An introduction to survival and event history analysis
This book is about survival and event history analysis. This is a statistical methodology used in many different settings where one is interested in the occurrence of events. By events we mean occurrences in the lives of individuals that are of interest in scientific studies in medicine, demography, biology, sociology, econometrics, etc. Examples of such events are: death, myocardial infarction, falling in love, wedding, divorce, birth of a child, getting the first tooth, graduation from school, cancer diagnosis, falling asleep, and waking up. All of these may be subject to scientific interest where one tries to understand their cause or establish risk factors. In classical survival analysis one focuses on a single event for each individual, describing the occurrence of the event by means of survival curves and hazard rates and analyzing the dependence on covariates by means of regression models.
The purpose of this introductory chapter is twofold. Our main purpose is to introduce the reader to some basic concepts and ideas in survival and event history analysis. But we will also take the opportunity to indicate what lies ahead in the remaining chapters of the book. In Section 1.1 we first consider some aspects of classical survival analysis where the focus is on the time to a single event. Sometimes the event in question may occur more than once for an individual, or more than one type of event is of interest. In Section 1.2 such event history data are considered, and we discuss some methodological issues they give rise to, while we in Section 1.3 briefly discuss why survival analysis methods may be useful also for data that do not involve time. When events occur, a natural approach for a statistician would be to count them. In fact, counting processes, a special kind of stochastic process, play a major role in this book, and in Section 1.4 we provide a brief introduction to counting processes and their associated intensity processes and martingales. Finally, in Section 1.5, we give an overview of some modeling issues for event history data.
KeywordsHazard Rate Counting Process Frailty Model Intensity Process Migrate Motor Complex
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