Steady-state statistical properties and implementation of randomization designs with maximum tolerated imbalance restriction for two-arm equal allocation clinical trials.

In recent decades, several randomization designs have been proposed in the literature as better alternatives to the traditional permuted block design (PBD), providing higher allocation randomness under the same restriction of the maximum tolerated imbalance (MTI). However, PBD remains the most frequently used method for randomizing subjects in clinical trials. This status quo may reflect an inadequate awareness and appreciation of the statistical properties of these randomization designs, and a lack of simple methods for their implementation. This manuscript presents the analytic results of statistical properties for five randomization designs with MTI restriction based on their steady-state probabilities of the treatment imbalance Markov chain and compares them to those of the PBD. A unified framework for randomization sequence generation and real-time on-demand treatment assignment is proposed for the straightforward implementation of randomization algorithms with explicit formulas of conditional allocation probabilities. Topics associated with the evaluation, selection, and implementation of randomization designs are discussed. It is concluded that for two-arm equal allocation trials, several randomization designs offer stronger protection against selection bias than the PBD does, and their implementation is not necessarily more difficult than the implementation of the PBD.

A roadmap to using randomization in clinical trials.

BACKGROUND: Randomization is the foundation of any clinical trial involving treatment comparison. It helps mitigate selection bias, promotes similarity of treatment groups with respect to important known and unknown confounders, and contributes to the validity of statistical tests. Various restricted randomization procedures with different probabilistic structures and different statistical properties are available. The goal of this paper is to present a systematic roadmap for the choice and application of a restricted randomization procedure in a clinical trial. METHODS: We survey available restricted randomization procedures for sequential allocation of subjects in a randomized, comparative, parallel group clinical trial with equal (1:1) allocation. We explore statistical properties of these procedures, including balance/randomness tradeoff, type I error rate and power. We perform head-to-head comparisons of different procedures through simulation under various experimental scenarios, including cases when common model assumptions are violated. We also provide some real-life clinical trial examples to illustrate the thinking process for selecting a randomization procedure for implementation in practice. RESULTS: Restricted randomization procedures targeting 1:1 allocation vary in the degree of balance/randomness they induce, and more importantly, they vary in terms of validity and efficiency of statistical inference when common model assumptions are violated (e.g. when outcomes are affected by a linear time trend; measurement error distribution is misspecified; or selection bias is introduced in the experiment). Some procedures are more robust than others. Covariate-adjusted analysis may be essential to ensure validity of the results. Special considerations are required when selecting a randomization procedure for a clinical trial with very small sample size. CONCLUSIONS: The choice of randomization design, data analytic technique (parametric or nonparametric), and analysis strategy (randomization-based or population model-based) are all very important considerations. Randomization-based tests are robust and valid alternatives to likelihood-based tests and should be considered more frequently by clinical investigators.

Conditional estimation and inference to address observed covariate imbalance in randomized clinical trials.

BACKGROUND: Baseline covariate imbalance (between treatment groups) is a common problem in randomized clinical trials which often raises questions about the validity of trial results. Answering these questions requires careful consideration of the statistical implications of covariate imbalance. The possibil ity of having covariate imbalance contributes to the marginal variance of an unadjusted treatment difference estimator, which can be reduced by making appropriate adjustments. Actual observed imbalance introduces a conditional bias into an unadjusted estimator, which may increase the conditional size of an unadjusted test. METHODS: This article provides conditional estimation and inference procedures to address the conditional bias due to observed imbalance. Interestingly, it is possible to use the same adjusted treatment difference estimator to address the marginal variance issue and the conditional bias issue associated with covariate imbalance. Its marginal variance estimator tends to be conservative for conditional inference, and we propose a conditionally appropriate variance estimator. We also provide an estimator of the conditional bias in an unadjusted treatment difference estimator, together with a conditional variance estimator. RESULTS: The proposed methodology is illustrated with real data from a stroke trial and evaluated in simulation experiments based on the same trial. The simulation results show that covariate imbalance can result in a substantial conditional bias and that the proposed methods deal with the conditional bias quite effectively. DISCUSSION: We recommend that the proposed methodology be used routinely to address the observed covariate imbalance in randomized clinical trials.

The asymptotic maximal procedure for subject randomization in clinical trials.

The maximal procedure is a restricted randomization method that maximizes the number of feasible allocation sequences under the constraints of the maximum tolerated imbalance and the allocation sequence length. It assigns an equal probability to all feasible sequences. However, its implementation is not easy due to the lack of the Markovian property of the conditional allocation probabilities. In this paper, we propose the asymptotic maximal procedure, which replaces the sequence-length-dependent conditional allocation probabilities with their asymptotic values. The new randomization procedure is compared with the original maximal procedure and few other randomization procedures with the maximum tolerated imbalance via simulations and is found to be a practical choice for future clinical trials.

Risk of selection bias in randomized trials: further insight.

The quality of randomization is an under-appreciated facet of trial design. The present piece represents an advance in our collective understanding of how allocation concealment and randomization relate to risk of selection bias in randomized trials, and other measures are also considered. Though the overwhelming majority of the advice given is timely and correct, it is more instructive to focus on the relatively narrow sliver of advice that is incorrect (namely, that trials should not stratify by site, and that unrestricted randomization is a solution to the problem of selection bias), so it is in this context that the comments here must be understood. In no way is this intended to be a rebuttal of the excellent work we have before us. Rather, it is a refinement.

Comparing MTI randomization procedures to blocked randomization.

Randomization is one of the cornerstones of the randomized clinical trial, and there is no shortage of methods one can use to randomize patients to treatment groups. When deciding which one to use, researchers must bear in mind that not all randomization procedures are equally adept at achieving the objective of randomization, namely, balanced treatment groups. One threat is chronological bias, and permuted blocks randomization does such a good job at controlling chronological bias that it has become the standard randomization procedure in clinical trials. But permuted blocks randomization is especially vulnerable to selection bias, so as a result, the maximum tolerated imbalance (MTI) procedures were proposed as better alternatives. In comparing the procedures, we have somewhat of a false controversy, in that actual practice goes uniformly one way (permuted blocks), whereas scientific arguments go uniformly the other way (MTI procedures). There is no argument in the literature to suggest that the permuted block design is better than or even as good as the MTI procedures, but this dearth is matched by an equivalent one regarding actual trials using the MTI procedures. So the 'controversy', if we are to call it that, pits misguided precedent against sound advice that tends to be ignored in practice. We shall review the issues to determine scientifically which of the procedures is better and, therefore, should be used.

Characterizing permuted block randomization as a big stick procedure.

There are numerous approaches to randomizing patients to treatment groups in clinical trials. The most popular is permuted block randomization, and a newer and better class, which is gaining in popularity, is the so-called class of MTI procedures, which use a big stick to force the allocation sequence back towards balance when it reaches the MTI (maximally tolerated imbalance). Three prominent members of this class are the aptly named big stick procedure, Chen's procedure, and the maximal procedure. As we shall establish in this article, blocked randomization, though not typically cast as an MTI procedure, does in fact use the big stick as well. We shall argue that its weaknesses, which are well known, arise precisely from its improper use, bordering on outright abuse, of this big stick. Just as rocket powered golf clubs add power to a golf swing, so too does the big stick used by blocked randomization hit with too much power. In addition, the big stick is invoked when it need not be, thereby resulting in the excessive prediction for which permuted blocks are legendary. We bridge the gap between the MTI procedures and block randomization by identifying a new randomization procedure intermediate between the two, namely based on an excessively powerful big stick, but one that is used only when needed. We shall then argue that the MTI procedures are all superior to this intermediate procedure by virtue of using a restrained big stick, and that this intermediate procedure is superior to block randomization by virtue of restraint in when the big stick is invoked. The transitivity property then completes our argument.