Modeling Zero Inflation and Overdispersion in the Length of Hospital Stay for Patients with Ischaemic Heart Disease

Abstract

Ischaemic heart disease is the top one cause of death in the world; however, quantifying its burden in a population is a challenge. Hospitalization data provide a proxy for measuring the severity of ischaemic heart disease. Length of stay (LOS) in hospital is often used as an indicator of hospital efficiency and a proxy of resource consumption, which may be characterized as zero-inflated if there is an over-abundance of zeros, or zero-deflated if there are fewer zeros than expected under a standard count model. Such data may also have a highly right-skewed distribution for the nonzero values. Hurdle models and zero inflated models were developed to accommodate both the excess zeros and skewness of the data with various configuration of spatial random effects, as well as allowing for analysis of nonlinear effect of seasonality and other fixed effect covariates. We draw attention to considerable drawbacks with regards to model misspecifications. Modeling and inference use the fully Bayesian approach via Markov Chain Monte Carlo (MCMC) simulation techniques. Our results indicate that both hurdle and zero inflated models accounting for clustering at the residential neighborhood level outperforms the models without counterpart models, and modeling the count component as a negative binomial distribution is significantly superior to ones with a Poisson distribution. Additionally, hurdle models provide a better fit compared to the counterpart zero-inflated models in our application.