Sample Size Estimation for Correlated Count Data With Changes in Dispersion

Clinical endpoints based on repeated measurements arise in many clinical research studies, and require specialized methods for sample size and power calculations. In clinical trials that measure counts over time, such as bleeding events in hemophilia, the dispersion of their distributions might change upon treatment and the measurements might be correlated. The generalized estimating equations (GEE) approach has been widely used for modeling correlated data and comparing rates. In this paper, we investigate the properties of GEE when applied to count outcomes with changes in dispersion. We derive general closed-form formulas to estimate sample size when the dispersion parameters and distributions of count data vary across two correlated measurements based on the GEE approach. These formulas allow for power and sample size estimation for intra-participant comparison of rates before and after an intervention, randomized controlled trials with equal allocation, or matched pairs designs. These formulas are derived for the following distributions: Poisson, negative binomial, zero-inflated Poisson, and zero-inflated negative binomial distributions, and do not assume that measurements before and after an intervention come from the same distribution. Furthermore, we propose modified methods for estimating sample size and confidence intervals for the negative binomial distributions to overcome Type I error inflation, which is especially useful for large changes in the negative binomial dispersion parameter. We perform simulations, and evaluate the performance of the empirical power and Type I error over a range of parameters. Applications and R functions implementing the methods are also provided.