Forecasting Combination of Hierarchical Time Series: A Novel Method with an Application to CoVid-19

Multiple, hierarchically organized time series are routinely submitted to the forecaster upon request to provide estimates of their future values, regardless the level occupied in the hierarchy. In this paper, a novel method for the prediction of hierarchically structured time series will be presented. The idea is to enhance the quality of the predictions obtained using a technique of the type forecast reconciliation, by applying this procedure to a set of optimally combined predictions, generated by different statistical models. The goodness of the proposed method will be evaluated using the official time series related to the number of people tested positive to the SARS-CoV-2 in each of the Italian regions, between February 24th 2020 and August 31th 2020. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Epidemic responses under uncertainty.

We examine how policymakers react to a pandemic with uncertainty around key epidemiological and economic policy parameters by embedding a macroeconomic SIR model in a robust control framework. Uncertainty about disease virulence and severity leads to stricter and more persistent quarantines, while uncertainty about the economic costs of mitigation leads to less stringent quarantines. On net, an uncertainty-averse planner adopts stronger mitigation measures. Intuitively, the cost of underestimating the pandemic is out-of-control growth and permanent loss of life, while the cost of underestimating the economic consequences of quarantine is more transitory.

Bayesian Model Averaging to Account for Model Uncertainty in Estimates of a Vaccine's Effectiveness.

Purpose: Vaccine effectiveness (VE) studies are often conducted after the introduction of new vaccines to ensure they provide protection in real-world settings. Control of confounding is often needed during the analyses, which is most efficiently done through multivariable modeling. When many confounders are being considered, it can be challenging to know which variables need to be included in the final model. We propose an intuitive Bayesian model averaging (BMA) framework for this task. Patients and Methods: Data were used from a matched case-control study that aimed to assess the effectiveness of the Lyme vaccine post-licensure. Cases were residents of Connecticut, 15-70 years of age with confirmed Lyme disease. Up to 2 healthy controls were matched to each case subject by age. All participants were interviewed, and medical records were reviewed to ascertain immunization history and evaluate potential confounders. BMA was used to systematically search for potential models and calculate the weighted average VE estimate from the top subset of models. The performance of BMA was compared to three traditional single-best-model-selection methods: two-stage selection, stepwise elimination, and the leaps and bounds algorithm. Results: The analysis included 358 cases and 554 matched controls. VE ranged between 56% and 73% and 95% confidence intervals crossed zero in <5% of all candidate models. Averaging across the top 15 models, the BMA VE was 69% (95% CI: 18-88%). The two-stage, stepwise, and leaps and bounds algorithm yielded VE of 71% (95% CI: 21-90%), 73% (95% CI: 26-90%), and 74% (95% CI: 27-91%), respectively. Conclusion: This paper highlights how the BMA framework can be used to generate transparent and robust estimates of VE. The BMA-derived VE and confidence intervals were similar to those estimated using traditional methods. However, by incorporating model uncertainty into the parameter estimation, BMA can lend additional rigor and credibility to a well-designed study.

Analyzing the effects of observation function selection in ensemble Kalman filtering for epidemic models.

The Ensemble Kalman Filter (EnKF) is a popular sequential data assimilation method that has been increasingly used for parameter estimation and forecast prediction in epidemiological studies. The observation function plays a critical role in the EnKF framework, connecting the unknown system variables with the observed data. Key differences in observed data and modeling assumptions have led to the use of different observation functions in the epidemic modeling literature. In this work, we present a novel computational analysis demonstrating the effects of observation function selection when using the EnKF for state and parameter estimation in this setting. In examining the use of four epidemiologically-inspired observation functions of different forms in connection with the classic Susceptible-Infectious-Recovered (SIR) model, we show how incorrect observation modeling assumptions (i.e., fitting incidence data with a prevalence model, or neglecting under-reporting) can lead to inaccurate filtering estimates and forecast predictions. Results demonstrate the importance of choosing an observation function that well interprets the available data on the corresponding EnKF estimates in several filtering scenarios, including state estimation with known parameters, and combined state and parameter estimation with both constant and time-varying parameters. Numerical experiments further illustrate how modifying the observation noise covariance matrix in the filter can help to account for uncertainty in the observation function in certain cases.

CoViD-19: an automatic, semiparametric estimation method for the population infected in Italy.

To date, official data on the number of people infected with the SARS-CoV-2-responsible for the Covid-19-have been released by the Italian Government just on the basis of a non-representative sample of population which tested positive for the swab. However a reliable estimation of the number of infected, including asymptomatic people, turns out to be crucial in the preparation of operational schemes and to estimate the future number of people, who will require, to different extents, medical attentions. In order to overcome the current data shortcoming, this article proposes a bootstrap-driven, estimation procedure for the number of people infected with the SARS-CoV-2. This method is designed to be robust, automatic and suitable to generate estimations at regional level. Obtained results show that, while official data at March the 12th report 12.839 cases in Italy, people infected with the SARS-CoV-2 could be as high as 105.789.

Rational policymaking during a pandemic.

Policymaking during a pandemic can be extremely challenging. As COVID-19 is a new disease and its global impacts are unprecedented, decisions are taken in a highly uncertain, complex, and rapidly changing environment. In such a context, in which human lives and the economy are at stake, we argue that using ideas and constructs from modern decision theory, even informally, will make policymaking a more responsible and transparent process.