A sequential test to compare the real-time fatality rates of a disease among multiple groups with an application to COVID-19 data.

Infectious diseases, such as the ongoing COVID-19 pandemic, pose a significant threat to public health globally. Fatality rate serves as a key indicator for the effectiveness of potential treatments or interventions. With limited time and understanding of novel emerging epidemics, comparisons of the fatality rates in real-time among different groups, say, divided by treatment, age, or area, have an important role to play in informing public health strategies. We propose a statistical test for the null hypothesis of equal real-time fatality rates across multiple groups during an ongoing epidemic. An elegant property of the proposed test statistic is that it converges to a Brownian motion under the null hypothesis, which allows one to develop a sequential testing approach for rejecting the null hypothesis at the earliest possible time when statistical evidence accumulates. This property is particularly important as scientists and clinicians are competing with time to identify possible treatments or effective interventions to combat the emerging epidemic. The method is widely applicable as it only requires the cumulative number of confirmed cases, deaths, and recoveries. A large-scale simulation study shows that the finite-sample performance of the proposed test is highly satisfactory. The proposed test is applied to compare the difference in disease severity among Wuhan, Hubei province (exclude Wuhan) and mainland China (exclude Hubei) from February to March 2020. The result suggests that the disease severity is potentially associated with the health care resource availability during the early phase of the COVID-19 pandemic in mainland China.