book

Age-Period-Cohort Analysis

Name: Age-Period-Cohort Analysis
ISBN: 9781466507531

by Yang Yang, Kenneth C. Land

April 2016

Intermediate to advanced

352 pages

10h 7m

English

Chapman and Hall/CRC

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Cover
Title Page
Copyright Page
Preface
Table of Contents
1 Introduction
References
2 Why Cohort Analysis?
2.1 Introduction2.2 The Conceptualization of Cohort Effects2.3 Distinguishing Age, Period, and Cohort2.4 SummaryReferences
3 APC Analysis of Data from Three Common Research Designs
3.1 Introduction3.2 Repeated Cross-Sectional Data Designs3.3 Research Design I: Age-by-Time Period Tabular Array of Rates/Proportions3.3.1 Understanding Cancer Incidence and Mortality Using APC Analysis: Biodemography, Social Disparities, and Forecasting3.3.2 Cancer Incidence Rates from Surveillance, Epidemiology, and End Results (SEER): 1973–20083.3.3 Cancer Mortality Rates from the National Center for Health Statistics (NCHS): 1969–20073.4 Research Design II: Repeated Cross-Sectional Sample Surveys3.4.1 General Social Survey (GSS) 1972–2006: Verbal Test Score and Subjective Well-Being3.4.2 National Health and Nutrition Examination Surveys (NHANES) 1971–2008: The Obesity Epidemic3.4.3 National Health Interview Surveys (NHIS) 1984–2007: Health Disparities3.4.4 Birth Cohort and Time Period Covariates Related to Cancer Trends3.5 Research Design III: Prospective Cohort Panels and the Accelerated Longitudinal Design3.5.1 Americans’ Changing Lives (ACL) Study 1986–2002: Depression, Physical Disability, and Self-Rated Health3.5.2 Health and Retirement Survey (HRS) 1992–2008: Frailty IndexReferences
4 Formalities of the Age-Period-Cohort Analysis Conundrum and a Generalized Linear Mixed Models (GLMM) Framework
4.1 Introduction4.2 Descriptive APC Analysis4.3 Algebra of the APC Model Identification Problem4.4 Conventional Approaches to the APC Identification Problem,,,4.4.1 Reduced Two-Factor Models4.4.2 Constrained Generalized Linear Models (CGLIMs)4.4.3 Nonlinear Parametric Transformation4.4.4 Proxy Variables4.4.5 Other Approaches in Biostatistics4.5 Generalized Linear Mixed Models (GLMM) FrameworkReferences
5 APC Accounting/Multiple Classification Model, Part I: Model Identification and Estimation Using the Intrinsic Estimator
5.1 Introduction5.2 Algebraic, Geometric, and Verbal Definitions of the Intrinsic Estimator5.2.1 Algebraic Definition5.2.2 Geometric Representation5.2.3 Verbal Description5.2.4 Computational Tools5.3 Statistical Properties5.3.1 Estimability, Unbiasedness, and Relative Efficiency5.3.2 Asymptotic Properties5.3.3 Implications5.4 Model Validation: Empirical Example5.5 Model Validation: Monte Carlo Simulation Analyses5.5.1 Results for APC Models: True Effects of A, P, and C All Present5.5.1.1 Property of Estimable Constraints5.5.2 Misuse of APC Models: Revisiting a Numerical Example5.6 Interpretation and Use of the Intrinsic EstimatorAppendix 5.1: Proof of Unbiasedness of the IE as an Estimator of the b0 = Pprojb Constrained APC Coefficient VectorAppendix 5.2: Proof of Relative Efficiency of the IE as an Estimator of the b0 = Pprθj b Constrained APC Coefficient VectorAppendix 5.3: IE as a Minimum Norm Quadratic Unbiased Estimator of the b0 = Pprojb Constrained APC Coefficient VectorAppendix 5.4: Interpreting the Intrinsic Estimator, Its Relationship to Other Constrained Estimators in APC Accounting Models, and Limits on Its Empirical ApplicabilityReferences

6 APC Accounting/Multiple Classification Model, Part II: Empirical Applications
6.1 Introduction6.2 Recent U.S. Cancer Incidence and Mortality Trends by Sex and Race: A Three-Step Procedure6.2.1 Step 1: Descriptive Analysis Using Graphics6.2.2 Step 2: Model Fit Comparisons6.2.3 Step 3: IE Analysis6.2.3.1 All Cancer Sites Combined6.2.3.2 Age Effects by Site6.2.3.3 Period Effects by Site6.2.3.4 Cohort Effects on Cancer Incidence6.2.3.5 Cohort Effects on Cancer Mortality6.2.4 Summary and Discussion of Findings6.3 APC Model-Based Demographic Projection and Forecasting6.3.1 Two-Dimensional versus Three-Dimensional View6.3.2 Forecasting of the U.S. Cancer Mortality Trends for Leading Causes of Death6.3.2.1 Methods of Extrapolation6.3.2.2 Prediction Intervals6.3.2.3 Internal Validation6.3.2.4 Forecasting ResultsAppendix 6.1: The Bootstrap Method Using a Residual Resampling Scheme for Prediction IntervalsReferences
7 Mixed Effects Models: Hierarchical APC-Cross-Classified Random Effects Models (HAPC-CCREM), Part I: The Basics
7.1 Introduction7.2 Beyond the Identification Problem7.3 Basic Model Specification7.4 Fixed versus Random Effects HAPC Specifications7.5 Interpretation of Model Estimates7.6 Assessing the Significance of Random Period and Cohort Effects7.6.1 HAPC Linear Mixed Models7.6.1.1 Step 1: Study the Patterns and Statistical Significance of the Individual Estimated Coefficients for Time Periods and Birth Cohorts7.6.1.2 Step 2: Test for the Statistical Significance of the Period and Cohort Effects Taken as a Group7.6.2 HAPC Generalized Linear Mixed Models7.7 Random Coefficients HAPC-CCREMAppendix 7.1: Matrix Algebra Representations of Linear Mixed Models and Generalized Linear Mixed ModelsReferences
8 Mixed Effects Models: Hierarchical APC-Cross-Classified Random Effects Models (HAPC-CCREM), Part II: Advanced Analyses
8.1 Introduction8.2 Level 2 Covariates: Age and Temporal Changes in Social Inequalities in Happiness8.3 HAPC-CCREM Analysis of Aggregate Rate Data on Cancer Incidence and Mortality8.3.1 Trends in Age, Period, and Cohort Variations: Comparison with the IE Analysis8.3.2 Sex and Race Differentials8.3.3 Cohort and Period Mechanisms: Cigarette Smoking, Obesity, Hormone Replacement Therapy, and Mammography8.4 Full Bayesian Estimation8.4.1 REML-EB Estimation8.4.2 Gibbs Sampling and MCMC Estimation8.4.3 Discussion and Summary8.5 HAPC-Variance Function Regression8.5.1 Variance Function Regression: A Brief Overview8.5.2 Research Topic: Changing Health Disparities8.5.3 Intersecting the HAPC and VFR Models8.5.4 Results: Variations in Health and Health Disparities by Age, Period, and Cohort, 1984–20078.5.5 SummaryReferences
9 Mixed Effects Models: Hierarchical APC-Growth Curve Analysis of Prospective Cohort Data
9.1 Introduction9.2 Intercohort Variations in Age Trajectories9.2.1 Hypothesis9.2.2 Model Specification9.2.3 Results9.3 Intracohort Heterogeneity in Age Trajectories9.3.1 Hypothesis9.3.2 Results9.4 Intercohort Variations in Intracohort Heterogeneity Patterns9.4.1 Hypothesis9.4.2 Model Specification9.4.3 Results9.5 SummaryReferences
10 Directions for Future Research and Conclusion
10.1 Introduction10.2 Additional Models10.2.1 The Smoothing Cohort Model and Nonparametric Methods10.2.2 The Continuously Evolving Cohort Effects Model10.3 Longitudinal Cohort Analysis of Balanced Cohort Designs of Age Trajectories10.4 ConclusionReferences
Index

Overview

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.

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