Biostatistics of Aging

GILBERTO LEVY, MD, DRPH, is a neurologist with a primary research interest in aging and aging-related diseases, particularly dementia. He conducted clinical research within the spheres of epidemiological studies and clinical trials at Columbia University for more than ten years. Dr. Levy is the author of over thirty journal articles and three book chapters.BRUCE LEVIN, PHD, is Professor of Biostatistics and past chair of the Department of Biostatistics in the Mailman School of Public Health at Columbia University. A Fellow of the American Statistical Association, his research interests include sequential selection procedures and their use in adaptive clinical trial designs. He is the coauthor (with J.L. Fleiss and M.C. Paik) of Statistical Methods for Rates and Proportions, Third Edition, published by Wiley.

• PREFACE AND ACKNOWLEDGMENT ix1 Introduction 12 An Account of Gompertzian Mortality through Statistical and Evolutionary Arguments 62.1 The Statistical Theory of Extreme Values 102.2 The Evolutionary Theory of Aging 363 The Argument against Gompertzian Mortality 693.1 Departures from the Gompertz Model 703.2 An Evolution-Based Model of Causation 724 The Index of Aging-Relatedness 934.1 A Survival Mixture Model of the Gompertz and Weibull Distributions 944.2 Definition and Interpretation of the Index of Aging-Relatedness 974.3 The Survival Mixture Model and Competing Risks 1034.4 Estimation of the Model Parameters 1074.5 Illustrative Application: The Israeli Ischemic Heart Disease Study 1094.6 Precision of Estimation 1225 Discussion: Implications 1285.1 The Meaning of the Gompertz Parameter 1285.2 Age as a Risk Factor for Disease 1325.3 Are Aging-Related Diseases an Integral Part of Aging? 1345.4 Biological versus Chronological Aging 1355.5 The Public Health Notion of Compression of Morbidity 1385.6 A Picture of Aging for the Twenty-First Century 143APPENDIX A: PROOFS OF RESULTS IN SECTION 2.1.2 WITH SOME EXTENSIONS 154APPENDIX B: DERIVATION OF HAMILTON’S EQUATION FOR THE FORCE OF NATURAL SELECTION ON MORTALITY 170APPENDIX C: SOME PROPERTIES OF THE GOMPERTZ AND WEIBULL DISTRIBUTIONS 174APPENDIX D: FIRST AND SECOND PARTIAL DERIVATIVES OF THE MIXTURE LOG-LIKELIHOOD FUNCTION 178APPENDIX E: EXPECTATION–CONDITIONAL MAXIMIZATION (ECM) ALGORITHM 183APPENDIX F: R PROGRAM 190REFERENCES 226AUTHOR INDEX 245SUBJECT INDEX 253

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