization analyses of designed experiments. This application is made to data collected in a biopharmaceutical experiment.     

Sensitivity analyses comparing outcomes only existing in a subset selected post-randomization, conditional on covariates, with application to HIV vaccine trials

In many experiments, researchers would like to compare between treatments and outcome that only exists in a subset of participants selected after randomization. For example, in preventive HIV vaccine efficacy trials it is of interest to determine whether randomization to vaccine causes lower HIV viral load, a quantity that only exists in participants who acquire HIV. To make a causal comparison and account for potential selection bias we propose a sensitivity analysis following the principal stratification framework set forth by Frangakis and Rubin (2002, Biometrics58, 21-29). Our goal is to assess the average causal effect of treatment assignment on viral load at a given baseline covariate level in the always infected principal stratum (those who would have been infected whether they had been assigned to vaccine or placebo). We assume stable unit treatment values (SUTVA), randomization, and that subjects randomized to the vaccine arm who became infected would also have become infected if randomized to the placebo arm (monotonicity). It is not known which of those subjects infected in the placebo arm are in the always infected principal stratum, but this can be modeled conditional on covariates, the observed viral load, and a specified sensitivity parameter. Under parametric regression models for viral load, we obtain maximum likelihood estimates of the average causal effect conditional on covariates and the sensitivity parameter. We apply our methods to the world's first phase III HIV vaccine trial.     

Improving the Flexibility and Efficiency of Phase II Designs for Oncology Trials

Summary Phase II trials in oncology are usually conducted as single-arm two-stage designs with binary endpoints. Currently available adaptive design methods are tailored to comparative studies with continuous test statistics. Direct transfer of these methods to discrete test statistics results in conservative procedures and, therefore, in a loss in power. We propose a method based on the conditional error function principle that directly accounts for the discreteness of the outcome. It is shown how application of the method can be used to construct new phase II designs that are more efficient as compared to currently applied designs and that allow flexible mid-course design modifications. The proposed method is illustrated with a variety of frequently used phase II designs.     

A comparison of experimental designs for selection in breeding trials with nested treatment structure

Plant breeders frequently evaluate large numbers of entries in field trials for selection. Generally, the tested entries are related by pedigree. The simplest case is a nested treatment structure, where entries fall into groups or families such that entries within groups are more closely related than between groups. We found that some plant breeders prefer to plant close relatives next to each other in the field. This contrasts with common experimental designs such as the α-design, where entries are fully randomized. A third design option is to randomize in such a way that entries of the same group are separated as much as possible. The present paper compares these design options by simulation. Another important consideration is the type of model used for analysis. Most of the common experimental designs were optimized assuming that the model used for analysis has fixed treatment effects. With many entries that are related by pedigree, analysis based on a model with random treatment effects becomes a competitive alternative. In simulations, we therefore study the properties of best linear unbiased predictions (BLUP) of genetic effects based on a nested treatment structure under these design options for a range of genetic parameters. It is concluded that BLUP provides efficient estimates of genetic effects and that resolvable incomplete block designs such as the α-design with restricted or unrestricted randomization can be recommended.