Statistical Adjustment for Reporting Bias in Surveillance Data of Infectious Diseases

Reporting bias is common in the surveillance of infectious diseases and takes different forms. A typical example is that outbreaks are investigated only if the number of cases exceeds a prespecified threshold. Another example is that most outbreak investigations only survey cases, ignoring individuals who are at risk but not infected, to which we refer as a missing denominator problem. Such bias, if left unaddressed, can lead to erroneous estimation of key epidemiological parameters. To adjust for the selection bias associated with reporting threshold, the likelihood for the transmission dynamic need to be conditioned on the observation that final size of the outbreak exceeds the threshold. However, traditional final size algorithms soon become numerically unstable even for moderate sizes. For the missing denominator problem, branching processes are often used, but the assumption of independent offspring distributions is questionable, especially in small close contact groups. We propose methods for addressing these challenges. Interestingly, our solution to the missing denominator problem relies on the final size approach to the reporting threshold problem. We will discuss simulation results for validating these methods and their application to real surveillance data of influenza and MERS-CoV.