Survival Models and Their Estimation

Description

It has been nearly ten years since the publication of the second edition of Survival Models and Their Estimation, and its adoption by the Society of Actuaries as the principal references for its Course 160 examination. It ap­pears that the text has proved satisfactory in that role from the point of view of exam candidate and examiner alike. The mathematics of survival models themselves, and how they might be estimated from sample data, has been a fairly stable topic, so that a revision of the theory presented in the first eight chapters of the textbook does not seem to be required at this time. Consequently, the reader familiar with the second edition will note various clarifications and improvements in presentation in these chapters, but no substantive change in the overall content. Why, then, is a new edition appearing at this time? Beginning in 1994, a Society of Actuaries Board Task Force on Education has been working toward a new model of actuarial education for the twenty-first century. Among many other important principles, the Task Force has established that actuarial education in the future should include guidance for the application of standard actuarial techniques in disciplines beyond the traditional actuarial areas of insurance and pensions. Since Survival Models and Their Estimation plays its small part in the actuarial education arena, as the reference text for Course 160, it naturally follows that a revision of the text, guided by the Task Force principle of broadened application, is now appropriate. The result is the appearance of new Chapters I0, 11, and 12, which present applications of the general theory of survival models in such fields as epidemiology, facilities planning, economics, in­vestments, reliability engineering, and others. Two other issues have affected certain changes from the prior to the current edition of this text as well. The first is that Chapter 9 in the prior edition, which described the demographer's process of estimating survival models from general popula­tion data, has been deleted from the text. The material in the prior edition was based on out-of-date studies, namely the Canadian census of 1981 and the U.S. census of 1980, and is not included in the course of reading for the Course 160 exam. Furthermore, the content of that chapter is also included, in up-dated form, in the new (third) edition of Robert L. Brown's Introduc­tion to the Mathematics of Demography [16], and interested readers are directed to that reference. Preface to the Second Edition Preface to the Third Edition PART I THE NATURE AND PROPERTIES OF SURVIVAL MODELS Chapter 1: INTRODUCTION Chapter 2: THE MATHEMATICS OF SURVIVAL MODELS Chapter 3: THE LIFE TABLE PART II ESTIMATION OF SURVIVAL MODELS FROM SAMPLE DATA Chapter 4: TABULAR SURVIVAL MODELS ESTIMATED FROM COMPLETE DATA SAMPLES Chapter 5: TABULAR SURVIVAL MODELS ESTIMATED FROM INCOMPLETE DATA SAMPLES: STUDY DESIGN Chapter 6: TABULAR SURVIVAL MODELS ESTIMATED FROM INCOMPLETE DATA SAMPLES: MOMENT PROCEDURES Chapter 7: TABULAR SURVIVAL MODELS ESTIMATED FROM INCOMPLETE DATA SAMPLES: MAXIMUM LIKELIHOOD PROCEDURES Chapter 8: ESTIMATION OF PARAMETRIC SURVIVAL MODELS PART III APPLICATIONS AND EXTENSIONS Chapter 9: TRADITIONAL ACTUARIAL APPLICATIONS Chapter 10: MULTI-STATE MODELS Chapter 11: APPLICATIONS IN ECONOMICS AND FINANCE Chapter 12: ADDITIONAL MISCELLANEOUS APPLICATIONS Appendix A: PROPERTIES OF ESTIMATORS Appendix B: ASYMPTOTIC PROPERTIES OF MAXIMUM LIKELIHOOD ESTIMATORS Appendix C: DERIVATION OF EQUATION (8.49) Appendix D: EQUIVALENCE OF EQUATIONS (10.22a) and (10.22b) ANSWERS TO THEEXERCISES Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 BIBLIOGRAPHY 19