Sample size planning in the design and analysis of cluster randomized trials using the symbolic two-step method

Introduction: Evidence that can be used to improve clinical practice patterns and processes is frequently generated through standard, parallel-arms cluster randomized trial (CRT) designs that test interventions implemented at the center-level. Although the primary endpoint of these trials is often a center-level outcome, patient-level factors may vary between centers and, consequently, may influence the center-level outcome. Furthermore, there may be important factors that predict the variation in the center-level outcome and this knowledge can help contextualize the trial results and inform practice patterns. Methods: Our symbolic two-step method that applies symbolic data analysis to account for patient-level factors when estimating and testing a center-level effect on both the average center-level outcome and its variation was developed for such settings. Herein, we sought to extend the method to prospectively size a CRT so that the application of our method in data analysis is consistent with the design. Results: Our formulaic approach to sample size planning incorporated predictive factors of the within-center variation and accounted for patient-level characteristics. The sample size approximation performed well in many different pragmatic settings. Conclusions: Our symbolic two-step method provides an alternate approach in the design and analysis of CRTs evaluating novel improvement processes within care delivery research.