Unraveling the COVID-19 hospitalization dynamics in Spain using Bayesian inference

Abstract

Background: One of the main challenges of the COVID-19 pandemic is to make sense of available, but often heterogeneous and noisy data. This contribution presents a data-driven methodology that allows exploring the hospitalization dynamics of COVID-19, exemplified with a study of 17 autonomous regions in Spain from summer 2020 to summer 2021.

Methods: We use data on new daily cases and hospitalizations reported by the Spanish Ministry of Health to implement a Bayesian inference method that allows making short-term predictions of bed occupancy of COVID-19 patients in each of the autonomous regions of the country.

Results: We show how to use the temporal series for the number of daily admissions and discharges from hospital to reproduce the hospitalization dynamics of COVID-19 patients. For the case-study of the region of Aragon, we estimate that the probability of being admitted to hospital care upon infection is 0.090 [0.086-0.094], (95% C.I.), with the distribution governing hospital admission yielding a median interval of 3.5 days and an IQR of 7 days. Likewise, the distribution on the length of stay produces estimates of 12 days for the median and 10 days for the IQR. A comparison between model parameters for the regions analyzed allows to detect differences and changes in policies of the health authorities.

Conclusions: We observe important regional differences, signaling that to properly compare very different populations, it is paramount to acknowledge all the diversity in terms of culture, socio-economic status, and resource availability. To better understand the impact of this pandemic, much more data, disaggregated and properly annotated, should be made available.

Keywords: Bayesian inference; Covid-19; Hospitalization dynamics; Public health; Regional differences.

Fig. 1

Number of daily admissions to hospitals in the region of Aragon. To estimate the parameters of the model, we use the information available up to December 1, 2020. From December 1 the number of admissions is obtained using the estimated parameters and the observed number of daily detected cases, applying Eq. (1). The solid line represents the median value of the estimation and the shaded area the 95% C.I, while the dots represent the observed data. Note that on December 28 the vaccine roll-out started in Spain. The estimated parameters are $\left\{{\text{p}}_{\text{H}}^{\text{AR}},,,{\mathrm{\beta }}^{\text{AR}},,,{\mathrm{\alpha }}^{\text{AR}}\right\}=0.09,3.56,38.06$

Fig. 2

Daily number of beds occupied by COVID-19 patients in Aragon. To estimate the parameters of the model, we used information up to December 1, 2020. From December 1, the occupancy is obtained using the number of new detected cases, together with Eqs. (1) and (5). The solid line represents the median value of the estimation and the shaded area its 95% C.I., while the dots represent the observed data. Note that on December 28 vaccine roll-out started. The estimated parameters are $\left\{{\mathrm{\mu }}^{\text{AR}},,,{\mathrm{\sigma }}^{\text{AR}},,,{\mathrm{\sigma }}_{\text{N}}^{\text{AR}}\right\}=2.48,0.62,42.63$

Fig. 3

Forecasting bed occupancy in Aragon during the 2020-2021 Christmas wave. Dots show the actual value of bed occupancy, while solid lines represent the median value of the forecast, and their shaded regions display the 95% C.I. of the forecast for the week starting at the indicated date. At each date depicted in the figure, rather than using the observed incidence as in Fig. 2, the prediction algorithm runs on the number of cases detected up to that date and forecasts occupancy assuming a certain change of R(t). In the prediction made on January 11, 2021, the change is assumed to be + 0%. Following the introduction of several containment measures on January 15, the daily change was assumed to be − 5%

Fig. 4

Admission dynamics in each region of Spain. Estimated value of the probability of being admitted into the hospital upon detection, p_H, versus the parameters of the Half-Cauchy distribution governing the delay between detection and admission, β. The horizontal and vertical errorbars indicate the 95% C.I. Labels represent the ISO abbreviation of each autonomous region in Spain. The complete list of equivalences in shown in Table S2