Title: Statistical analysis of epidemic counts data: modeling, detection of outbreaks, and recovery of missing data
Speaker: Michael Baron
Abstract: Official counts from the seasonal flu, 2009 H1N1 flu, and the COVID-19 epidemics are analyzed with the goals of (1) detecting epidemic outbreaks and any anomalous deviations from the expected trends; and (2) estimating the counts that are not included in official reports.
An influenza outbreak becomes an epidemic when its caused mortality exceeds the epidemic threshold. It is possible though to use statistical change-point detection tools to identify an outbreak earlier and to predict an epidemic. Construction of a change-point algorithm for the popular SIR epidemic model brings us to a more general class of binomial thinning processes. The standard CUSUM stopping rule is no longer optimal in this case. We show how it can be improved with a dynamically adaptive threshold. The resulting scheme attains a shorter detection delay under asymptotically the same rate of false alarms.
As we learn from the current COVID-19 pandemic, the officially reported daily counts of infected, recovered, and perished people are underestimated. A substantial portion of infected people is not tested, many recovered cases are not reported, and the proportion of unobserved and under-observed counts varies by territory and changes in time, because of different and changing diagnostics and reporting standards.
We develop a stochastic model that includes untested individuals and unobserved COVID-19 recoveries and casualties, extending the SIR model to include additional compartments. Its parameters such as the infection rate, the testing rate, the recovery rate, the mortality rate, and the reporting rate may vary continuously in time. The proposed Bayesian algorithm uses observed counts to estimate the model parameters and unobserved counts, continuously updating the estimates with new data.