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Power calculation for cross-sectional stepped wedge cluster randomized trials with variable cluster sizes.

ABSTRACT: Standard sample size calculation formulas for stepped wedge cluster randomized trials (SW-CRTs) assume that cluster sizes are equal. When cluster sizes vary substantially, ignoring this variation may lead to an under-powered study. We investigate the relative efficiency of a SW-CRT with varying cluster sizes to equal cluster sizes, and derive variance estimators for the intervention effect that account for this variation under a mixed effects model-a commonly used approach for analyzing data from cluster randomized trials. When cluster sizes vary, the power of a SW-CRT depends on the order in which clusters receive the intervention, which is determined through randomization. We first derive a variance formula that corresponds to any particular realization of the randomized sequence and propose efficient algorithms to identify upper and lower bounds of the power. We then obtain an "expected" power based on a first-order approximation to the variance formula, where the expectation is taken with respect to all possible randomization sequences. Finally, we provide a variance formula for more general settings where only the cluster size arithmetic mean and coefficient of variation, instead of exact cluster sizes, are known in the design stage. We evaluate our methods through simulations and illustrate that the average power of a SW-CRT decreases as the variation in cluster sizes increases, and the impact is largest when the number of clusters is small.

SUBMITTER: Harrison LJ

PROVIDER: S-EPMC7165039 | biostudies-literature | 2020 Sep

REPOSITORIES: biostudies-literature

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Power calculation for cross-sectional stepped wedge cluster randomized trials with variable cluster sizes.

Harrison Linda J LJ Chen Tom T Wang Rui R

Biometrics 20191114 3

Standard sample size calculation formulas for stepped wedge cluster randomized trials (SW-CRTs) assume that cluster sizes are equal. When cluster sizes vary substantially, ignoring this variation may lead to an under-powered study. We investigate the relative efficiency of a SW-CRT with varying cluster sizes to equal cluster sizes, and derive variance estimators for the intervention effect that account for this variation under a mixed effects model-a commonly used approach for analyzing data fro ...[more]

PMID: 31625596

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Project description:BackgroundThe stepped-wedge cluster randomized trial (SW-CRT) design has become popular in healthcare research. It is an appealing alternative to traditional cluster randomized trials (CRTs) since the burden of logistical issues and ethical problems can be reduced. Several approaches for sample size determination for the overall treatment effect in the SW-CRT have been proposed. However, in certain situations we are interested in examining the heterogeneity in treatment effect (HTE) between groups instead. This is equivalent to testing the interaction effect. An important example includes the aim to reduce racial disparities through healthcare delivery interventions, where the focus is the interaction between the intervention and race. Sample size determination and power calculation for detecting an interaction effect between the intervention status variable and a key covariate in the SW-CRT study has not been proposed yet for binary outcomes.MethodsWe utilize the generalized estimating equation (GEE) method for detecting the heterogeneity in treatment effect (HTE). The variance of the estimated interaction effect is approximated based on the GEE method for the marginal models. The power is calculated based on the two-sided Wald test. The Kauermann and Carroll (KC) and the Mancl and DeRouen (MD) methods along with GEE (GEE-KC and GEE-MD) are considered as bias-correction methods.ResultsAmong three approaches, GEE has the largest simulated power and GEE-MD has the smallest simulated power. Given cluster size of 120, GEE has over 80% statistical power. When we have a balanced binary covariate (50%), simulated power increases compared to an unbalanced binary covariate (30%). With intermediate effect size of HTE, only cluster sizes of 100 and 120 have more than 80% power using GEE for both correlation structures. With large effect size of HTE, when cluster size is at least 60, all three approaches have more than 80% power. When we compare an increase in cluster size and increase in the number of clusters based on simulated power, the latter has a slight gain in power. When the cluster size changes from 20 to 40 with 20 clusters, power increases from 53.1% to 82.1% for GEE; 50.6% to 79.7% for GEE-KC; and 48.1% to 77.1% for GEE-MD. When the number of clusters changes from 20 to 40 with cluster size of 20, power increases from 53.1% to 82.1% for GEE; 50.6% to 81% for GEE-KC; and 48.1% to 79.8% for GEE-MD.ConclusionsWe propose three approaches for cluster size determination given the number of clusters for detecting the interaction effect in SW-CRT. GEE and GEE-KC have reasonable operating characteristics for both intermediate and large effect size of HTE.

Project description:BACKGROUND:Cluster randomised trials with unequal sized clusters often have lower precision than with clusters of equal size. To allow for this, sample sizes are inflated by a modified version of the design effect for clustering. These inflation factors are valid under the assumption that randomisation is stratified by cluster size. We investigate the impact of unequal cluster size when that constraint is relaxed, with particular focus on the stepped-wedge cluster randomised trial, where this is more difficult to achieve. METHODS:Assuming a multi-level mixed effect model with exchangeable correlation structure for a cross-sectional design, we use simulation methods to compare the precision for a trial with clusters of unequal size to a trial with clusters of equal size (relative efficiency). For a range of scenarios we illustrate the impact of various design features (the cluster-mean correlation - a function of the intracluster correlation and the cluster size, the number of clusters, number of randomisation sequences) on the average and distribution of the relative efficiency. RESULTS:Simulations confirm that the average reduction in precision, due to varying cluster sizes, is smaller in a stepped-wedge trial compared to the parallel trial. However, the variance of the distribution of the relative efficiency is large; and is larger under the stepped-wedge design compared to the parallel design. This can result in large variations in actual power, depending on the allocation of clusters to sequences. Designs with larger variations in cluster sizes, smaller number of clusters and studies with smaller cluster-mean correlations (smaller cluster sizes or smaller intra-cluster correlation) are particularly at risk. CONCLUSION:The actual realised power in a stepped-wedge trial might be substantially higher or lower than that estimated. This is particularly important when there are a small number of clusters or the variability in cluster sizes is large. Constraining the randomisation on cluster size, where feasible, might mitigate this effect.

Project description:BackgroundIn a cross-sectional stepped-wedge trial with unequal cluster sizes, attained power in the trial depends on the realized allocation of the clusters. This attained power may differ from the expected power calculated using standard formulae by averaging the attained powers over all allocations the randomization algorithm can generate. We investigated the effect of design factors and allocation characteristics on attained power and developed models to predict attained power based on allocation characteristics.MethodBased on data simulated and analyzed using linear mixed-effects models, we evaluated the distribution of attained powers under different scenarios with varying intraclass correlation coefficient (ICC) of the responses, coefficient of variation (CV) of the cluster sizes, number of cluster-size groups, distributions of group sizes, and number of clusters. We explored the relationship between attained power and two allocation characteristics: the individual-level correlation between treatment status and time period, and the absolute treatment group imbalance. When computational time was excessive due to a scenario having a large number of possible allocations, we developed regression models to predict attained power using the treatment-vs-time period correlation and absolute treatment group imbalance as predictors.ResultsThe risk of attained power falling more than 5% below the expected or nominal power decreased as the ICC or number of clusters increased and as the CV decreased. Attained power was strongly affected by the treatment-vs-time period correlation. The absolute treatment group imbalance had much less impact on attained power. The attained power for any allocation was predicted accurately using a logistic regression model with the treatment-vs-time period correlation and the absolute treatment group imbalance as predictors.ConclusionIn a stepped-wedge trial with unequal cluster sizes, the risk that randomization yields an allocation with inadequate attained power depends on the ICC, the CV of the cluster sizes, and number of clusters. To reduce the computational burden of simulating attained power for allocations, the attained power can be predicted via regression modeling. Trial designers can reduce the risk of low attained power by restricting the randomization algorithm to avoid allocations with large treatment-vs-time period correlations.

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Power calculation for cross-sectional stepped wedge cluster randomized trials with variable cluster sizes.

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Power calculation for cross-sectional stepped wedge cluster randomized trials with variable cluster sizes.

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