Reproduction number estimation using smoothing methods

Abstract

The reproduction number is estimated to understand the potential spread of an infectious disease within a population. Current estimation methods can be broadly categorized into mathematical and statistical methodological frameworks. Within the latter, renewal process, exponential growth and smoothing methods infer reproduction numbers from generation time distributions, growth rates, or smoothed epidemic trajectories. Our evaluation was based on three epidemic scenarios with distinct transmissibility levels (R0= 11.52, 2.88, and 1.06), simulated using stochastic SEIR models, and on the Hagelloch measles outbreak data. We compared five statistical methodsthe exponential growth method (EG), the renewal process method (RP), the Bayesian P-spline smoothing method (BPS), the filtering-based Bayesian inference method (FBI), and a smoothing method that integrates spline smoothing, derivative estimation, and exponential growth analysis within a generalized additive model (DSS). The performance criteria comprised the estimated bias, mean squared error (MSE), coverage rate (CR), significance rate (SR), and false negative rate (FNR). Across the three scenarios, no method was uniformly superior; the ranking depended on the criterion prioritized. RP and DSS produced the most accurate and stable point estimates (bias between − 0.45 and 1.69; MSE ≤ 7.31) together with the best-calibrated and narrowest 95% uncertainty intervals (coverage up to 97%). BPS was particularly unstable: its inflated mean drove MSE, bias, and coverage to 13.51%. FBI reached the highest significance rate at R0 = 1.06 (65.49%), although this sensitivity partly reflected their upward bias; EG showed the only substantial FNR (15.11%). The Hagelloch measles data corroborated these patterns. Under the significance constraint (SR), RP maximized risk control (CR/FNR) and DSS maximized accuracy (Bias/MSE).