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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.

We present a procedure that divides a set of experimental units into two groups that are similar on a prespecified set of covariates and are almost as random as with a complete randomization. Under complete randomization, the difference in the standardized average between treatment and control is O p (n -1/2), which may be material in small samples. We present an algorithm that reduces imbalance to O p (n⁻³) for one covariate and O p {n -(1+2/p)} for p covariates, but whose assignments are, strictly speaking, nonrandom. In addition to the metric of maximum eigenvalue of allocation variance, we introduce two metrics that capture departures from randomization and show that our assignments are nearly as random as complete randomization in terms of all measures. Simulations illustrate the results, and inference is discussed. An R package to generate designs according to our algorithm and other popular designs is available.

Textbooks on response surface methodology generally stress the importance of lack-of-fit tests and estimation of pure error. For lack-of-fit tests to be possible and other inference to be unbiased, experiments should allow for pure-error estimation. Therefore, they should involve replicated treatments. While most textbooks focus on lack-of-fit testing in the context of completely randomized designs, many response surface experiments are not completely randomized and require block or split-plot structures. The analysis of data from blocked or split-plot experiments is generally based on a mixed regression model with two variance components instead of one. In this article, we present a novel approach to designing blocked and split-plot experiments which ensures that the two variance components can be efficiently estimated from pure error and guarantees a precise estimation of the response surface model. Our novel approach involves a new Bayesian compound D-optimal design criterion which pays attention to both the variance components and the fixed treatment effects. One part of the compound criterion (the part concerned with the treatment effects) is based on the response surface model of interest, while the other part (which is concerned with pure-error estimates of the variance components) is based on the full treatment model. We demonstrate that our new criterion yields split-plot designs that outperform existing designs from the literature both in terms of the precision of the pure-error estimates and the precision of the estimates of the factor effects.

Field experiments are run under two competing objectives, high precision and minimal cost. The precision can be increased either by using sound experimentation techniques that account for the sources of variation with reasonable statistical models or by increasing the sample size. Large sample sizes usually increase the cost of the experiment and may not be feasible. This paper uses order restricted randomized designs (ORRD) to increase the precision while keeping the sample size and cost of the experiment minimal. The ORRD described here starts with a randomized block design but adds a second layer of blocking by ranking plots within each block. This creates a two-way lay-out, blocks and ranking groups, and uses a restricted randomization to improve the precision of estimation of the treatment parameters. Ranking groups create a correlation structure for within-block units. The restricted randomization uses this correlation structure to reduce the error variance of the experiment. The paper computes the expected mean square for each source of variation in the ORRD design under a suitable linear model. It also provides approximate F-tests for treatment and ranking group effects. The efficiency of the ORRD is investigated through empirical power studies. Finally, an example based on a uniformity field trial illustrates the use of the method in a split-plot experiment. Supplementary material to this paper is provided online.

Background Randomization is considered to be a key feature to protect against bias in randomized clinical trials. Randomization induces comparability with respect to known and unknown covariates, mitigates selection bias, and provides a basis for inference. Although various randomization procedures have been proposed, no single procedure performs uniformly best. In the design phase of a clinical trial, the scientist has to decide which randomization procedure to use, taking into account the practical setting of the trial with respect to the potential of bias. Less emphasis has been placed on this important design decision than on analysis, and less support has been available to guide the scientist in making this decision. Methods We propose a framework that weights the properties of the randomization procedure with respect to practical needs of the research question to be answered by the clinical trial. In particular, the framework assesses the impact of chronological and selection bias on the probability of a type I error. The framework is applied to a case study with a 2-arm parallel group, single center randomized clinical trial with continuous endpoint, with no-interim analysis, 1:1 allocation and no adaptation in the randomization process. Results In so doing, we derive scientific arguments for the selection of an appropriate randomization procedure and develop a template which is illustrated in parallel by a case study. Possible extensions are discussed. Conclusion The proposed ERDO framework guides the investigator through a template for the choice of a randomization procedure, and provides easy to use tools for the assessment. The barriers for the thorough reporting and assessment of randomization procedures could be further reduced in the future when regulators and pharmaceutical companies employ similar, standardized frameworks for the choice of a randomization procedure.

Reviews have repeatedly noted important methodological issues in the conduct and reporting of cluster randomized controlled trials (C-RCTs). These reviews usually focus on whether the intracluster correlation was explicitly considered in the design and analysis of the C-RCT. However, another important aspect requiring special attention in C-RCTs is the risk for imbalance of covariates at baseline. Imbalance of important covariates at baseline decreases statistical power and precision of the results. Imbalance also reduces face validity and credibility of the trial results. The risk of imbalance is elevated in C-RCTs compared to trials randomizing individuals because of the difficulties in recruiting clusters and the nested nature of correlated patient-level data. A variety of restricted randomization methods have been proposed as way to minimize risk of imbalance. However, there is little guidance regarding how to best restrict randomization for any given C-RCT. The advantages and limitations of different allocation techniques, including stratification, matching, minimization, and covariate-constrained randomization are reviewed as they pertain to C-RCTs to provide investigators with guidance for choosing the best allocation technique for their trial.

Background and aim Some parallel-group cluster-randomized trials use covariate-constrained rather than simple randomization. This is done to increase the chance of balancing the groups on cluster- and patient-level baseline characteristics. This study assessed how well two covariate-constrained randomization methods balanced baseline characteristics compared with simple randomization. Methods We conducted a mock 3-year cluster-randomized trial, with no active intervention, that started April 1, 2014, and ended March 31, 2017. We included a total of 11,832 patients from 72 hemodialysis centers (clusters) in Ontario, Canada. We randomly allocated the 72 clusters into two groups in a 1:1 ratio on a single date using individual- and cluster-level data available until April 1, 2013. Initially, we generated 1000 allocation schemes using simple randomization. Then, as an alternative, we performed covariate-constrained randomization based on historical data from these centers. In one analysis, we restricted on a set of 11 individual-level prognostic variables; in the other, we restricted on principal components generated using 29 baseline historical variables. We created 300,000 different allocations for the covariate-constrained randomizations, and we restricted our analysis to the 30,000 best allocations based on the smallest sum of the penalized standardized differences. We then randomly sampled 1000 schemes from the 30,000 best allocations. We summarized our results with each randomization approach as the median (25th and 75th percentile) number of balanced baseline characteristics. There were 156 baseline characteristics, and a variable was balanced when the between-group standardized difference was ≤ 10%. Results The three randomization techniques had at least 125 of 156 balanced baseline characteristics in 90% of sampled allocations. The median number of balanced baseline characteristics using simple randomization was 147 (142, 150). The corresponding value for covariate-constrained randomization using 11 prognostic characteristics was 149 (146, 151), while for principal components, the value was 150 (147, 151). Conclusion In this setting with 72 clusters, constraining the randomization using historical information achieved better balance on baseline characteristics compared with simple randomization; however, the magnitude of benefit was modest.

Fatty acid taste (FAT) perception is involved in the regulation of dietary fat intake, where impaired FAT is associated with increased fatty food intake. There are a number of FAT receptors identified on human taste cells that are potentially responsible for FAT perception. Manipulating dietary fat intake, and in turn FAT perception, would elucidate the receptors that are associated with long-term regulation of FAT perception. The present study aimed to assess associations between diet-mediated changes to FAT receptors and FAT perception in humans. A co-twin randomised controlled trial was conducted, where each matching twin within a pair were randomly allocated to either an 8-week low-fat (LF; <20 % energy fat) or an 8-week high-fat (HF; >35 % energy fat) diet. At baseline and week 8, fungiform papillae were biopsied in the fasted state and FAT receptor gene expressions (cluster of differentiation 36 ( CD36 ), free fatty acid receptor 2 ( FFAR2 ), FFAR4 , G protein-coupled receptor 84 ( GPR84 ) and a delayed rectifying K + channel (K + voltage-gated channel subfamily A member 2; KCNA2 )) were measured using RT-PCR; and FAT threshold (FATT) was assessed using three-alternate forced choice methodology. Linear mixed models were fitted, adjusting for correlation between co-twins. Intake was compliant with the study design, with the LF and HF groups consuming 14·8 and 39·9 % energy from fat, respectively. Expression of FFAR4 increased by 38 % in the LF group ( P = 0·023; time–diet interaction P = 0·063). Δ FFAR4 (Δ, week 8–baseline) was associated with Δfat intake (g) ( = −159·4; P < 0·001) and ΔFATT ( = −8·8; P = 0·016). In summary, FFAR4 is involved in long-term diet-mediated changes to FAT perception. Manipulating dietary fat intake, and therefore FFAR4 expression, might aid in reducing taste-mediated passive overconsumption of fatty foods.

Reviews of the handling of covariates in trials have explicitly excluded cluster randomized trials (CRTs). In this study, we review the use of covariates in randomization, the reporting of covariates, and adjusted analyses in CRTs. We reviewed a random sample of 300 CRTs published between 2000 and 2008 across 150 English language journals. Fifty-eight percent of trials used covariates in randomization. Only 69 (23%) included tables of cluster- and individual-level covariates. Fifty-eight percent reported significance tests of baseline balance. Of 207 trials that reported baseline measures of the primary outcome, 155 (75%) subsequently adjusted for these in analyses. Of 174 trials that used covariates in randomization, 30 (17%) included an analysis adjusting for all those covariates. Of 219 trial reports that included an adjusted analysis of the primary outcome, only 71 (32%) reported that covariates were chosen a priori. There are some marked discrepancies between practice and guidance on the use of covariates in the design, analysis, and reporting of CRTs. It is essential that researchers follow guidelines on the use and reporting of covariates in CRTs, promoting the validity of trial conclusions and quality of trial reports.

Regression discontinuity (RD) is a quasi-experimental design that may provide valid estimates of treatment effects in case of continuous outcomes. We aimed to evaluate validity and precision in the RD design for dichotomous outcomes. We performed validation studies in three large randomized controlled trials (RCTs) (Corticosteroid Randomization After Significant Head injury [CRASH], the Global Utilization of Streptokinase and Tissue Plasminogen Activator for Occluded Coronary Arteries [GUSTO], and PROspective Study of Pravastatin in elderly individuals at risk of vascular disease [PROSPER]). To mimic the RD design, we selected patients above and below a cutoff (e.g., age 75 years) randomized to treatment and control, respectively. Adjusted logistic regression models using restricted cubic splines (RCS) and polynomials and local logistic regression models estimated the odds ratio (OR) for treatment, with 95% confidence intervals (CIs) to indicate precision. In CRASH, treatment increased mortality with OR 1.22 [95% CI 1.06–1.40] in the RCT. The RD estimates were 1.42 (0.94–2.16) and 1.13 (0.90–1.40) with RCS adjustment and local regression, respectively. In GUSTO, treatment reduced mortality (OR 0.83 [0.72–0.95]), with more extreme estimates in the RD analysis (OR 0.57 [0.35; 0.92] and 0.67 [0.51; 0.86]). In PROSPER, similar RCT and RD estimates were found, again with less precision in RD designs. We conclude that the RD design provides similar but substantially less precise treatment effect estimates compared with an RCT, with local regression being the preferred method of analysis.