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Table 2 Bias and MSE of initial reproduction number estimation methods

From: The R0 package: a toolbox to estimate reproduction numbers for epidemic outbreaks

   Bias (MSE)
R0 Aggregation (days) Method
EG ML TD SB
No overdispersion (k = 1)
1.5 1 0.12 (0.0467) 0.02 (0.0164) 0.04 (0.0336) −0.15 (0.0745)
3 0.07 (0.0386) −0.38 (0.1429) −0.4 (0.16) −0.1 (0.0277)
6 0.07 (0.0431) −0.49 (0.2408) −0.79 (0.6281) −0.09 (0.0371)
2 1 0.11 (0.0589) −0.17 (0.0571) −0.11 (0.0736) −0.4 (0.1814)
3 0 (0.0496) −0.84 (0.7041) −0.87 (0.7573) −0.32 (0.1222)
6 −0.03 (0.0618) −0.99 (0.9789) −1.33 (1.781) −0.31 (0.1306)
3 1 −0.07 (0.1449) −0.67 (0.5547) −0.47 (0.317) −1.1 (1.2532)
3 −0.3 (0.2492) −1.8 (3.2396) −1.86 (3.4432) −0.92 (0.8585)
6 −0.33 (0.2872) −1.99 (3.9521) −2.45 (5.9935) −0.89 (0.8277)
Large overdispersion (k = 4)
1.5 1 0.28 (0.1609) 0.16 (0.0679) 0.33 (0.1913) −0.05 (0.0881)
3 0.11 (0.0715) −0.38 (0.1444) −0.42 (0.1816) −0.06 (0.035)
6 0.08 (0.0694) −0.49 (0.2415) −0.83 (0.6906) −0.04 (0.0574)
2 1 0.13 (0.1109) −0.15 (0.0696) 0.05 (0.1238) −0.4 (0.197)
3 0 (0.086) −0.84 (0.7108) −0.89 (0.8007) −0.32 (0.1328)
6 −0.03 (0.0988) −0.99 (0.9792) −1.36 (1.8686) −0.3 (0.1517)
3 1 −0.07 (0.2157) −0.65 (0.5699) −0.45 (0.3457) −1.11 (1.2745)
3 −0.3 (0.3035) −1.8 (3.2337) −1.86 (3.4698) −0.93 (0.898)
6 −0.36 (0.366) −1.99 (3.9527) −2.43 (5.9218) −0.94 (0.9421)
  1. For each fixed value of R0, 4.000 epidemics were simulated at an individual-based level. A first index case is set at the initial time, and contaminated descendants are sampled in a negative binomial distribution. For each case, we sample a latency period dlat during which the individual is infected, but not contagious, and an infectious period dinf, both from Gamma distributions of parameters already described for influenza (gamma distributions with mean+/−sd 1.6+/−0.3 days for latency and 1+/−1 days for infectious period [19]). Incidence data are computed as class of time of infection, defined as t inf (o) = t inf (p) + dlat(p) + runif(1) * dinf (p), where p is the parent case and 0 the offspring case.
  2. Epidemics that didn’t start due to too few cases were discarded, and estimations were run by batch. For each batch of simulations, we report the bias between the value used to generate the epidemics and the average of all estimates, along with the Mean Square Estimator (MSE) of the simulation series.