Gilberto Levy & Bruce Levin 
The Biostatistics of Aging [EPUB ebook] 
From Gompertzian Mortality to an Index of Aging-Relatedness

PREFACE AND ACKNOWLEDGMENT ix
1 Introduction 1
2 An Account of Gompertzian Mortality through Statistical and
Evolutionary Arguments 6
2.1 The Statistical Theory of Extreme Values 10
2.2 The Evolutionary Theory of Aging 36
3 The Argument against Gompertzian Mortality 69
3.1 Departures from the Gompertz Model 70
3.2 An Evolution-Based Model of Causation 72
4 The Index of Aging-Relatedness 93
4.1 A Survival Mixture Model of the Gompertz and Weibull
Distributions 94
4.2 Definition and Interpretation of the Index of
Aging-Relatedness 97
4.3 The Survival Mixture Model and Competing Risks 103
4.4 Estimation of the Model Parameters 107
4.5 Illustrative Application: The Israeli Ischemic Heart Disease
Study 109
4.6 Precision of Estimation 122
5 Discussion: Implications 128
5.1 The Meaning of the Gompertz Parameter 128
5.2 Age as a Risk Factor for Disease 132
5.3 Are Aging-Related Diseases an Integral Part of Aging?
134
5.4 Biological versus Chronological Aging 135
5.5 The Public Health Notion of Compression of Morbidity 138
5.6 A Picture of Aging for the Twenty-First Century 143
APPENDIX A: PROOFS OF RESULTS IN SECTION 2.1.2 WITH SOME
EXTENSIONS 154
APPENDIX B: DERIVATION OF HAMILTON’S EQUATION FOR THE
FORCE OF NATURAL SELECTION ON MORTALITY 170
APPENDIX C: SOME PROPERTIES OF THE GOMPERTZ AND WEIBULL
DISTRIBUTIONS 174
APPENDIX D: FIRST AND SECOND PARTIAL DERIVATIVES OF THE
MIXTURE LOG-LIKELIHOOD FUNCTION 178
APPENDIX E: EXPECTATION-CONDITIONAL MAXIMIZATION (ECM)
ALGORITHM 183
APPENDIX F: R PROGRAM 190
REFERENCES 226
AUTHOR INDEX 245
SUBJECT INDEX 253

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.