Scalable model selection for count time series with structural breaks: application to solid-organ transplantation during and after COVID-19 in the USA and Italy

TL;DR

This paper develops scalable count time-series models to analyze healthcare activity data affected by systemic shocks, exemplified by solid organ transplant counts during COVID-19 in the US and Italy.

Contribution

It introduces a model selection framework for count time series with structural breaks, tailored for large datasets and pandemic-related disruptions.

Findings

Models effectively capture pandemic deviations and post-pandemic trajectories.

Auxiliary COVID variables add limited predictive value beyond autoregressive and calendar effects.

Deceased-donor series tend to return to pre-pandemic levels, US living-donor series show gradual recovery.

Abstract

Weekly healthcare activity data are typically non-negative counts with temporal dependence and occasional system-wide disruptions, settings in which Gaussian time-series models may be inadequate. Solid organ transplant (SOT) activity provides a representative case study of a count process affected by a large external shock. We analyse weekly SOT counts in the USA and Italy from 2014 to October 2024, stratified by donor type (deceased vs living) and organ (kidney and liver). We fit Poisson and negative-binomial count time-series models incorporating short-term dynamics, calendar effects (holiday weeks), and pre-specified pandemic-period level and/or slope indicators. Candidate specifications are screened within a pre-defined portfolio and selected using BIC within each training window. Forecasting performance is evaluated with an expanding-window design at horizons $h\in\{4,8,12\}$ weeks. Alongside RMSE, we report empirical coverage of nominal $95\%$ predictive intervals and interval widths to summarise calibration and forecast uncertainty. Across strata, selected models capture substantial pandemic-period deviations and varying post-period trajectories. Deceased-donor series are broadly consistent with a return towards pre-pandemic baselines in both countries, whereas the US living-donor series shows a more gradual convergence in this application. Within the explored model class and validation protocol, auxiliary covariates representing COVID burden and mortality add limited incremental predictive contribution beyond autoregressive and calendar components. Our analysis shows that donation time series represent an unconditional phenomenon, with auxiliary variables having a statistically negligible impact on donations, thus allowing a focus on more practical aspects related to ongoing challenges in the post-pandemic era, such as hospital overloads and changes in public perception.