Systematic errors in estimates of $R_t$ from symptomatic cases in the presence of observation bias

TL;DR

This paper identifies biases in estimating the epidemic reproduction number $R_t$ when detection probabilities vary with covariates, proposing Bayesian and simplified solutions to improve accuracy, especially relevant for COVID-19 data.

Contribution

It highlights a systematic error in $R_t$ estimation due to observation bias and introduces Bayesian and simplified methods to correct this bias.

Findings

Normal estimators can be biased when detection probabilities change over time.

Bayesian strategy effectively corrects for observation bias.

Simplified solutions work well with large case numbers.

Abstract

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.