Since many empirical and scientific analyses are based on count data, modeling such data is of great importance. Examples of these analyses include regression of the number of doctor visits based on a set of predictor variables. Obviously, access to an appropriate predictive regression model can have a significant impact on decision-making and planning.

In this research, aiming to improve modeling accuracy, Poisson regression has been combined with an artificial neural network to provide a better modeling framework for count data. In this regard, a Poisson neural network regression model along with a computational algorithm is presented. To evaluate its performance in terms of parameter estimation and predictive accuracy, it is compared with two ensemble machine learning models: Random Forest and XGBoost.

On the other hand, to investigate the overdispersion phenomenon, the Conway–Maxwell–Poisson neural network model was used and compared with the Poisson neural network.

By implementing the aforementioned models on a real medical dataset, we demonstrate that the Conway–Maxwell–Poisson neural network regression model exhibits superior performance.