Technical note on Short-term predictions of daily intensive care unit (ICU) hospitalizations due to Covid-19

Stat-Group-19[1]

Italy and its health care system are currently under great pressure due to the SARS-Cov-2 pandemic. Here we attempt to provide an analysis and short-term predictions of the daily number of ICU beds dedicated to patients with Covid-19. To allow for good medical resource management, we have validated our approach at a regional basis and for a time span of three to five days.

Ensemble predictor. We are combining two predictive methods. The first method is a Poisson Generalized Linear Mixed Model (GLMM) with a random intercept and random quadratic trend term. These are distributed according to a multivariate Gaussian distribution, with a variance-covariance matrix where the off-diagonal elements for the intercept-quadratic term and for linear-quadratic terms are set to zero. Furthermore, we used the number of residents on 31/12/2019 as an offset term. Regional data is therefore used as a single panel, although each region might have its own trend and intercept in the Poisson parameter logarithmic reparameterization. The second method uses non-stationary INAR(1) models with Poisson innovations, where each model is evaluated separately for each region. The stationary model, the linear trend model, and the quadratic trend model are compared using the BIC for each region. The prediction for each specific region is the one corresponding to the model with the lowest BIC score. An additional cubic term is included for Lombardy and Emilia Romagna. In order to limit long-term effects, only daily observations in the last 18 days are used.

Predictions are then linearly combined through a convex combination. The weights are calculated by re-estimating the model after leaving out the last observations and minimizing the sum of the absolute values of the prediction error for the last time point. 99% prediction intervals are obtained via non-parametric bootstrap and were aggregated by the union operator. This approach has wide improvement margins and is approximative, as it does not keep track of the real data-generating process (which is probably a non-homogenous, non-stationary INAR(1) process with Poisson-Binomial innovations and with shared parameters) since publicly available information would not allow estimating models with such complex specifications.

We have successfully validated this technique in the last seven days and on all 20 regions. For each day we produced estimates in the morning, and in the evening, estimates were validated by checking whether the observed value was contained in the prediction interval. Nevertheless, due to the scarcity of information at our disposal and model misspecifications, it’s likely that some confidence interval may not cover the real value. This might also be caused by unpredictable inter-region patient transfers, clusters of risky behavior in the last few days, or the onset of improvements due to adopted restrictive measures.

Data: The data is official data shared by the Protezione Civile, available at both regional and national level https://github.com/pcm-dpc/COVID-19

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Results: The table reporting results can be found at the following link

http://afarcome.altervista.org/ICU.predictions.html

and will be updated regularly with new predictions.

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[1] Stat-Group-19: Fabio Divino (Università del Molise), Alessio Farcomeni (Università di Roma Tor Vergata), Giovanna Jona Lasinio (Università di Roma La Sapienza), Gianfranco Lovison (Università di Palermo), Antonello Maruotti (LUMSA, Roma).