Analyzing the COVID-19 intensive care unit bed occupancy with random regression coefficient Poisson models

Abstract COVID-19 has shown the need for spatio-temporal monitoring of the saturation of healthcare capacity in epidemic contexts. However, the scarcity and lack of homogeneity of data is a challenge. Under a random regression coefficient Poisson model, this work derives area-level predictors of occupied bed counts and occupancy ratios in intensive care units, and introduces bootstrap estimators of mean squared errors. Maximum likelihood estimators of model parameters and mode predictors of random effects are calculated using a Laplace approximation algorithm. Simulation experiments are conducted to investigate the behaviour of the fitting algorithm, the predictors and the mean squared error estimators. A forward prediction study is also initiated, defining the out-of-sample predictors and their mean squared errors. The new statistical methodology is applied to data from the Spanish region Castilla y León. The target is to estimate and predict the proportions of beds occupied by COVID-19 patients in intensive care units by health areas and days. Mathematics Subject Classiffication: 62F40 Bootstrap, jacknife and other resampling methods; 62J12 Generalized linear models; 62P10 Applications of statistics to biology and medical sciences.