As an outbreak progresses in real time, epidemiological curves can be distorted by reporting delays arising from several factors that include (i) delays in case detection during field investigations, (ii) delays in symptom onset after infection, (iii) delays in seeking medical care, (iv) delays in diagnostics, and (v) delays in processing data in surveillance systems [32]. However, it is possible to generate reporting-delay-adjusted incidence curves using standard statistical methods [33]. Briefly, the reporting delay for a case is defined as the time lag in days between the date of onset and date of reporting. Here we adjusted the COVID-19 epidemic curve of local cases by reporting delays using a non-parametric method that employs survival analysis known as the Actuaries method for use with right truncated data, employing reverse time hazards to adjust for reporting delays as described in a previous publication [34,35,36]. The 95% prediction limits are derived according to Lawless and Kalbfleisch [37]. For this analysis, we exclude 7 imported cases and 5 local cases for which dates of symptoms onset are unavailable.
A second method of inferring the reproduction number applies branching process theory to cluster size data to infer the degree of transmission heterogeneity [49, 50]. Simultaneous inference of heterogeneity and the reproduction number has been shown to improve the reliability of confidence intervals for the reproduction number [51]. In the branching process analysis, the number of transmissions caused by each new infection is modeled as a negative binomial distribution. This is parameterized by the effective reproduction number, R, and the dispersion parameter, k. The reproduction number provides the average number of secondary cases per index case, and the dispersion parameter varies inversely with the heterogeneity of the infectious disease. In this parameterization, a lower dispersion parameter indicates higher transmission heterogeneity.
Serial para Wizteach 3
Branching process theory provides an analytic representation of the size distribution of cluster sizes as a function of R, k, and the number of primary infections in a cluster (as represented in equation of 6 of the supplement of [52]). This permits direct inference of the maximum likelihood estimate and confidence interval for R and k. In this manuscript, we modify the calculation of the likelihood of a cluster size to account for the possibility that truncation of case counts at a specific time point (i.e., March 17, 2020) may result in some infections being unobserved. This is accomplished by denoting x as the sum of the observed number of serial intervals in a cluster. Then the likelihood that an observed cluster of size j containing m imported cases is generated by x infectious intervals is given by:
Based on the entire distribution of cluster sizes, we jointly estimated the overall reproduction number R and the dispersion parameter k as of March 17, 2020. Fitting the negative binomial distribution to the cluster data in the empirical distributions of the realizations during the early stages of the outbreak in Singapore, the reproduction number is estimated at 0.61 (95% CI 0.39, 1.02) after adjusting for the truncation of the time series leading to the possibility that some infected cases might still cause new infections after March 17, 2020. The dispersion parameter is estimated at 0.11 (95% CI 0.05, 0.25) consistent with SARS-CoV-2 transmission heterogeneity. 2ff7e9595c
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