  Cluster randomized trails (CRT) have been widely employed in medical and
public health research. Many clinical count outcomes, such as the number of
falls in nursing homes, exhibit excessive zero values. In the presence of zero
inflation, traditional power analysis methods for count data based on Poisson
or negative binomial distribution may be inadequate. In this study, we present
a sample size method for CRTs with zero-inflated count outcomes. It is
developed based on GEE regression directly modeling the marginal mean of a ZIP
outcome, which avoids the challenge of testing two intervention effects under
traditional modeling approaches. A closed-form sample size formula is derived
which properly accounts for zero inflation, ICCs due to clustering, unbalanced
randomization, and variability in cluster size. Robust approaches, including
t-distribution-based approximation and Jackknife re-sampling variance
estimator, are employed to enhance trial properties under small sample sizes.
Extensive simulations are conducted to evaluate the performance of the proposed
method. An application example is presented in a real clinical trial setting.
