BACKGROUND

The stepped-wedge (SW) cluster-randomized trial design is particularly suitable for, and has been frequently adopted for, pragmatic clinical trials. Initially, all clusters receive control treatment. Subsequently, at predefined steps, clusters are randomized to switch to intervention. Outcomes are measured at every step. All participants receive the intervention at the end of the study. An SW trial is advantageous in eliminating the ethical dilemma of withholding an effective treatment (for closed-cohort trials); is logistically more manageable due to stepwise switchover from control to intervention; and, because it is based on longitudinal measurements, is informative about the trend in treatment effect.

OBJECTIVES

The goal of this study was to develop novel SW design methodologies, specifically focusing on making them more pragmatic for patient-centered outcome research. Successful completion of the proposed research could advance patient-centered outcomes research and methodological research by providing scientifically rigorous design tools for pragmatic trials. Such methodologies could help attract patients to enroll into trials because eventually all participants receive the active intervention. The specific aims were as follows: : Use mixed methods to help prioritize design issues in pragmatic SW trials from patients' and clinical stakeholders' perspectives. : Develop a unified generalized estimating equation (GEE) framework that accommodates different types of SW trials and addresses pragmatic issues identified in aim 1. : Incorporate bayesian adaptive approaches into SW trial design. : Develop methods to estimate sample size for longitudinal and crossover cluster-randomized trials. : Facilitate the dissemination and implementation of novel design methods.

METHODS

We developed a unified GEE framework for the design of different types of SW trials. We derived closed-form sample-size formulas using independent working correlation matrices. The sample-size formulas were further extended to accommodate various types of patient-centered outcomes, missing data, unbalanced randomization, randomly varying cluster sizes, and complicated correlation structures. Stakeholders were actively engaged to identify high-priority issues to guide our research effort. We developed a bayesian adaptive strategy for SW trials based on posterior predictive probability. At each step, we calculate the predictive probability of declaring the intervention effective at the end of trial given interim data. We constructed decision rules to determine whether the trial should be stopped early due to overwhelming evidence of efficacy/futility. The predictive probability was estimated through Markov chain Monte Carlo (MCMC) simulation, and values of design parameters were specified by numerical search to achieve desired operational characteristics. Our design methods were evaluated based on extensive simulation. We considered the methods to perform well if, over a wide range of design configurations, the empirical powers and type I errors were close to their nominal levels. For the bayesian adaptive design, we also evaluated metrics such as probability of early stopping and expected number of steps.

RESULTS

Based on the GEE framework, we developed closed-form sample-size solutions that can be applied to different types of SW trials, as well as to longitudinal and crossover cluster-randomized trials. The sample-size solutions accommodate pragmatic design issues, including different types of outcomes, unbalanced randomization, arbitrary patterns and probabilities of missing data, complicated correlation structures, and randomly varying cluster sizes. For count outcomes, the sample-size solution further accounts for overdispersion and unequal lengths of follow-up. Based on theory, we characterized the impact of design parameters on sample size. We present strategies to address the problem of underestimated variance by the GEE sandwich estimator when the number of clusters is small. We developed a bayesian group sequential method for SW trials, based on the posterior predictive probability of declaring the intervention effective at the end of study conditional on interim data. Detailed algorithms to numerically determine design parameters and evaluate operational characteristics are presented. For both GEE and bayesian methods, we developed free R codes to obtain experimental design solutions and conduct simulation.

CONCLUSIONS

Our research resulted in closed-form sample-size formulas for the design of different types of SW trials and longitudinal and crossover cluster-randomized trials. These formulas accommodate different types of patient-centered outcomes and various pragmatic design issues. We incorporated bayesian group sequential strategy into the design of SW trials, which will enable researchers to stop trials early if they observe overwhelming evidence of efficacy/futility in the interim data. R codes to implement the developed design methods are freely available to the research community. These methodology developments facilitate proper design and conduct of SW trials in everyday clinical settings.

LIMITATIONS

GEE sample-size formulas, which were derived through the use of independent working correlations, might be less efficient than those derived using the true correlation. We have provided practical guidelines when efficiency loss might become severe. Another limitation is that in this study, we assumed missing data to be missing completely at random (MCAR). Non-MCAR missing data were not investigated.