Modelling in Healthcare is an astonishingly broad overview of mathematical and statistical techniques used in healthcare, made concrete by the inclusion of detailed summaries of consequential healthcare research making use of each technique. The book’s novel structure made it a fun read, and I enjoyed it from cover to cover. Each chapter introduces a modeling approach, such as regression analysis or networks and graph theory with a quick sketch of the common uses of the models in health care. Mathematical details follow, and finally each chapter leads the reader through a handful of examples ranging from toy problems (regression analysis fitting number of toes stubbed to number of stairs) to substantial research papers (network models for containing the spread of mycoplasma pneumoniae in a hospital setting). The reader will find it easy to identify helpful references, since the authors describe carefully the content of each source.
The book has fifteen authors, which may explain the wide variation in level of exposition for the mathematical details sections. For instance, one chapter uses a table showing all the outcomes of rolling two dice to explain conditional probability, while the optimization chapter includes a technical discussion of the need to find the infimum in cases where the minimum is not achieved in the feasible set. I wished for more than one chapter on optimization, but the authors do acknowledge that each of the chapters deserves its own textbook. I also note the glaring omission of optimization software from the appendix’s listing of simulation and statistical packages.
As I dug into the book, I kept wondering who it had been written for. Lacking exercises, it is not primarily aimed at the textbook market, although a valuable seminar course for med school students or undergraduates could be generated with some delving into the papers referenced here. The real audience for this book are my colleagues in medicine who want to read modeling papers and use appropriate quantitative techniques in their research, but need help deciphering the jargon of modeling and identifying the right approaches. The queueing chapter, for example, has a lovely section describing how the different queueing disciplines of last in first out, service in random order, and priority queues correspond to the healthcare scenarios of blood banking, available hospital bed counts, and emergency room arrivals, respectively. I particularly wish that those in medicine who insist on referring to any quantitative analyst as a “statistician” would read this book!
Sommer Gentry is an Associate Professor of Mathematics at the United States Naval Academy, and a research associate in the Johns Hopkins School of Medicine’s Department of Surgery. She studied operations research at Stanford University and M.I.T. Her research is in optimization and simulation for improving transplantation and organ allocation policy. She designed optimization methods used for nationwide kidney paired donation registries in both the United States and Canada. She is a recipient of the Mathematical Association of America's Alder Award for distinguished teaching by a beginning college or university mathematics faculty member.