Sample size requirements for testing treatment effect heterogeneity in cluster randomized trials with binary outcomes

Cluster randomized trials (CRTs) refer to a popular class of experiments in which randomization is carried out at the group level. While methods have been developed for planning CRTs to study the average treatment effect, and more recently, to study the heterogeneous treatment effect, the development for the latter objective has currently been limited to a continuous outcome. Despite the prevalence of binary outcomes in CRTs, determining the necessary sample size and statistical power for detecting differential treatment effects in CRTs with a binary outcome remain unclear. To address this methodological gap, we develop sample size procedures for testing treatment effect heterogeneity in two-level CRTs under a generalized linear mixed model. Closed-form sample size expressions are derived for a binary effect modifier, and in addition, a computationally efficient Monte Carlo approach is developed for a continuous effect modifier. Extensions to multiple effect modifiers are also discussed. We conduct simulations to examine the accuracy of the proposed sample size methods. We present several numerical illustrations to elucidate features of the proposed formulas and to compare our method to the approximate sample size calculation under a linear mixed model. Finally, we use data from the Strategies and Opportunities to Stop Colon Cancer in Priority Populations (STOP CRC) CRT to illustrate the proposed sample size procedure for testing treatment effect heterogeneity.

Power and sample size calculation for stepped-wedge designs with discrete outcomes

BACKGROUND

Stepped-wedge designs (SWD) are increasingly used to evaluate the impact of changes to the process of care within health care systems. However, to generate definitive evidence, a correct sample size calculation is crucial to ensure such studies are properly powered. The seminal work of Hussey and Hughes (Contemp Clin Trials 28(2):182-91, 2004) provides an analytical formula for power calculations with normal outcomes using a linear model and simple random effects. However, minimal development and evaluation have been done for power calculation with non-normal outcomes on their natural scale (e.g., logit, log). For example, binary endpoints are common, and logistic regression is the natural multilevel model for such clustered data.

METHODS

We propose a power calculation formula for SWD with either normal or non-normal outcomes in the context of generalized linear mixed models by adopting the Laplace approximation detailed in Breslow and Clayton (J Am Stat Assoc 88(421):9-25, 1993) to obtain the covariance matrix of the estimated parameters.

RESULTS

We compare the performance of our proposed method with simulation-based sample size calculation and demonstrate its use on a study of patient-delivered partner therapy for STI treatment and a study that assesses the impact of providing additional benchmark prevalence information in a radiologic imaging report. To facilitate adoption of our methods we also provide a function embedded in the R package "swCRTdesign" for sample size and power calculation for multilevel stepped-wedge designs.

CONCLUSIONS

Our method requires minimal computational power. Therefore, the proposed procedure facilitates rapid dynamic updates of sample size calculations and can be used to explore a wide range of design options or assumptions.

Sample size determination for multilevel hierarchical designs using generalized linear mixed models

A unified statistical methodology of sample size determination is developed for hierarchical designs that are frequently used in many areas, particularly in medical and health research studies. The solid foundation of the proposed methodology opens a new horizon for power analysis in presence of various conditions. Important features such as joint significance testing, unequal allocations of clusters across intervention groups, and differential attrition rates over follow up time points are integrated to address some useful questions that investigators often encounter while conducting such studies. Proposed methodology is shown to perform well in terms of maintaining type I error rates and achieving the target power under various conditions. Proposed method is also shown to be robust with respect to violation of distributional assumptions of random-effects.

Power and sample size for the S:T repeated measures design combined with a linear mixed-effects model allowing for missing data

Tango (Biostatistics 2016) proposed a new repeated measures design called the S:T repeated measures design, combined with generalized linear mixed-effects models and sample size calculations for a test of the average treatment effect that depend not only on the number of subjects but on the number of repeated measures before and after randomization per subject used for analysis. The main advantages of the proposed design combined with the generalized linear mixed-effects models are (1) it can easily handle missing data by applying the likelihood-based ignorable analyses under the missing at random assumption and (2) it may lead to a reduction in sample size compared with the simple pre-post design. In this article, we present formulas for calculating power and sample sizes for a test of the average treatment effect allowing for missing data within the framework of the S:T repeated measures design with a continuous response variable combined with a linear mixed-effects model. Examples are provided to illustrate the use of these formulas.

On the repeated measures designs and sample sizes for randomized controlled trials

For the analysis of longitudinal or repeated measures data, generalized linear mixed-effects models provide a flexible and powerful tool to deal with heterogeneity among subject response profiles. However, the typical statistical design adopted in usual randomized controlled trials is an analysis of covariance type analysis using a pre-defined pair of "pre-post" data, in which pre-(baseline) data are used as a covariate for adjustment together with other covariates. Then, the major design issue is to calculate the sample size or the number of subjects allocated to each treatment group. In this paper, we propose a new repeated measures design and sample size calculations combined with generalized linear mixed-effects models that depend not only on the number of subjects but on the number of repeated measures before and after randomization per subject used for the analysis. The main advantages of the proposed design combined with the generalized linear mixed-effects models are (1) it can easily handle missing data by applying the likelihood-based ignorable analyses under the missing at random assumption and (2) it may lead to a reduction in sample size, compared with the simple pre-post design. The proposed designs and the sample size calculations are illustrated with real data arising from randomized controlled trials.