Estimating the real-time case fatality rate of COVID-19 using Poisson mixtures model

Paul Hong Lee

We assumed that a confirmed case will either die or recover and it is determined a priori through a Bernoulli process with a parameter p, which is the CFR. If a case is deemed to die, the time to death (in days) follows a Poisson distribution with a mean of λ d , and the time to recovery for a case who will survive follows a Poisson distribution with a mean of λ r . We call this model the Poisson mixtures model. The 95% confidence interval of the CFR estimates can be estimated using bootstrap method. Both parametric and non-parametric bootstrap can be used, and here we used non-parametric bootstrap that simulated 1000 datasets with D(t), R(t), and C(t) follow multinomial distribution with the observed proportions as the parameters, and the 2.5 th percentile and 97.5 th percentile of the estimated CFR from these 1000 datasets were the 95% confidence interval of the corresponding CFR estimate.