Length of Stay Analysis of COVID-19 Hospitalizations Using a Count Regression Model and Quantile Regression: A Study in Bologna, Italy

This study aimed to identify and explore the hospital admission risk factors associated with the length of stay (LoS) by applying a relatively novel statistical method for count data using predictors among COVID-19 patients in Bologna, Italy. The second goal of this study was to model the LoS of COVID patients to understand which covariates significantly influenced it and identify the potential risk factors associated with LoS in Bolognese hospitals from 1 February 2020 to 10 May 2021. The clinical settings we focused on were the Intensive Care Unit (ICU) and ordinary hospitalization, including low-intensity stays. We used Poisson, negative binomial (NB), Hurdle–Poisson, and Hurdle–NB regression models to model the LoS. The fitted models were compared using the Akaike information criterion (AIC), Vuong’s test criteria, and Rootograms. We also used quantile regression to model the effects of covariates on the quantile values of the response variable (LoS) using a Poisson distribution, and to explore a range of conditional quantile functions, thereby exposing various forms of conditional heterogeneity and controlling for unobserved individual characteristics. Based on the chosen performance criteria, Hurdle–NB provided the best fit. As an output from the model, we found significant changes in average LoS for each predictor. Compared with ordinary hospitalization and low-intensity stays, the ICU setting increased the average LoS by 1.84-fold. Being hospitalized in long-term hospitals was another contributing factor for LoS, increasing the average LoS by 1.58 compared with regular hospitals. When compared with the age group [50, 60) chosen as the reference, the average LoS decreased in the age groups [0, 10), [30, 40), and [40, 50), and increased in the oldest age group [80, 102). Compared with the second wave, which was chosen as the reference, the third wave did not significantly affect the average LoS, whereas it increased by 1.11-fold during the first wave and decreased by 0.77-fold during out-wave periods. The results of the quantile regression showed that covariates related to the ICU setting, hospitals with longer hospitalization, the first wave, and the out-waves were statistically significant for all the modeled quantiles. The results obtained from our study can help us to focus on the risk factors that lead to an increased LoS among COVID-19 patients and benchmark different models that can be adopted for these analyses.