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In stepped-wedge cluster randomized trials (SW-CRTs), clusters are randomized not to treatment and control arms but to sequences dictating the times of crossing from control to intervention conditions. Randomization is an essential feature of this design but application of standard methods to promote and report on balance at baseline is not straightforward. We aimed to describe current methods of randomization and reporting of balance at baseline in SW-CRTs. We used electronic searches to identify primary reports of SW-CRTs published between 2016 and 2022. Across 160 identified trials, the median number of clusters randomized was 11 (Q1-Q3: 8-18). Sixty-three (39%) used restricted randomization—most often stratification based on a single cluster-level covariate; 12 (19%) of these adjusted for the covariate(s) in the primary analysis. Overall, 50 (31%) and 134 (84%) reported on balance at baseline on cluster- and individual-level characteristics, respectively. Balance on individual-level characteristics was most often reported by condition in cross-sectional designs and by sequence in cohort designs. Authors reported baseline imbalances in 72 (45%) trials. SW-CRTs often randomize a small number of clusters using unrestricted allocation. Investigators need guidance on appropriate methods of randomization and assessment and reporting of balance at baseline.

Background The HEALing (Helping to End Addiction Long-term SM ) Communities Study (HCS) is a multi-site parallel group cluster randomized wait-list comparison trial designed to evaluate the effect of the Communities That Heal (CTH) intervention compared to usual care on opioid overdose deaths. Covariate-constrained randomization (CCR) was applied to balance the community-level baseline covariates in the HCS. The purpose of this paper is to evaluate the performance of model-based tests and permutation tests in the HCS setting. We conducted a simulation study to evaluate type I error rates and power for model-based and permutation tests for the multi-site HCS as well as for a subgroup analysis of a single state (Massachusetts). We also investigated whether the maximum degree of imbalance in the CCR design has an impact on the performance of the tests. Methods The primary outcome, the number of opioid overdose deaths, is count data assessed at the community level that will be analyzed using a negative binomial regression model. We conducted a simulation study to evaluate the type I error rates and power for 3 tests: (1) Wald-type t -test with small-sample corrected empirical standard error estimates, (2) Wald-type z -test with model-based standard error estimates, and (3) permutation test with test statistics calculated by the difference in average residuals for the two groups. Results Our simulation results demonstrated that Wald-type t -tests with small-sample corrected empirical standard error estimates from the negative binomial regression model maintained proper type I error. Wald-type z -tests with model-based standard error estimates were anti-conservative. Permutation tests preserved type I error rates if the constrained space was not too small. For all tests, the power was high to detect the hypothesized 40% reduction in opioid overdose deaths for the intervention vs. comparison group both for the overall HCS and the subgroup analysis of Massachusetts (MA). Conclusions Based on the results of our simulation study, the Wald-type t -test with small-sample corrected empirical standard error estimates from a negative binomial regression model is a valid and appropriate approach for analyzing cluster-level count data from the HEALing Communities Study. Trial registration ClinicalTrials.gov http://www.clinicaltrials.gov ; Identifier: NCT04111939

IntroductionLow back pain is a common problem and a substantial source of morbidity and disability worldwide. Patients frequently visit the emergency department (ED) for low back pain, but many experience persistent symptoms at 3 months despite frequent receipt of opioids. Although physical therapy interventions have been demonstrated to improve patient functioning in the outpatient setting, no randomised trial has yet to evaluate physical therapy in the ED setting.Methods and analysisThis is a single-centre cluster-randomised trial of an embedded ED physical therapy intervention for acute low back pain. We used a covariate-constrained approach to randomise individual physicians (clusters) at an urban academic ED in Chicago, Illinois, USA, to receive, or not receive, an embedded physical therapist on their primary treatment team to evaluate all patients with low back pain. We will then enrol individual ED patients with acute low back pain and allocate them to the embedded physical therapy or usual care study arms, depending on the randomisation assignment of their treating physician. We will follow patients to a primary endpoint of 3 months and compare a primary outcome of change in PROMIS-Pain Interference score and secondary outcomes of change in modified Oswestry Disability Index score and patient-reported opioid use. Our primary approach will be a modified intention-to-treat analysis, whereby all participants who complete at least one follow-up data time point will be included in analyses, regardless of their or their physicians’ adherence to their assigned study arm.Ethics and disseminationThis trial is funded by the US Agency for Healthcare Research and Quality (R01HS027426) and was approved by the Northwestern University Institutional Review Board. All physician and patient participants will give written informed consent to study participation. Trial results will be submitted for presentation at scientific meetings and for publication in peer-reviewed journals.Trial registration numberClinicalTrials.gov (NCT04921449)

Background In cluster-randomized controlled trials (C-RCTs), covariate-constrained randomization (CCR) methods efficiently control imbalance in multiple baseline cluster-level variables, but the choice of imbalance metric to define the subset of “adequately balanced” possible allocation schemes for C-RCTs involving more than two arms and continuous variables is unclear. In an ongoing three-armed C-RCT, we chose the min(three Kruskal–Wallis [KW] test P values) > 0.30 as our metric. We use simulation studies to explore the performance of this and other metrics of baseline variable imbalance in CCR. Methods We simulated three continuous variables across three arms under varying allocation ratios and assumptions. We compared the performance of min(analysis of variance [ANOVA] P value) > 0.30, min(KW P value) > 0.30, multivariate analysis of variance (MANOVA) P value > 0.30, min(nine possible t test P values) > 0.30, and min(Wilcoxon rank-sum [WRS] P values) > 0.30. Results Pairwise comparison metrics ( t test and WRS) tended to be the most conservative, providing the smallest subset of allocation schemes (10%–13%) meeting criteria for acceptable balance. Sensitivity of the min( t test P values) > 0.30 for detecting non-trivial imbalance was 100% for both hypothetical and resampled simulation scenarios. The KW criterion maintained higher sensitivity than both the MANOVA and ANOVA criteria (89% to over 99%) but was not as sensitive as pairwise criteria. Conclusions Our criterion, the KW P value > 0.30, to signify “acceptable” balance was not the most conservative, but it appropriately identified imbalance in the majority of simulations. Since all are related, CCR algorithms involving any of these imbalance metrics for continuous baseline variables will ensure robust simultaneous control over multiple continuous baseline variables, but we recommend care in determining the threshold of “acceptable” levels of (im)balance. Trial registration This trial is registered on ClinicalTrials.gov (initial post: December 1, 2016; identifier: NCT02979444 ).

Background Pragmatic trials often consist of cluster-randomized controlled trials (C-RCTs), where staff of existing clinics or sites deliver interventions and randomization occurs at the site level. Covariate-constrained randomization (CCR) methods are often recommended to minimize imbalance on important site characteristics across intervention and control arms because sizable imbalances can occur by chance in simple randomizations when the number of units to be randomized is relatively small. CCR methods involve multiple random assignments initially, an assessment of balance achieved on site-level covariates from each randomization, and the final selection of an allocation that produces acceptable balance. However, no clear consensus exists on how to assess imbalance or identify allocations with sufficient balance. In this article, we describe an overall imbalance index ( I ) that is based on the mean of the absolute value of the standardized differences in means on the site characteristics. Methods We derive the theoretical distribution of I , then conduct simulation studies to examine its empirical properties under the varying covariate distributions and inter-correlations. Results I has an expected value of 0.798 and, assuming independent site characteristics, a variance of 0.363/ k , where k is the number of site characteristics being balanced. Simulations indicated that the properties of I are robust under varying covariate circumstances as long as k is greater than 3 and the covariates are not too highly inter-correlated. Conclusions We recommend that values of I below the 10th percentile indicate sufficient overall site balance in CCRs. Definitions of acceptable randomizations might also include individual covariate criteria specified in advance, in addition to overall balance criteria.

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.