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The Biostatistics of Aging: From Gompertzian Mortality to an Index of Aging-Relatedness

The Biostatistics of Aging: From Gompertzian Mortality to an Index of Aging-Relatedness

Gilberto Levy, Bruce Levin

ISBN: 978-1-118-64585-7

May 2014

272 pages

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£91.50

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Description

A practical and clarifying approach to aging and aging-related diseases

Providing a thorough and extensive theoretical framework, The Biostatistics of Aging: From Gompertzian Mortality to an Index of Aging-Relatedness addresses the surprisingly subtlenotion—with consequential biomedical and public health relevance—of what it means for acondition to be related to aging. In this pursuit, the book presents a new quantitative methodto examine the relative contributions of genetic and environmental factors to mortality anddisease incidence in a population.

With input from evolutionary biology, population genetics, demography, and epidemiology, this medically motivated book describes an index of aging-relatedness and also features:

  • Original results on the asymptotic behavior of the minimum of time-to-event random variables, which extends those of the classical statistical theory of extreme values
  • A comprehensive and satisfactory explanation based on biological principles of the Gompertz pattern of mortality in human populations
  • The development of an evolution-based model of causation relevant to mortality and aging-related diseases of complex etiology
  • An explanation of how and why the description of human mortality by the Gompertz distribution can be improved upon from first principles
  • The amply illustrated analysis of real-world data, including a program for conducting the analysis written in the freely available R statistical software
  • Technical appendices including mathematical material as well as an extensive and multidisciplinary bibliography on aging and aging-related diseases

The Biostatistics of Aging: From Gompertzian Mortality to an Index of Aging-Relatedness is an excellent resource for practitioners and researchers with an interest in aging and aging-related diseases from the fields of medicine, biology, gerontology, biostatistics, epidemiology, demography, and public health.

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