<p>Marginal Poisson regression models are a common choice for modeling count responses in longitudinal studies. However, these models often encounter a high prevalence of zero counts in the outcome variable, potentially exceeding what is expected by the Poisson distribution. Such zero-inflated scenarios can lead to overdispersion, compromising the validity of inferences derived from Poisson regression models. In this paper, we introduce novel tests for detecting zero inflation or more broadly, zero modification (including both zero inflation and zero deflation) within marginal Poisson regression models. Our methodology involves a direct comparison between the observed frequency of zeros and the expected count based on Poisson models for longitudinal data, obviating the need to specify zero-inflated Poisson models. We assess the performance of these tests through comprehensive simulation studies, evaluating their ability to control Type I errors and achieve statistical power under various conditions. Our findings demonstrate that the proposed test statistics exhibit robust performance across a wide spectrum of scenarios. The methods are illustrated using data from a clinical trial on urinary catheter management.</p>