Statistical methods for the fatality rate of emerging infectious diseases

Abstract

Emerging infectious disease presents a huge challenge to human health globally. In recent decades, various statistical methods have been proposed to measure the overall disease fatality. However, limited attention has been paid to the changes in the fatality rate over the course of an epidemic. For infectious diseases that persist over a long period of time with several mutations, calculating the overall fatality rate is not meaningful, whereas the changes in the fatality rate in real-time convey more valuable information, such as changes in the deadliness of new variants, the effectiveness of potential treatments as well as the quality of healthcare system. In this thesis, three approaches regarding real-time monitoring of the fatality rate are developed to address the challenges encountered in epidemiological applications.

In principle, disease fatality is expected to decline with the implementation of effective interventions; otherwise, it may stabilize at a certain level. This is a reasonable assumption, at least in the short term. To identify an effective treatment, a statistical test with the null hypothesis of constant fatality rate is developed in the first part of the thesis. Application to the 2014-2016 Ebola outbreak in Sierra Leone demonstrates the positive effect of adequate healthcare personnel and sufficient bed capacity in lowering the fatality rate. However, one should be cautious about the test result in the long run as a progressive reduction in fatality rate can be caused by other factors, such as a rise in temperature. A more promising test for identifying a potential factor that affects the disease severity is to compare fatality rates among multiple independent groups, say, divided by treatment, age or area, over time. In that case, the effects of the above-mentioned confounding factors are shared by all groups. Therefore, a $K$-sample statistical test for the null hypothesis of equal fatality rates between subgroups over time is proposed in the second part of the thesis. The proposed test is applied to compare differences in disease severity between different age groups during Hong Kong's fifth wave of the COVID-19 epidemic, and to monitor differences in fatality rates across regions, during the early stage of the COVID-19 pandemic in mainland China.

Another concern in the current COVID-19 epidemic is that the data on recoveries are often missing. In most countries, patients with mild illnesses are self-isolated and recovered at home, which makes information on recovered patients missing and unreliable. To address this problem, a novel time-varying fatality rate estimator is developed in the third part of the thesis using only the aggregate count of cases and deaths. It is applied to the COVID-19 pandemic in Germany and other European countries that have chosen to coexist with the virus. The results show that the proposed method outperforms the two commonly-used case fatality rate estimators in capturing the latest changes in disease severity during the course of epidemics. All proposed methods in this thesis enjoy the advantage of minimal data input requirement and are widely applicable to fight against emerging epidemics worldwide.