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1 Introduction: The Biodemography of Complex Relationships Among Aging, Health, and Longevity |
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1 | (20) |
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1 | (6) |
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2 | (1) |
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1.1.2 Biodemographic Ideas in Genetic Analyses of Human Longevity |
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3 | (1) |
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1.1.3 Evolution of Aging, Health, and Mortality: Many Open Questions |
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4 | (1) |
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1.1.4 Strehler and Mildvan's Model of Aging and Mortality |
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5 | (1) |
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1.1.5 Historical Roots of the Stochastic Process Model |
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6 | (1) |
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1.2 Information on Aging, Health, and Longevity from Available Data: Part I |
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7 | (3) |
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1.3 Statistical Modeling and Other Advanced Methods of Analyzing Data on Aging, Health, and Longevity: Part II |
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10 | (3) |
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13 | (1) |
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14 | (7) |
Part I Information on Aging, Health, and Longevity from Available Data |
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2 Age Trajectories of Physiological Indices: Which Factors Influence Them? |
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21 | (26) |
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21 | (2) |
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2.2 Data: The Framingham Heart Study (FHS) |
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23 | (2) |
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25 | (1) |
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25 | (17) |
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2.4.1 Average Age Trajectories of Physiological Variables |
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25 | (3) |
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2.4.2 Age Trajectories of Standard Deviations (SD) of Physiological Variables |
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28 | (1) |
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2.4.3 Age Patterns of Survival and Physiological Variables for Smokers and Non-smokers |
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29 | (2) |
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2.4.4 Effects of Education on Survival and Average Age Trajectories of Physiological Indices |
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31 | (2) |
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2.4.5 Age Trajectories of Long Lived (LL) and Short Lived (SL) Individuals |
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33 | (4) |
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2.4.6 Effects of Disease on Dynamic Properties of Physiological Indices |
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37 | (3) |
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2.4.7 Effects of Genetic Dose on Age Patterns of Physiological Indices |
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40 | (2) |
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42 | (2) |
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44 | (3) |
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3 Health Effects and Medicare Trajectories: Population-Based Analysis of Morbidity and Mortality Patterns |
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47 | (48) |
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47 | (1) |
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48 | (3) |
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3.2.1 Data: SEER-M and NLTCS-M |
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48 | (2) |
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3.2.2 Definitions of Dates of Disease Onset and Dates of Recovery/Remission |
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50 | (1) |
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51 | (35) |
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3.3.1 Age Patterns of Age-Associated Disease Incidence |
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52 | (2) |
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3.3.2 Incidence Rates: Comparisons with Other Studies |
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54 | (9) |
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3.3.3 Age-Adjusted Rates: Gender Disparities, Time Trends, and Sensitivity Analysis |
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63 | (2) |
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3.3.4 Disability and Comorbidity Patterns of Incidence Rates |
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65 | (5) |
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3.3.5 Mortality Age Patterns and Medicare Data |
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70 | (2) |
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3.3.6 Recovery or Long-Term Remission |
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72 | (2) |
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3.3.7 Risk Factors for Disease Incidence |
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74 | (4) |
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3.3.8 Mutual Dependence in Disease Risks: Age-Patterns |
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78 | (1) |
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3.3.9 Comorbidity and Multimorbidity |
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79 | (2) |
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3.3.10 Predictive Population Models |
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81 | (5) |
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86 | (3) |
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89 | (6) |
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4 Evidence for Dependence Among Diseases |
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95 | (18) |
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95 | (1) |
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96 | (2) |
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98 | (4) |
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4.3.1 Empirical Analyses Reveal Negative Correlations among Major Causes of Death |
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98 | (2) |
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4.3.2 A Dependent Competing Risk Model Capturing Negative Correlations Between Causes of Death |
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100 | (2) |
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102 | (5) |
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4.4.1 Evidence of Trade-Offs Between Cancer and Aging |
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103 | (1) |
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4.4.2 Trade-Offs Between Cancer and Other Diseases |
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104 | (1) |
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4.4.3 Time Trends in Negative Correlations Between Cancer and Other Diseases |
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105 | (1) |
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4.4.4 Cancer and Anti-aging Interventions |
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106 | (1) |
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107 | (1) |
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107 | (6) |
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5 Factors That May Increase Vulnerability to Cancer and Longevity in Modern Human Populations |
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113 | (30) |
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5.1 Introduction: Economic Prosperity, Longevity, and Cancer Risk |
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113 | (6) |
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5.2 The Proportion of People Who Are More Susceptible to Cancer May Be Higher in the More Developed World |
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119 | (9) |
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5.2.1 Improved Survival of Frail Individuals |
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120 | (2) |
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5.2.2 Avoiding or Reducing Traditional Exposures |
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122 | (1) |
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5.2.3 Burden of Novel and Nontraditional Exposures |
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123 | (5) |
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5.3 Some of the Factors Associated with Economic Development and the Western Lifestyle May Antagonistically Influence Aging and Vulnerability to Cancer |
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128 | (3) |
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5.3.1 Cancer and Aging: A Trade-Off7 |
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128 | (1) |
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5.3.2 Increased Exposure to Growth Factors |
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128 | (1) |
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129 | (1) |
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5.3.4 Giving Birth at Later Age |
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130 | (1) |
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131 | (1) |
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132 | (11) |
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6 Medical Cost Trajectories and Onset of Age-Associated Diseases |
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143 | (20) |
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143 | (2) |
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145 | (2) |
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145 | (1) |
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6.2.2 Date of Disease Onset Definitions |
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146 | (1) |
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6.2.3 Medical Cost Trajectories |
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147 | (1) |
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147 | (9) |
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6.3.1 Medical Cost as Disease Severity |
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153 | (1) |
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154 | (2) |
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156 | (4) |
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160 | (3) |
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7 Indices of Cumulative Deficits |
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163 | (24) |
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163 | (1) |
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7.2 Conceptualization of the Deficits Index |
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164 | (1) |
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7.3 Cross-Sectional Age Patterns of the Deficits Index as Characteristics of Aging-Related Processes |
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164 | (1) |
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7.4 Deficits Indices and Age as Indicators of Aging-Related Processes |
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165 | (7) |
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7.4.1 Frequency Distributions |
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166 | (1) |
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7.4.2 Correlation of the DI and Age |
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167 | (1) |
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7.4.3 DI-Specific Age Patterns for Decedents and Survivors |
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167 | (1) |
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7.4.4 The DI and Age Patterns of Time to Death |
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168 | (1) |
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7.4.5 The DI and Age Specific Mortality Rates |
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169 | (1) |
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7.4.6 Relative Risks of Death |
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170 | (2) |
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7.5 Longitudinal Analyses: The DI as an Indicator and Predictor of Long Life |
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172 | (11) |
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7.5.1 Construction of Long- and Short-Life Phenotypes |
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173 | (1) |
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7.5.2 Longitudinal Changes of the Mean DI in the SL, LLD, and LLA Cohorts |
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173 | (1) |
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7.5.3 The DI as an Indicator of Frailty |
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174 | (2) |
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7.5.4 The Phenotypic Frailty Index (PH) and the DI |
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176 | (1) |
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7.5.5 The PH and DI as Predictors of Death |
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177 | (3) |
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7.5.6 Mid-to-Late Life DIs and Physiological Indices as Characteristics of Long-Term Survival |
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180 | (1) |
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7.5.7 The DI, Endophenotypes, and Long-Term Survival in the FHS |
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181 | (2) |
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183 | (1) |
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183 | (4) |
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8 Dynamic Characteristics of Aging-Related Changes as Predictors of Longevity and Healthy Lifespan |
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187 | (24) |
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187 | (3) |
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190 | (11) |
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8.2.1 Definitions and Evaluation of Dynamic Risk Factors |
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190 | (6) |
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8.2.2 Statistical Analyses |
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196 | (5) |
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201 | (3) |
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8.3.1 Effects of Individual Dynamics of Physiological Indices at Ages 40-60 on Mortality Risk and Risk of Onset of "Unhealthy Life" at Ages 60+ |
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201 | (1) |
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8.3.2 Effects of Dynamic Characteristics of Physiological Indices with Non-monotonic Age Trajectories on Mortality Risk and Risk of Onset of "Unhealthy Life" |
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201 | (1) |
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8.3.3 Effects of Dichotomized Dynamic Characteristics of Physiological Indices with Non-monotonic Age Trajectories |
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202 | (1) |
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8.3.4 Sensitivity Analyses |
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203 | (1) |
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204 | (3) |
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207 | (1) |
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208 | (3) |
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9 The Complex Role of Genes in Diseases and Traits in Late Life: An Example of the Apolipoprotein E Polymorphism |
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211 | (20) |
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9.1 Genes and Diseases in Late Life |
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211 | (2) |
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9.2 The Antagonistic Role of the APOE Gene and Two Types of Sexually Dimorphic Tradeoffs: The Case of CVD and Cancer |
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213 | (9) |
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9.2.1 The FHSO: Tradeoffs in the Effects of the APOE Polymorphism on the Ages at Onset of CVD and Cancer |
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213 | (3) |
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9.2.2 The FHS: The Antagonistic Role of the APOE Polymorphism in CVD and Its Tradeoffs with Cancer |
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216 | (2) |
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9.2.3 The FHS and the FHSO: Aging-Related Heterogeneity in a Changing Environment |
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218 | (4) |
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9.3 Tradeoffs in the Effects of APOE on Risks of CVD and Cancer Influence Human Lifespan |
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222 | (6) |
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9.3.1 The FHS and FHSO: Survival |
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222 | (6) |
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228 | (1) |
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228 | (3) |
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10 Conclusions Regarding Empirical Patterns of Aging, Health, and Longevity |
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231 | (10) |
Part II Statistical Modeling of Aging, Health, and Longevity |
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11 Approaches to Statistical Analysis of Longitudinal Data on Aging, Health, and Longevity: Biodemographic Perspectives |
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241 | (22) |
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241 | (3) |
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11.2 Statistical Approaches to Joint Analysis of Longitudinal and Time-to-Event Outcomes |
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244 | (9) |
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11.2.1 Standard Joint Models and Their Extensions |
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244 | (6) |
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11.2.2 The Use of Stochastic Processes to Capture Biological Variation and Heterogeneity in Longitudinal Patterns in Joint Models |
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250 | (3) |
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11.3 Bringing Biology to Statistics: Biodemographic Models for Analysis of Longitudinal Data on Aging, Health, and Longevity |
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253 | (2) |
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255 | (8) |
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12 Stochastic Process Models of Mortality and Aging |
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263 | (22) |
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263 | (3) |
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266 | (9) |
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12.2.1 General Description |
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266 | (2) |
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12.2.2 Estimation Procedure |
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268 | (4) |
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12.2.3 Simulation Studies |
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272 | (3) |
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275 | (10) |
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12.3.1 To What Extent Can Mortality Rates Characterize Aging? |
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275 | (1) |
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12.3.2 The Strehler and Mildvan Model |
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275 | (1) |
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12.3.3 Comparing Two Versions of the Stochastic Process Model |
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276 | (3) |
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12.3.4 Modeling Personalized Aging Changes |
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279 | (1) |
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279 | (6) |
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13 The Latent Class Stochastic Process Model for Evaluation of Hidden Heterogeneity in Longitudinal Data |
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285 | (18) |
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285 | (1) |
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13.2 Approaches to the Incorporation of Hidden Heterogeneity in Analyses of Longitudinal and Time-to-Event Data |
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286 | (3) |
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13.3 The Latent Class Stochastic Process Model |
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289 | (5) |
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13.3.1 Specification of the Model |
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289 | (2) |
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13.3.2 Likelihood Estimation Procedure |
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291 | (3) |
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294 | (4) |
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13.4.1 Simulation Study for Latent Class Stochastic Process Model |
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294 | (1) |
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13.4.2 Simulation Study for Stochastic Process Model That Ignores Latent Classes |
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295 | (3) |
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13.5 Discussion and Conclusion |
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298 | (2) |
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300 | (3) |
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14 How Biodemographic Approaches Can Improve Statistical Power in Genetic Analyses of Longitudinal Data on Aging, Health, and Longevity |
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303 | (18) |
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303 | (3) |
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14.2 Simulation Studies of the Longitudinal Genetic-Demographic Model |
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306 | (4) |
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14.3 Simulation Studies in Genetic Stochastic Process Model |
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310 | (4) |
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314 | (4) |
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318 | (3) |
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15 Integrative Mortality Models with Parameters That Have Biological Interpretations |
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321 | (10) |
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321 | (2) |
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15.2 Conditional Risk of Death and Demographic Mortality Rate |
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323 | (1) |
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15.3 Description of the Processes θt and Yt and Their Connections to t |
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324 | (1) |
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15.4 Evolution of the Conditional Distribution of θt and Yt Among Those Who Survived to Age t |
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325 | (2) |
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15.5 Gaussian Approximation |
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327 | (1) |
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328 | (2) |
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330 | (1) |
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16 Integrative Mortality Models for the Study of Aging, Health, and Longevity: Benefits of Combining Data |
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331 | (22) |
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331 | (1) |
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16.2 Observational Plans and Combining Data |
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332 | (11) |
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16.2.1 Likelihood Function of Life Span Data |
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332 | (1) |
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16.2.2 Longitudinal Data on Physiological Variables: Health Changes Are Not Observed: Observational Plan #1 |
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333 | (2) |
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16.2.3 Gaussian Approximation of the Model of Physiological Variables |
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335 | (2) |
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16.2.4 Data on Health Transitions Without Measurements of the Physiological State: Observational Plan #2 |
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337 | (1) |
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16.2.5 The Likelihood of the Data on Health Transitions |
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338 | (1) |
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16.2.6 Gaussian Approximation of the Model with Health Transitions |
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338 | (1) |
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16.2.7 Discrete Time Observations of the Physiological State and Health Transitions: Observational Plan #3 |
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339 | (2) |
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16.2.8 Gaussian Approximation of the Model of Longitudinal Data on Physiological Variables and Health Transitions |
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341 | (2) |
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343 | (7) |
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16.3.1 The Model with Repeated Measurements of a Physiological Variable and Changes in Health State: Observational Plan #3 |
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343 | (4) |
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16.3.2 Combining Data with Observational Plans #1 and #2 |
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347 | (3) |
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16.4 Discussion and Conclusion |
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350 | (1) |
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351 | (2) |
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17 Analysis of the Natural History of Dementia Using Longitudinal Grade of Membership Models |
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353 | (66) |
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353 | (3) |
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356 | (19) |
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356 | (5) |
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361 | (2) |
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363 | (1) |
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17.2.4 Derivatives of Log-Likelihood |
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363 | (1) |
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17.2.5 Constrained Log-Likelihood |
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364 | (1) |
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17.2.6 Kuhn-Tucker Conditions |
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364 | (1) |
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17.2.7 Derivatives of Constrained Log-Likelihood |
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365 | (2) |
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17.2.8 Constrained Newton-Raphson Procedures |
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367 | (3) |
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17.2.9 Consistency and Asymptotic Normality |
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370 | (3) |
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373 | (2) |
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375 | (5) |
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17.3.1 National Long Term Care Survey |
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375 | (2) |
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377 | (3) |
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380 | (27) |
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380 | (3) |
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383 | (12) |
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17.4.3 Ancillary Analysis: Mortality |
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395 | (3) |
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17.4.4 Ancillary Analysis: Acute and Long-Term Care |
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398 | (9) |
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407 | (3) |
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410 | (1) |
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Synthesis of Known Results Regarding the Consistency of the General (Cross-Sectional) Empirical GoM Model |
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410 | (5) |
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415 | (4) |
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18 Linear Latent Structure Analysis: Modeling High-Dimensional Survey Data |
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419 | (26) |
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419 | (1) |
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18.2 Linear Latent Structure Analysis |
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420 | (8) |
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18.2.1 Structure of Datasets and Population Characteristics |
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420 | (1) |
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18.2.2 LLS Task: Statistical, Geometrical, and Mixing Distribution Points of View |
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421 | (2) |
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18.2.3 Moment Matrix and the Main System of Equations |
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423 | (5) |
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18.3 Computational Algorithm for Estimating LLS Model |
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428 | (8) |
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18.3.1 Moment Matrix Calculation |
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428 | (1) |
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18.3.2 Computational Rank of the Frequency Matrix |
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429 | (1) |
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18.3.3 Finding the Supporting Plane |
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429 | (4) |
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433 | (1) |
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18.3.5 Calculation of Individual Conditional Expectations |
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433 | (1) |
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18.3.6 Mixing Distribution |
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434 | (1) |
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18.3.7 Properties of LLS Estimator |
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434 | (1) |
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435 | (1) |
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436 | (1) |
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436 | (5) |
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18.4.1 Simulation Studies |
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436 | (1) |
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18.4.2 LLS and Latent Class Models |
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437 | (1) |
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18.4.3 LLS and Grade of Membership (GoM) Models |
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437 | (2) |
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18.4.4 Application to the NLTCS Data |
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439 | (2) |
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441 | (2) |
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443 | (2) |
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19 Conclusions Regarding Statistical Modeling of Aging, Health, and Longevity |
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445 | (8) |
Part III Conclusions |
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20 Continuing the Search for Determinants of Healthy Life Span and Longevity |
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453 | |
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456 | |