Delay-robust Estimation of the Reproduction Number and Comparative Evaluation on Generated Synthetic Data

Abstract

AbstractThe reproduction number is an indicator of the evolution of an epidemic. Consequently, accurate estimators for this number are essential for decision making in politics. Many estimators use filtered data as input to compensate for fluctuations of reported cases. However, for daily-based estimations, this filtering leads to delays. Some approaches use small window sizes for filtering to overcome this issue. This, in turn, leads to an increased periodic behavior of estimators. To overcome these issues, in the present paper, we introduce an estimator for the reproduction number that uses an acausally filtered number of cases as input, hence avoiding both the periodic behavior and the delay. For the filter size, we suggest using a multiple of one week since reported cases often exhibit a weekly pattern. We show that this approach is more robust against periodicities, and that it does not exhibit any delays in the estimation compared to estimators with smaller filter sizes.Moreover, often it is hard to examine estimators in detail because a ground truth is missing. For analyzing different properties of the estimators, we propose a method to generate synthetic datasets that can be taken as ground truths. Importantly, the synthetic data contains all relevant real-world behavior.Finally, we apply the proposed estimator to the publicly available coronavirus disease 2019 (COVID-19) data for Germany. We compare the proposed estimator to two estimators used by the federal German Robert Koch Institut (RKI). We observe that our estimator is more stable than the benchmarks especially if the reproduction number is close to 1. Based on the observation that the proposed estimator appears more robust, it may be a useful asset when considering governmental interventions.The accompanying source code is published under the Apache-2.0 license (https://github.com/timueh/C0VID-19).