Zero-Inflated Count Regression Models in Solving Challenges Posed by Outlier-Prone Data; an Application to Length of Hospital Stay.

Abstract

Ignoring outliers in data may lead to misleading results. Length of stay (LOS) is often considered a count variable with a high frequency of outliers. This study exemplifies the potential of robust methodologies in enhancing the accuracy and reliability of analyses conducted on skewed and outlier-prone count data of LOS. The application of Zero-Inflated Poisson (ZIP) and robust Zero-Inflated Poisson (RZIP) models in solving challenges posed by outlier LOS data were evaluated. The ZIP model incorporates two components, tackling excess zeros with a zero-inflation component and modeling positive counts with a Poisson component. The RZIP model introduces the Robust Expectation-Solution (RES) algorithm to enhance parameter estimation and address the impact of outliers on the model's performance. Data from 254 intensive care unit patients were analyzed (62.2% male). Patients aged 65 or older accounted for 58.3% of the sample. Notably, 38.6% of patients exhibited zero LOS. The overall mean LOS was 5.89 (± 9.81) days, and 9.45% of cases displayed outliers. Our analysis using the RZIP model revealed significant predictors of LOS, including age, underlying comorbidities (p<0.001), and insurance status (p=0.013). Model comparison demonstrated the RZIP model's superiority over ZIP, as evidenced by lower Akaike information criteria (AIC) and Bayesians information criteria (BIC) values. The application of the RZIP model allowed us to uncover meaningful insights into the factors influencing LOS, paving the way for more informed decision-making in hospital management.