  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.
