Navigating hospitals safely through the COVID-19 epidemic tide: Predicting case load for adjusting bed capacity

Abstract

Background: The pressures exerted by the coronavirus disease 2019 (COVID-19) pandemic pose an unprecedented demand on healthcare services. Hospitals become rapidly overwhelmed when patients requiring life-saving support outpace available capacities.

Objective: We describe methods used by a university hospital to forecast case loads and time to peak incidence.

Methods: We developed a set of models to forecast incidence among the hospital catchment population and to describe the COVID-19 patient hospital-care pathway. The first forecast utilized data from antecedent allopatric epidemics and parameterized the care-pathway model according to expert opinion (ie, the static model). Once sufficient local data were available, trends for the time-dependent effective reproduction number were fitted, and the care pathway was reparameterized using hazards for real patient admission, referrals, and discharge (ie, the dynamic model).

Results: The static model, deployed before the epidemic, exaggerated the bed occupancy for general wards (116 forecasted vs 66 observed), ICUs (47 forecasted vs 34 observed), and predicted the peak too late: general ward forecast April 9 and observed April 8 and ICU forecast April 19 and observed April 8. After April 5, the dynamic model could be run daily, and its precision improved with increasing availability of empirical local data.

Conclusions: The models provided data-based guidance for the preparation and allocation of critical resources of a university hospital well in advance of the epidemic surge, despite overestimating the service demand. Overestimates should resolve when the population contact pattern before and during restrictions can be taken into account, but for now they may provide an acceptable safety margin for preparing during times of uncertainty.

Fig. 1.

Model structure. The COVID-19 care pathway describes how patients progress from confirmed cases in the community (C), to be admitted on general wards (GW), to intensive care units (ICU), and to step-down units. Some COVID-19 patients are admitted directly to the ICU from the community. The step-down unit was only included in the agent-based model.

Fig. 2.

Early forecast using the static model. (A) The trajectory of the number of confirmed cases in Germany, Italy, Region of Lombardy, and Province of Lodi were (B) normalized and projected as a single curve by compensating for the apparent delay between locations, and (C) the downward slope (grey) was predicted assuming a symmetry conjecture of the observed upward slope (black). (D) Expected bed occupancy for the UKF (catchment size 290,000 people; general wards in blue and ICU in red). Light shades indicate 95% CI and dark shades indicate interquartile ranges. Predictions are based on the COVID-19 care pathway using expert consensus. Bed demand peaked on the general wards at 116 beds on April 9 and in ICUs at 47 beds on April 19.

Fig. 3.

Survival analysis (A–E) Kaplan-Meier estimators for the stay on the general ward (A and D), ICU (B and C), and step-down unit (C), for patients that are discharged (A, B, and C) and transferred to the following ward (D and E), based on the data observed on April 5. (F) The estimated rates of discharge, death, and transfers over time, based on continuously accumulating data.

Fig. 4.

Late forecast using the dynamic model based on locally available data on April 5. (A) The observed incidence of confirmed cases in the Freiburg, Breisgau, and Hochschwarzwald health districts combined. (B) Backward model: Estimates of the time-varying Reproduction number (blue dots) over 100 stochastic simulations, with fitted R_f(t) trajectories (black lines). (C) Forward model: Forecasted incidence of confirmed cases, grey lines show single simulation results, green line show the median, with green shade showing the interquartile range and green light shade 5%–95% of the simulation results. (D) Estimated bed demand (median, IQR, 5%–95% range) for the general wards (blue) and ICU (red). Circles denote actual observed number of beds occupied (closed: past days; open: future days not known at the time of the analysis on April 5).