Age-Period-Cohort Analysis

New Models, Methods, and Empirical Applications

Yang Yang, Kenneth C. Land

• Publisher: CRC Press
• Year: 2016
• Print ISBN: 9781466507524
• eBook ISBN: 9781000218732
• Edition: 1
• Topic: Social Sciences
• Subtopic: Social Science Research & Methodology
• Index: Social Sciences

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.

1

Introduction

Demographers, epidemiologists, and social scientists often deal with temporally ordered datasets, that is, population or sample survey data in the form of observations or measurements on individuals or groups/populations of individuals that are repeated or ordered along a time dimension. In this context, a long-standing analytic problem is the conceptualization, estimation, and interpretation of the differential contributions of three time-related changes to the phenomena of interest, namely, the effects of differences in the ages of the individuals at the time of observation on an outcome of interest, termed age (A) effects; the effects of differences in the time periods of observation or measurement of the outcome, termed period (P) effects; and the effects of differences in the year of birth or some other shared life events for a set of individuals, termed cohort (C) effects. To address this problem, researchers need to compare age-specific data recorded at different points in time and from different cohorts. A systematic study of such data is termed age-period-cohort (APC) analysis. APC analysis has the unique ability to depict parsimoniously the entire complex of social, historical, and environmental factors that simultaneously affect individuals and populations of individuals. It has thus been widely used to address questions of enduring importance to the studies of social change, etiology of diseases, aging, and population processes and dynamics.

The distinct meanings of A, P, and C effects will be elaborated and become more concrete in specific contexts. As a first specification, consider the definition of these terms in the context of aging and human development across the life course, health, and chronic disease epidemiology (Yang 2007, 2009, 2010). In this context, the following applies:

Age effects are variations associated with chronological age groups. They can arise from physiological changes, accumulation of social experience, social role or status changes, or a combination of these. Age effects therefore reflect biological and social processes of aging internal to individuals and represent developmental changes across the life course. This can clearly be seen in the considerable regularities of age variations across time and space in many outcomes, such as fertility, schooling, employment, marriage and family structure, disease prevalence and incidence, and mortality.

Period effects are variations over time periods or calendar years that influence all age groups simultaneously. Period effects subsume a complex set of historical events and environmental factors, such as world wars, economic expansions and contractions, famine and pandemics of infectious diseases, public health interventions, and technology breakthroughs. Shifts in social, cultural, economic, or physical environments may in turn induce similar changes in the lives of all individuals at a point in time. Thus, period effects are evident from a correspondence in timing of changes in events and social and epidemiologic conditions that influence these events. For example, the decrease in lung cancer mortality in the United States after 1990 followed reductions in tar and nicotine yield per cigarette and increases in smoking cessation in earlier years (Jemal, Chu, and Tarone 2001). In addition to these direct effects, there may also be changes in disease classification or diagnostic techniques that affect the incidence of, or mortality from, certain diseases. For example, the increase in the slope of the period trend of U.S. female breast cancer mortality in the 1980s coincided with the marked increase in breast cancer incidence due to expanded use of diagnosis via mammography (Tarone, Chu, and Gaudette 1997).

Cohort effects are changes across groups of individuals who experience an initial event such as birth or marriage in the same year or years. Birth cohorts are the most commonly examined unit of analysis in APC analysis. A birth cohort moves through life together and encounters the same historical and social events at the same ages. Birth cohorts that experience different historical and social conditions at various stages of their life course therefore have diverse exposures to socioeconomic, behavioral, and environmental risk factors. Cohort effects are evident in many cancer sites, chronic diseases, and human mortality. An in-depth discussion of the concept of cohort effects is given in the next chapter.

The challenges posed by APC analysis are well known. Whether observed time-related changes can be distilled out and separated into aging, time period, and cohort components is a question usually deemed conceptually important but empirically intractable. It has been termed the “conundrum” of APC analysis (Glenn 2005: 20) for two reasons. The first is data limitations. Using cross-sectional data at one point in time, for example, aging and cohort effects are intermingled and confounded. Using longitudinal panel data for a single cohort, on the other hand, aging and period effects are intermingled and confounded. The second reason is the use of conventional linear regression models that suffer from either specification errors or an identification problem and consequently are incapable of distinguishing A, P, and C effects.

The identification problem has been a topic of intense discussion and research since the 1970s. This led to a synthesis of APC methodology for the social sciences and demography based on the work of William M. Mason and Stephen E. Fienberg in the 1970s and 1980s (Fienberg and Mason 1979; Mason and Fienberg 1985). The Mason-Fienberg synthesis so dominated these disciplines in the 1980s and 1990s that relatively few new contributions to APC methodology were published in these decades. By comparison, APC methodology continued to be of interest in epidemiology, within which several new graphical and analytic methods were published during this period.

Although a variety of approaches has been proposed to solve the APC conundrum, each has limitations. Yet another challenge is a criticism often lodged against general-purpose methods of APC analysis, namely, they provide no avenue for testing specific, substantive, and mechanism-based hypotheses and thus are mere accounting devices of algebraic convenience that may be misleading. This leads to the question: What should an analyst do to model APC data in empirical research to further an understanding of the social and biological mechanisms generating the data? Since the year 2000, new interest in APC models and methods has emerged in the social sciences to address this question. This includes a series of studies by us as well as works by others exemplified in a special issue of the Sociological Methods & Research (36(3) February 2008).

The major objective of this book is to present new APC models, methods, and empirical applications. Statistics has continued to develop as a discipline since the Mason-Fienberg synthesis of 1985. New statistical models and new computationally intensive estimation methods have been developed (e.g., mixed [fixed and random] effects models, Markov chain Monte Carlo methods). For another, datasets with new research designs that invite or even require the analysis of separate age, period, and cohort components of change are available. Accordingly, we seek to show some ways in which these statistical models and methods and research designs can be applied to open new possibilities for APC analysis. We aim to articulate and compare new and extant models and methods that can be widely used by analysts. We also aim to provide some useful guidelines on how to conduct APC analysis. In doing so, this book intends to make two essential contributions to quantitative studies of time-related change. First, through the introduction of the generalized linear mixed model (GLMM) framework, we show how innovative estimation methods and new model specifications resolve the “model identification problem” that has hampered the development of APC analysis for the past decades. Second, we address the major criticism against the utility of APC analysis by explaining and demonstrating the use of new models within the GLMM framework to uncover the mechanisms underlying age patterns and temporal trends in phenomena of interest to researchers. We achieve these goals through both methodological expositions and empirical studies. For empirical illustrations, we draw examples on a wide variety of disciplines, such as sociology, demography, and epidemiology but focus on aging, longevity, and health disparities. We do not, however, claim that the new models and methods presented here are “solutions” to the APC analysis problem in any absolute sense. As articulated in Chapter 4, the classical APC identification problem in tabular arrays of population rates or proportions is a member of a class of structural underidentification problems for which there can never be a “complete” resolution.

The contents of the volume are as follows: Chapter 2 discusses the conceptualization of cohort effects and theoretical rationale for the importance of cohort analysis. Chapter 3 introduces prototypical datasets to be analyzed in further detail in subsequent chapters that characterize the application of APC analysis in three common research designs. Chapter 4 lays out the formal algebra of the APC analysis conundrum, reviews some conventional approaches to this problem, and sketches a GLMM framework that we use to organize the new families of models and methods.

Chapter 5 focuses on an innovation within the conventional linear regression models: the Intrinsic Estimator (IE) as a new method of coefficient estimation. Chapter 6 introduces a three-step procedure for APC analysis through empirical studies of U.S. cancer incidence and mortality trends by sex and race. It also illustrates the utility of APC models in demographic projections and forecasts through an empirical APC analysis and construction of the associated implied projections of cancer mortality in the period 2010–2029. As part of the methodological exposition of the nature and utilities of the IE method, we include in this chapter algebraic details of its statistical properties with proofs (Section 5.3; Appendice 5.1, Appendice 5.2 and Appendice 5.3) and model validation through Monte Carlo simulation analysis (Section 5.5). We also include computational algorithms for obtaining the prediction intervals for forecasting (Appendix 6.1). Readers not adept with or interested in advanced statistical methods can skip these sections.

Chapters 7 and 8 introduce the mixed effects models for APC analysis using the hierarchical APC (HAPC) models. We emphasize two breakthroughs of this type of models compared to the linear fixed effects models classically used in APC analysis: contextualization of individual lives within cohorts and periods, which avoids the model identification problem, and incorporation of additional covariates, which allows for mechanism-based hypothesis testing. We illustrate in Chapter 7 the application of these models in studies of verbal ability trends in the United States and changing sex and race disparities in obesity. In Chapter 8 we analyze the social inequalities of happiness in relation to macroeconomic conditions and cohort characteristics and cancer mortality rates in relation to known risk factors and diagnostic and treatment factors. We also discuss in Chapter 8 extensions to HAPC models such as the full Bayesian estimation for small sample size problems and conjunction with the heteroscedastic regression for ascertainment of between-group and within-group variations. Readers who are not statistically sophisticated can skip these extensions in Sections 8.4 and 8.5.

Chapter 9 develops a similar GLMM approach to the analysis of prospective panel data using accelerated longitudinal cohort designs. Through empirical examples in studies of social stratification of aging and health, we show how to model age trajectories and cohort variations using HAPC-growth curve models. Chapter 10 concludes the volume with recaps of new avenues for APC analysis presented in previous chapters and suggestions for future directions of methodological research and data collection.

To facilitate the application of the methods described in the volume (in Chapter 5, Chapter 6, Chapter 7, Chapter 8 and Chapter 9), we have developed a companion World Wide Web page on APC analysis (http://www.unc.edu/~yangy819/apc/index.html). This page provides links to PDF files of major methodological and substantive articles on APC analysis we reference in the book. It also provides sample codes using existing general-purpose statistical software packages, including R, SAS, and Stata. These are connected to the empirical analyses reported in the book.

References

Fienberg, S. E., and W. M. Mason. 1979. Identification and estimation of age-period-cohort models in the analysis of discrete archival data. Sociological Methodology 10:1–67.

Glenn, N. D. 2005. Cohort analysis. 2nd ed. Thousand Oaks, CA: Sage.

Jemal, A., K. C. Chu, and R. E. Tarone. 2001. Recent trends in lung cancer mortality in the United States. Journal of the National Cancer Institute 93:277–283.

Mason, W. M., and S. E. Fienberg, Eds. 1985. Cohort analysis in social research: Beyond the identification problem. New York: Springer-Verlag.

Tarone, R. E., K. C. Chu, and L. A. Gaudette. 1997. Birth cohort and calendar period trends in breast cancer mortality in the United States and Canada. Journal of the National Cancer Institute 89:251–256.

Yang, Y. 2007. Age/period/cohort distinctions. In Encyclopedia of health and aging, ed. K. S. Markides, 20–22. Los Angeles: Sage.

Yang, Y. 2009. Age, period, coh...

Table of contents

• Cover
• Title Page
• Copyright Page
• Preface
• Table of Contents
• 1 Introduction
• 2 Why Cohort Analysis?
• 3 APC Analysis of Data from Three Common Research Designs
• 4 Formalities of the Age-Period-Cohort Analysis Conundrum and a Generalized Linear Mixed Models (GLMM) Framework
• 5 APC Accounting/Multiple Classification Model, Part I: Model Identification and Estimation Using the Intrinsic Estimator
• 6 APC Accounting/Multiple Classification Model, Part II: Empirical Applications
• 7 Mixed Effects Models: Hierarchical APC-Cross-Classified Random Effects Models (HAPC-CCREM), Part I: The Basics
• 8 Mixed Effects Models: Hierarchical APC-Cross-Classified Random Effects Models (HAPC-CCREM), Part II: Advanced Analyses
• 9 Mixed Effects Models: Hierarchical APC-Growth Curve Analysis of Prospective Cohort Data
• 10 Directions for Future Research and Conclusion
• Index