Characterizing the effect of covariates in the rate of admission and duration of stay in the hospital

Abstract

Forecasting the daily resource requirements is important to provide a way for healthcare planners to ensure optimal allocation of scarce resources. Providing the healthcare managers with a model aimed to optimize the scarce available resources could also help improve the problem of long waiting lists. Hospital admissions and patient Length of Stay (LOS) influence the availability of resources. Several factors may affect a patients' LOS and admission patterns. The factors considered in this study include patient characteristics (age, gender, source of admission and locality), weather covariates (minimum, maximum and average daily temperatures), air pollution (Particulate Matter 10 micrometers, Particulate Matter 2.5 micrometers, Carbon Monoxide and Nitrogen Dioxide) and the day of the week. Hospital admissions data was obtained from Mater Dei Hospital, Malta for the period between January 2011 to December 2015, while weather and pollution covariates were obtained from Free Meteo and Environment & Resource Authority (ERA) for the respective period. The distributions used to build these models consist of Coxian Phase-Type Distribution (C-PHD) and Gaussian Mixture Distribution (GMD). Parameter estimation was performed using the Expectation-Maximization algorithm, from which the Weighted-average Information Criterion (WIC) was computed. These distributions were further used to generate a Phase-Type Survival Tree and Gaussian Mixture Survival Tree for both admissions and LOS models, fitted to the previously mentioned covariates. The Survival Trees cluster patients' based on LOS and admissions data with the aim to improve within node homogeneity by selecting covariates providing the best prognostic significance (highest gain in WIC). Furthermore, the models' Goodness-Of-Fit was evaluated based on the WIC statistic, where C-PHD yielded best improvement for both LOS and admission models. Furthermore, the variance in data was analysed illustrating that the C-PHD model reduced within node homogeneity more than GMD did in the admissions model. In contrast, the LOS model showed that GMD reduced the variance more than C-PHD. The quality of work was analysed using Cumulative Distribution Function and Empirical Cumulative Distribution Function plots. These plots can be used effectively to characterize the effect of different factors on the patient LOS and admission patterns.