Statistics in Medicine

Abstract

In response to the ongoing global public health crisis since the Spring of 2020, there has been an urgent need to study infectious diseases by using massive amounts of collected data. A Bayesian inferential strategy allows us to simultaneously characterize and forecast the spread of infectious disease while quantifying the uncertainties. Bayesian Analysis of Infectious Diseases comes out at a perfect and critical time to introduce the latest Bayesian techniques for the statistical analysis of infectious diseases. Based on the authors’ cumulative expertise, comprehensive explorations of various topics and case studies are generously provided from beginning to end. This book will greatly benefit statisticians, epidemiologists, and especially graduate students who are interested in this popular topic. Chapter 1 provides a high-level overview of infectious diseases and their analyses using multiple reliable resources including books, articles, and websites. Chapter 2 starts with a brief introduction to the history of Bayesian statistics and the basic theory required for performing Bayesian data analysis. Fundamental concepts including data likelihood, prior, posterior, and predictive distributions are clearly explained and illustrated using several common models including Bernoulli, Poisson, Gaussian, and most importantly, the simplest epidemiological susceptible-infectious (SI) model. Three major types of inferences are discussed in great detail including estimation, hypothesis testing, and prediction. I truly appreciate that the authors provide straightforward R code to implement almost every illustrated model throughout the book, not only this chapter. In parallel with the previous chapter, Chapter 3 describes the underlying mechanism of infectious diseases that should be understood before statistical modeling, including how our immune system fights disease, how drugs attack infections, and how vaccines work. The authors make tremendous efforts to improve the reading experience especially for those with limited biological knowledge. I personally really like Table 3.1 on pp. 44–47, which summarizes the important characteristics of wellknown infectious diseases. The chapter also briefly introduces emerging infectious diseases such as the coronavirus. Chapters 4 and 5 focus on Bayesian inference of the discretetime Markov chain with applications in biology. Chapter 4 illustrates concepts of the discrete-time Markov chain, a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Those concepts are the theoretical foundation for Markov chain Monte Carlo techniques, which have significantly advanced Bayesian statistics in the past decades. Chapter 5 further illustrates how to apply Bayesian inference of discrete-time Markov chain to understand the mechanism of various biological phenomena through several classical processes including the stochastic susceptibleinfectious-susceptible (SIS) model. Chapters 6 and 7 explore Bayesian inference of the continuoustime Markov chain. Among many examples, the authors use various Poisson processes and the associated subjects, such as thinning and superposition, to illustrate the concepts. Chapter 7 reviews the theoretical foundation for the study of continuoustime Markov chains as well as many derived models including the susceptible-infectious-removed (SIR) model, which is the most fundamental compartmental model in epidemiology. Chapter 8 ends the journey with extra information about infectious diseases including a few vital theorems (e.g., epidemic threshold theorem), important research problems (e.g., final epidemic size estimation), and case studies (e.g., coronavirus and HIV) using Bayesian approaches. This book is very useful for statisticians new to the infectious disease field and for epidemiologists who aim to equip themselves with more powerful quantitative skills. It contains detailed examples and programming codes that can be quickly implemented by users of all levels. There is a good balance of statistical methodology and practical application. Every chapter begins with the motivations and basic concepts related to each topic. Relevant examples with provided data appear throughout the book. Additional readings and resources are listed at the end of each chapter to supplement the reader with an advanced understanding of the topics.