Meta-analyzing count data can be challenging when follow-up time varies across studies. Simply pooling aggregate data over time-periods would result in biased estimates, which may erroneously inform clinical decision-making. In this study, we exploit the convolution property of the Poisson distribution to develop a likelihood for observed cumulative counts over varying follow-up periods, where different Poisson distributions are used to represent the data generating processes for the latent counts in pre-defined successive intervals of follow-up. We illustrate this approach using an example of poststroke seizures, a case in which risk may change over time, and mimic its survival duration with time-varying hazard. Data were extracted from observational studies (1997-2016) reporting poststroke seizures over a maximum of 10 years of follow-up. Three clinically meaningful follow-up time intervals were considered: 0 to 7 days, 8 to 365 days, and 1 to 10 years poststroke. External validation was performed using claims data. Results suggest the incidence rate of seizures was 0.0452 (95% confidence interval: 0.0429, 0.0475), 0.0001 (0, 0.016), and 0.0647 (0.0441, 0.0941) for the three time intervals, respectively, indicating that the risk of seizures changes over time poststroke. We found that the model performed well against the incidence rate of seizures among actual retrospective cohort from claims data. The piecewise Poisson model presents a flexible way to meta-analyze count data over time and mimic survival curves. The results of the piecewise Poisson model are readily interpretable and may spur meaningful clinical action. The method may also be applied to other diseases.