Multistate Models for the Analysis of Life History Data

Multistate modelling is fundamental to modelling healthcare and health insurance, and a useful tool for actuarial analysis. It is widely used in health economics and public policy to determine costs and benefits and in biomedical statistics to determine outcomes.

Analysis of life history events often uses counting or point processes and uses multistate models to model dynamics of events and to predict outcomes. Transition intensities from one state to another use stochastic functions. Those who are familiar with Cox regressions and proportional hazard functions may find multistate models a natural extension to mathematical modelling of life history events.

This book applies probability models to medical data and shows various estimators that can be used in public health and biomedical case-studies, with advice on software. It begins with a comprehensive glossary of notation for each chapter. Each chapter ends with extensive sources for further study and bibliographic notes, and problems that would be valuable for class teaching. Solutions to exercises are not given, but references to relevant sections are indicated. Code for estimation of models and corresponding software packages are presented as examples. Bibliographic notes are comprehensive and provide hints to various research work with their particular slants and attention to specific approaches.

An important benefit of this book is the presentation of software code—invaluable for research and teaching. Knowledge of code writing or understanding is an advantage. The authors describe various estimation models, then apply them to clinical and medical data, explaining and presenting code, and then discuss results. Examples and their corresponding estimation are not directly relevant to insurance and actuarial science, though significant results from medical conditions can be of interest to risk and premium calculations.

Estimates from real case-study data and their plots are presented. Case-studies and examples are all from the Canadian medical profession. Various models are estimated and their adequacy, robustness and explanatory powers are examined against observations.

This book has four specialized appendices: selected software packages, simulation of multistate processes, code and output for illustrative analyses, and data sets. Data sets in Appendix D are publicly available and are posted on the book's web site (http://www.math.uwaterloo.ca/~rjcook/cook-lawless-multistate.html) which includes sample R code. A full list is given in Appendix A.

Researchers working in competing risks, survival analysis, time to failure, Cox regressions, proportional hazard functions and copulas—and specifically medical statisticians—will find this book very relevant and invaluable.