Properties of simple randomization in clinical trials

This article presents the properties of complete randomization (e.g., coin toss) and of the random allocation rule (random permutation of n/2 of n elements). The latter is principally used in cases where the total sample size n is known exactly a priori. The likelihood of treatment imbalances is readily computed and is shown to be negligible for large trials (n greater than 200), regardless of whether a stratified randomization is used. It is shown that substantial treatment imbalances are extremely unlikely in large trials, and therefore there is likely to be no substantial effect on power. The large-sample permutational distribution of the family of linear rank tests is presented for complete randomization unconditionally and conditionally, and for the random allocation rule. Asymptotically the three are equivalent to the distribution of these tests under a sampling-based population model. Permutation tests are also presented for a stratified analysis within one or more subgroups of patients defined post hoc on the basis of a covariate. This provides a basis for analysis when some patients' responses are assumed to be missing-at-random. Using the Blackwell-Hodges model, it is shown that complete randomization eliminates the potential for selection bias, but that the random allocation rule yields a substantial potential for selection bias in an unmasked trial. Finally, the Efron model for accidental bias is used to assess the potential for bias in the estimate of treatment effect due to covariate imbalance. Asymptotically, this probability approaches zero for complete randomization and for the random allocation rule. However, for finite n, complete randomization minimizes the probability of accidental bias, whereas this probability is slightly higher with a random allocation rule. It is concluded that complete randomization has merit in large clinical trials.     

Properties of permuted-block randomization in clinical trials

This article describes some of the important statistical properties of the commonly used permuted-block design, also known simply as blocked-randomization. Under a permutation model for statistical tests, proper analyses should employ tests that incorporate the blocking used in the randomization. These include the block-stratified Mantel-Haenszel chi-square test for binary data, the blocked analysis of variance F test, and the blocked nonparametric linear rank test. It is common, however, to ignore the blocking in the analysis. For these tests, it is shown that the size of a test obtained from an analysis incorporating the blocking (say T), versus an analysis ignoring the blocking (say TI), is related to the intrablock correlation coefficient (R) as TI = T(1-R). For blocks of common length 2m, the range of R is from -1/(2m-1) to 1. Thus, if there is a positive intrablock correlation, which is more likely than not for m greater than 1, an analysis ignoring blocking will be unduly conservative. Permutation tests are also presented for the case of stratified analyses within one or more subgroups of patients defined post hoc on the basis of a covariate. This provides a basis for the analysis when responses from some patients are assumed to be missing-at-random. An alternative strategy that requires no assumptions is to perform the analysis using only the subset of complete blocks in which no observations are missing. The Blackwell-Hodges model is used to assess the potential for selection bias induced by investigator attempts to guess which treatment is more likely to be assigned to each incoming patient. In an unmasked trial, the permuted-block design provides substantial potential for selection bias in the comparison of treatments due to the predictability of the assignments that is induced by the requirement of balance within blocks. Further, this bias is not eliminated by the use of random block sizes. We also modify the Blackwell-Hodges model to allow for selection bias only when the investigator is able to discern the next assignment with certainty. This type of bias is reduced by the use of random block sizes and is eliminated only if the possible block sizes are unknown to the investigators. Finally, the Efron model for accidental bias is used to assess the potential for bias in the estimation of treatment effects due to covariate imbalances. For the permuted-block design, the variance of this bias approaches that of complete randomization as the half-block length m----infinity.(ABSTRACT TRUNCATED AT 400 WORDS)     

Methods of randomization in controlled clinical trials

In this second article of a series that explores design and analysis issues in controlled clinical trials in emergency medicine, we have discussed the case for randomization, reviewed the methods involved in simple randomization, highlighted some of the practical problems involved with randomization, and presented some modified randomization schemes intended to remedy these problems.     

Statistical properties of randomization in clinical trials

This is the first of five articles on the properties of different randomization procedures used in clinical trials. This paper presents definitions and discussions of the statistical properties of randomization procedures as they relate to both the design of a clinical trial and the statistical analysis of trial results. The subsequent papers consider, respectively, the properties of simple (complete), permuted-block (i.e., blocked), and urn (adaptive biased-coin) randomization. The properties described herein are the probabilities of treatment imbalances and the potential effects on the power of statistical tests; the permutational basis for statistical tests; and the potential for experimental biases in the assessment of treatment effects due either to the predictability of the random allocations (selection bias) or the susceptibility of the randomization procedure to covariate imbalances (accidental bias). For most randomization procedures, the probabilities of overall treatment imbalances are readily computed, even when a stratified randomization is used. This is important because treatment imbalance may affect statistical power. It is shown, however, that treatment imbalance must be substantial before power is more than trivially affected. The differences between a population versus a permutation model as a basis for a statistical test are reviewed. It is argued that a population model can only be invoked in clinical trials as an untestable assumption, rather than being formally based on sampling at random from a population. On the other hand, a permutational analysis based on the randomization actually employed requires no assumptions regarding the origin of the samples of patients studied. The large sample permutational distribution of the family of linear rank tests is described as a basis for easily conducting a variety of permutation tests. Subgroup (stratified) analyses, analyses when some data are missing, and regression model analyses are also discussed. The Blackwell-Hodges model for selection bias in the composition of the study groups is described. The expected selection bias associated with a randomization procedure is a function of the predictability of the treatment allocations and is readily evaluated for any sequence of treatment assignments. In an unmasked study, the potential for selection bias may be substantial with highly predictable sequences. Finally, the Efron model for accidental bias in the estimate of treatment effect in a linear model is described. This is important because the potential for accidental bias is equivalent to the potential for a covariate imbalance.(ABSTRACT TRUNCATED AT 400 WORDS)     

Comparison of multi-arm multi-stage design and adaptive randomization in platform clinical trials

Platforms trials are clinical trials that allow for concurrent evaluations of multiple treatments, thus allowing for more efficient and ethical studies compared to traditional two-arm trials. Conventional group-sequential multi-arm multi-stage (MAMS) designs use pre-specified stopping boundaries and treatment selection rules to determine if experimental treatments should be dropped. Flexible MAMS designs allow for interim modifications to the design plan without compromising error rates. Bayesian response adaptive randomization (BRAR) designs increase patient allocation to treatment arms that are performing well during the course of the trial. In this paper, we compare these two major methods and their extensions under several scenarios in the platform trials setting. Results show that BRAR and flexible MAMS designs have comparable power and type 1 error rate under varying simulated scenarios, allowing for addition of flexible treatment selection. BRAR outperforms flexible MAMS when there is a single effective treatment. Flexible MAMS designs are more efficient compared to BRAR when there are no effective treatments. BRAR performance increases as the probability of a treatment arm being dropped increases.     

Block urn design - a new randomization algorithm for sequential trials with two or more treatments and balanced or unbalanced allocation

Permuted block design is the most popular randomization method used in clinical trials, especially for trials with more than two treatments and unbalanced allocation, because of its consistent imbalance control and simplicity in implementation. However, the risk of selection biases caused by high proportion of deterministic assignments is a cause of concern. Efron's biased coin design and Wei's urn design provide better allocation randomness without deterministic assignments, but they do not consistently control treatment imbalances. Alternative randomization designs with improved performances have been proposed over the past few decades, including Soares and Wu's big stick design, which has high allocation randomness, but is limited to two-treatment balanced allocation scenarios only, and Berger's maximal procedure design which has a high allocation randomness and a potential for more general trial scenarios, but lacks the explicit function for the conditional allocation probability and is more complex to implement than most other designs. The block urn design proposed in this paper combines the advantages of existing randomization designs while overcoming their limitations. Statistical properties of the new algorithm are assessed and compared to currently available designs via analytical and computer simulation approaches. The results suggest that the block urn design simultaneously provides consistent imbalance control and high allocation randomness. It can be easily implemented for sequential clinical trials with two or more treatments and balanced or unbalanced allocation.     

A computerized patient registration and treatment randomization system for multi-institutional clinical trials

Computerized registration and randomization for a cooperative clinical trials group is a useful addition to its data gathering and managing process. An automated system eliminates unnecessary paperwork, allows more sophisticated randomization algorithms to be implemented, and makes available a variety of computer-generated reports such as confirmation of registration forms, accrual results, and other statistical tables. This paper describes the design and implementation of such a system for a relatively large cooperative group, the Eastern Cooperative Oncology Group (ECOG), as well as gives general recommendations for conversion of a manual registration and randomization process to an automated one. Our general interactive system, known as PRS for Patient Randomization System, was designed to be easily expandable as its functions increase over time, and transportable to other clinical trials settings.     

An automated patient registration and treatment randomization system for multicenter clinical trials.

This article describes an automated patient registration/treatment randomization system for multicenter clinical trials. Registrations take place centrally using telephone keypads (tone-dial) for data entry and synthesized speech (at the coordinating center) for confirmation. The system permits a wide variety of protocol designs and treatment assignment schemes and presently supports more than 85 protocols of the Pediatric Oncology Group. It is developed in modules to permit easy addition/deletion of studies and treating sites. The system permits uninterrupted, unattended operation at the coordinating center 7 days a week, 24 hours a day.     

Allocation of patients to conditions in headache clinical trials: randomization, stratification, and treatment matching

Assuming control over the allocation of patients to treatment conditions is a fundamental element of any comparative clinical trial. There are three critical considerations investigators must balance in choosing an allocation scheme: reducing bias in patient allocation, producing balanced patient groups across treatment arms, and reducing the likelihood of errors attributable to chance variation. The authors review the principles of three key approaches to the allocation of patients to conditions within clinical trials, and their respective advantages with regard to these critical considerations. These allocation methods include randomization, stratification, and patient-treatment matching. Randomization is fundamental to most clinical trials. Stratification is an advanced step in a systematic program of research investigating the efficacy and effectiveness of an intervention. If the trial has less than 100 per arm and there is a known prognostic factor, stratification is the best choice to ensure equal allocation across groups. Treatment matching (tailoring) attempts to match the most appropriate treatment to a specific patient based on a priori hypotheses. Two techniques used for exploring treatment matching are: patient typologies (patient profiling), and aptitude-treatment interactions. Additional details pertaining to the rationale for selecting among these various approaches to patient allocation is provided, and their methodology is summarized with specific consideration for their application within clinical trials of headache treatment.     

Inept media trials of clinical trials

The Indian media in general, with the exception of a few domain expert journalists, have failed to comprehend the complexities involved in the clinical trial process. In the run up to the deadline-based coverage of a story, a majority of them fall short in conveying the right perspective to readers, but nevertheless they have been successful in sensationalizing an event in this arena. Possibly by unintended misrepresentation, or mostly out of ignorance of the nuances involved in the clinical trials process, the media has done more harm than good, and got away with it. On the other side, the industry has been reluctant to engage with the media in a meaningful dialog for too long now. It bears not only the consequences of damage to its professional reputation following such reportage, but also the repercussions of unnecessary clampdowns by the regulators. Science journalism in India has yet to rise as a profession.     

Meta-analysis in clinical trials

This paper examines eight published reviews each reporting results from several related trials. Each review pools the results from the relevant trials in order to evaluate the efficacy of a certain treatment for a specified medical condition. These reviews lack consistent assessment of homogeneity of treatment effect before pooling. We discuss a random effects approach to combining evidence from a series of experiments comparing two treatments. This approach incorporates the heterogeneity of effects in the analysis of the overall treatment efficacy. The model can be extended to include relevant covariates which would reduce the heterogeneity and allow for more specific therapeutic recommendations. We suggest a simple noniterative procedure for characterizing the distribution of treatment effects in a series of studies.