Age-Period-Cohort Analysis

Book description

This book explores the ways in which statistical models, methods, and research designs can be used to open new possibilities for APC analysis. Within a single, consistent HAPC-GLMM statistical modeling framework, the authors synthesize APC models and methods for three research designs: age-by-time period tables of population rates or proportions, repeated cross-section sample surveys, and accelerated longitudinal panel studies. They show how the empirical application of the models to various problems leads to many fascinating findings on how outcome variables develop along the age, period, and cohort dimensions.

Table of contents

  1. Cover
  2. Title Page
  3. Copyright Page
  4. Preface
  5. Table of Contents
  6. 1 Introduction
    1. References
  7. 2 Why Cohort Analysis?
    1. 2.1 Introduction
    2. 2.2 The Conceptualization of Cohort Effects
    3. 2.3 Distinguishing Age, Period, and Cohort
    4. 2.4 Summary
    5. References
  8. 3 APC Analysis of Data from Three Common Research Designs
    1. 3.1 Introduction
    2. 3.2 Repeated Cross-Sectional Data Designs
    3. 3.3 Research Design I: Age-by-Time Period Tabular Array of Rates/Proportions
      1. 3.3.1 Understanding Cancer Incidence and Mortality Using APC Analysis: Biodemography, Social Disparities, and Forecasting
      2. 3.3.2 Cancer Incidence Rates from Surveillance, Epidemiology, and End Results (SEER): 1973–2008
      3. 3.3.3 Cancer Mortality Rates from the National Center for Health Statistics (NCHS): 1969–2007
    4. 3.4 Research Design II: Repeated Cross-Sectional Sample Surveys
      1. 3.4.1 General Social Survey (GSS) 1972–2006: Verbal Test Score and Subjective Well-Being
      2. 3.4.2 National Health and Nutrition Examination Surveys (NHANES) 1971–2008: The Obesity Epidemic
      3. 3.4.3 National Health Interview Surveys (NHIS) 1984–2007: Health Disparities
      4. 3.4.4 Birth Cohort and Time Period Covariates Related to Cancer Trends
    5. 3.5 Research Design III: Prospective Cohort Panels and the Accelerated Longitudinal Design
      1. 3.5.1 Americans’ Changing Lives (ACL) Study 1986–2002: Depression, Physical Disability, and Self-Rated Health
      2. 3.5.2 Health and Retirement Survey (HRS) 1992–2008: Frailty Index
    6. References
  9. 4 Formalities of the Age-Period-Cohort Analysis Conundrum and a Generalized Linear Mixed Models (GLMM) Framework
    1. 4.1 Introduction
    2. 4.2 Descriptive APC Analysis
    3. 4.3 Algebra of the APC Model Identification Problem
    4. 4.4 Conventional Approaches to the APC Identification Problem,,,
      1. 4.4.1 Reduced Two-Factor Models
      2. 4.4.2 Constrained Generalized Linear Models (CGLIMs)
      3. 4.4.3 Nonlinear Parametric Transformation
      4. 4.4.4 Proxy Variables
      5. 4.4.5 Other Approaches in Biostatistics
    5. 4.5 Generalized Linear Mixed Models (GLMM) Framework
    6. References
  10. 5 APC Accounting/Multiple Classification Model, Part I: Model Identification and Estimation Using the Intrinsic Estimator
    1. 5.1 Introduction
    2. 5.2 Algebraic, Geometric, and Verbal Definitions of the Intrinsic Estimator
      1. 5.2.1 Algebraic Definition
      2. 5.2.2 Geometric Representation
      3. 5.2.3 Verbal Description
      4. 5.2.4 Computational Tools
    3. 5.3 Statistical Properties
      1. 5.3.1 Estimability, Unbiasedness, and Relative Efficiency
      2. 5.3.2 Asymptotic Properties
      3. 5.3.3 Implications
    4. 5.4 Model Validation: Empirical Example
    5. 5.5 Model Validation: Monte Carlo Simulation Analyses
      1. 5.5.1 Results for APC Models: True Effects of A, P, and C All Present
        1. 5.5.1.1 Property of Estimable Constraints
      2. 5.5.2 Misuse of APC Models: Revisiting a Numerical Example
    6. 5.6 Interpretation and Use of the Intrinsic Estimator
    7. Appendix 5.1: Proof of Unbiasedness of the IE as an Estimator of the b0 = Pprojb Constrained APC Coefficient Vector
    8. Appendix 5.2: Proof of Relative Efficiency of the IE as an Estimator of the b0 = Pprθj b Constrained APC Coefficient Vector
    9. Appendix 5.3: IE as a Minimum Norm Quadratic Unbiased Estimator of the b0 = Pprojb Constrained APC Coefficient Vector
    10. Appendix 5.4: Interpreting the Intrinsic Estimator, Its Relationship to Other Constrained Estimators in APC Accounting Models, and Limits on Its Empirical Applicability
    11. References
  11. 6 APC Accounting/Multiple Classification Model, Part II: Empirical Applications
    1. 6.1 Introduction
    2. 6.2 Recent U.S. Cancer Incidence and Mortality Trends by Sex and Race: A Three-Step Procedure
      1. 6.2.1 Step 1: Descriptive Analysis Using Graphics
      2. 6.2.2 Step 2: Model Fit Comparisons
      3. 6.2.3 Step 3: IE Analysis
        1. 6.2.3.1 All Cancer Sites Combined
        2. 6.2.3.2 Age Effects by Site
        3. 6.2.3.3 Period Effects by Site
        4. 6.2.3.4 Cohort Effects on Cancer Incidence
        5. 6.2.3.5 Cohort Effects on Cancer Mortality
      4. 6.2.4 Summary and Discussion of Findings
    3. 6.3 APC Model-Based Demographic Projection and Forecasting
      1. 6.3.1 Two-Dimensional versus Three-Dimensional View
      2. 6.3.2 Forecasting of the U.S. Cancer Mortality Trends for Leading Causes of Death
        1. 6.3.2.1 Methods of Extrapolation
        2. 6.3.2.2 Prediction Intervals
        3. 6.3.2.3 Internal Validation
        4. 6.3.2.4 Forecasting Results
    4. Appendix 6.1: The Bootstrap Method Using a Residual Resampling Scheme for Prediction Intervals
    5. References
  12. 7 Mixed Effects Models: Hierarchical APC-Cross-Classified Random Effects Models (HAPC-CCREM), Part I: The Basics
    1. 7.1 Introduction
    2. 7.2 Beyond the Identification Problem
    3. 7.3 Basic Model Specification
    4. 7.4 Fixed versus Random Effects HAPC Specifications
    5. 7.5 Interpretation of Model Estimates
    6. 7.6 Assessing the Significance of Random Period and Cohort Effects
      1. 7.6.1 HAPC Linear Mixed Models
        1. 7.6.1.1 Step 1: Study the Patterns and Statistical Significance of the Individual Estimated Coefficients for Time Periods and Birth Cohorts
        2. 7.6.1.2 Step 2: Test for the Statistical Significance of the Period and Cohort Effects Taken as a Group
      2. 7.6.2 HAPC Generalized Linear Mixed Models
    7. 7.7 Random Coefficients HAPC-CCREM
    8. Appendix 7.1: Matrix Algebra Representations of Linear Mixed Models and Generalized Linear Mixed Models
    9. References
  13. 8 Mixed Effects Models: Hierarchical APC-Cross-Classified Random Effects Models (HAPC-CCREM), Part II: Advanced Analyses
    1. 8.1 Introduction
    2. 8.2 Level 2 Covariates: Age and Temporal Changes in Social Inequalities in Happiness
    3. 8.3 HAPC-CCREM Analysis of Aggregate Rate Data on Cancer Incidence and Mortality
      1. 8.3.1 Trends in Age, Period, and Cohort Variations: Comparison with the IE Analysis
      2. 8.3.2 Sex and Race Differentials
      3. 8.3.3 Cohort and Period Mechanisms: Cigarette Smoking, Obesity, Hormone Replacement Therapy, and Mammography
    4. 8.4 Full Bayesian Estimation
      1. 8.4.1 REML-EB Estimation
      2. 8.4.2 Gibbs Sampling and MCMC Estimation
      3. 8.4.3 Discussion and Summary
    5. 8.5 HAPC-Variance Function Regression
      1. 8.5.1 Variance Function Regression: A Brief Overview
      2. 8.5.2 Research Topic: Changing Health Disparities
      3. 8.5.3 Intersecting the HAPC and VFR Models
      4. 8.5.4 Results: Variations in Health and Health Disparities by Age, Period, and Cohort, 1984–2007
      5. 8.5.5 Summary
    6. References
  14. 9 Mixed Effects Models: Hierarchical APC-Growth Curve Analysis of Prospective Cohort Data
    1. 9.1 Introduction
    2. 9.2 Intercohort Variations in Age Trajectories
      1. 9.2.1 Hypothesis
      2. 9.2.2 Model Specification
      3. 9.2.3 Results
    3. 9.3 Intracohort Heterogeneity in Age Trajectories
      1. 9.3.1 Hypothesis
      2. 9.3.2 Results
    4. 9.4 Intercohort Variations in Intracohort Heterogeneity Patterns
      1. 9.4.1 Hypothesis
      2. 9.4.2 Model Specification
      3. 9.4.3 Results
    5. 9.5 Summary
    6. References
  15. 10 Directions for Future Research and Conclusion
    1. 10.1 Introduction
    2. 10.2 Additional Models
      1. 10.2.1 The Smoothing Cohort Model and Nonparametric Methods
      2. 10.2.2 The Continuously Evolving Cohort Effects Model
    3. 10.3 Longitudinal Cohort Analysis of Balanced Cohort Designs of Age Trajectories
    4. 10.4 Conclusion
    5. References
  16. Index

Product information

  • Title: Age-Period-Cohort Analysis
  • Author(s): Yang Yang, Kenneth C. Land
  • Release date: April 2016
  • Publisher(s): Chapman and Hall/CRC
  • ISBN: 9781000218732