Sample Size Determination for Comparing Slopes in Cluster Randomized Trials With Longitudinal Measurements

In cluster randomized trials with longitudinal measurements (CRTLMs), clusters of subjects, rather than individual subjects, are randomly assigned to either control or intervention groups. Measurements are collected from these subjects repeatedly at prespecified times until the end of the study. In clinical research, the focus is typically on investigating trends or progress over time to evaluate the effectiveness of a new treatment or track disease progression, rather than solely analyzing mean values or endpoint measurements. For comparing slopes between two groups, we have derived closed-form sample size formulas based on the generalized estimating equation (GEE) approach under independence working correlation. Our proposed method is highly flexible, allowing for the incorporation of unbalanced randomization, arbitrary correlation structures, various missing data scenarios through observational probabilities and missing patterns, and variability in cluster sizes. This flexibility provides a practical and robust sample size solution for CRTLMs. Simulation studies demonstrate that the proposed method performs well, maintaining empirical power and type I error rate close to their nominal values. Additionally, we illustrate the application of our method using a real clinical trial, showcasing its practical utility in real-world implementation.