<p>This study introduces a novel statistical model, termed New Poisson Generalized Lindley (NP-GLindley) distribution, for analysing the count response variable and various associated patient outcomes. The model combines the advantages of the Poisson distribution and a generalisation of the Lindley distribution, offering a flexible approach for count data analysis. The structural characteristics of the presented discrete model have been thoroughly examined. The results demonstrate the efficacy of the NP-GLindley model in identifying the intricacies of count data associated with the healthcare domain. The new model outperforms traditional count regression models in terms of goodness of fit and predictive accuracy and establishes itself as a feasible alternative in case of over-dispersion as well. The proposed model emerges as a promising tool for researchers and practitioners for conducting analysis of healthcare related count data.</p>