Using symptom onsets instead of incidences results in time-lagged estimate of R(t).

We reanalyzed the epidemic curve in Pan et al. JAMA. 2020 (doi:10.1001/jama.2020.6130) using four methods to estimate the effective reproduction number:

1. The method proposed by Cori et al., applied to the curve of symptom onsets with a 5-day sliding-window smoothing (replicating Figure 4 in Pan et al.).
2. The method proposed by Wallinga and Teunis as implemented in the EpiEstim package with a 5-day sliding-window smoothing (replicating the commentary by Lipsitch et al.).
3. The method proposed by Cori et al., applied to a back-calculated incidence curve using an incubation period with median = 4.5 days and 95% quantile = 13.4 days.
4. The method proposed by Wallinga and Teunis with no smoothing (the original proposal of Wallinga and Teunis).

In short, we find that using symptom onsets instead of incidences results in time-lagged estimate of the instantaneous reproduction number R(t). More details can be found in this document.