A novel zero-inflated regression model for overdispersed count data with enhancing its estimation for multicollinearity in medical data

Zero-inflated data characterized by an excessive number of zero observations present significant challenges in statistical modelling, particularly in the presence of overdispersion and multicollinearity. Traditional count regression models often fail to adequately address these complexities, leading to biased and inefficient estimates, inflated variance, and increased mean squared error. To overcome these limitations, this study introduces a novel zero-inflated regression model based on the Poisson-modification of Quasi Lindley distribution, which offers enhanced flexibility for modelling count data with excess zeros and overdispersion. Additionally, to address multicollinearity among explanatory variables, a ridge regression estimator is integrated into the proposed zero-inflated Poisson modification of Quasi Lindley regression model, improving estimation accuracy and interpretability. The performance of the proposed zero-inflated regression model, along with its biased estimator, is evaluated through comprehensive simulation studies and real-world applications in medicine and health, where zero-inflation, overdispersion, and multicollinearity are common. Both simulation and applications demonstrate that the proposed zero-inflated regression model outperforms existing zero-inflated regression models in terms of goodness-of-fit and predictive accuracy. Furthermore, the zero-inflation Poisson-modification of Quasi Lindley ridge regression estimator is shown to be more effective than the zero-inflation Poisson-modification of Quasi Lindley maximum likelihood estimator in the presence of multicollinearity. These results show that the new zero-inflated regression model and the improved way of estimating its parameters work much better than traditional methods. This is helpful for statisticians and data analysts because it gives them a stronger and more reliable tool to handle count data that has many zeros, too much variation, and closely related variables. This leads to more accurate conclusions and better decisions in real-life situations.