Comparison of different approaches in estimating the time-varying reproductive number for COVID-19

Abstract

PurposeThe time-varying reproductive number (Rt) is an indicator of transmissibility that has utility in evaluating public health interventions and assessing transmission factors. However, the Rt may be biased by generation time misspecification, reporting delays, underestimation of cases, and day-to-day variations. We compared several methods of adjustments in developing an approach to estimating an unbiased Rt.Methods & MaterialsA meta-analysis of generations times was conducted to reduce misspecification. A probabilistic bias approach was compared to standardization by a test positivity of 5% in adjusting for underestimation. A Poisson deconvolution process using an incubation period of 5.2 days (95% CI: 4.9-5.5) and laboratory turnover times between 2-, 5- and 10-days was utilized to adjust for reporting delays. We compared smoothing (7- and 14-day moving averages), a generalized additive model (GAM), and a local regression (LOESS) model to adjust for day-to-day variation. The adjusted Rt was compared to a crude Rt by eyeballing, Mean Average Percentage Error (MAPE), and Mean Absolute Deviation (MAD). We estimated the Rt using Malaysian COVID-19 daily case data from 7 March 2020-20 June 2021 utilizing Cori et al.’s method.ResultsWe estimated a pooled serial interval of 4.95 days (95% CI: 4.62-5.29). The Rt estimated using case counts adjusted for underestimation using standardization by test positivity (MAPE: 0.31; 95% CI: 0.30-0.49, MAD: 0.5; 95%CI: 0.5-0.54) were more volatile, exhibited larger peaks and wider confidence intervals, especially in periods of lower incidence, compared to the probabilistic bias approach (MAPE: 0.07; 95% CI: 0.06-0.07, MAD: 0.26; 95%CI: 0.26-0.28). GAM (MAPE: 1.85, 95% CI: 1.63-2.08) and LOESS (MAPE: 0.29, 95% CI: 0.29-0.29) models had smoothed out almost all variations in the Rt. Longer lab turnover periods created smoother Rt with larger peaks and resulted in greater volatility in the estimates.ConclusionBiases in the estimation of the Rt may critically change its interpretation for public health interventions. It is important to adjust for these biases and understand the underlying limitations of these estimations; primarily when utilized within the context of pandemic control.