Closed athowes closed 1 year ago
The number of infections for variant $v$ is governed by
$$ I_v(t) = I_v(0) e^{r_v t} $$
where the variant-specific growth rate can also be defined in terms of a wild-type growth rate and a transmission advantage
$$ rv = r{wt} + \Delta_v $$
The chance of a randomly sampled sequence $S_i$ at time $t_i$ being of type $v$ is
$$ P(S_i = v) = I_v(t_i) / \sum_k I_k(t_i) $$
They manage to frame this as a multinomial logistic regression where you learn $\Delta_v$ for each variant (so I guess it's a baseline category with wild-type as baseline).
They used nnet
.
I think this is the same model as the one Charlie was using and also suffers from just being lines on the log-odds scale.
See also "Estimated transmissibility and impact of SARS-CoV-2 lineage B.1.1.7 in England" (Science)
https://www.eurosurveillance.org/content/10.2807/1560-7917.ES.2021.26.24.2100509
The appendix.