Systematic errors in estimates of R_t from symptomatic cases in the presence of observation bias
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We consider the problem of estimating the reproduction number R_t of an epidemic for populations where the probability of detection of cases depends on a known covariate. We argue that in such cases the normal empirical estimator can fail when the prevalence of cases among groups changes with time. We propose a Bayesian strategy to resolve the problem, as well as a simple solution in the case of large number of cases. We illustrate the issue and its solution on a simple yet realistic simulation study, and discuss the general relevance of the issue to the current covid19 pandemic.
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