Abstract
Age–period–cohort analysis is an essential epidemiologic tool for analyzing trends over time in health outcomes. Age effects describe the common developmental processes that are associated with particular ages or stages in the life course and can explain trends in health outcomes if the age distribution of the population shifts over time. Period effects describe changes in the prevalence of health outcomes associated with certain calendar years across all age groups. Cohort effects describe changes in the prevalence of an outcome associated with certain age groups in certain years. Thus, cohort effects can be best conceptualized as a population-level interaction between age and period. In this chapter, we (1) review essential concepts in age–period–cohort effect estimation using examples from injury epidemiology; (2) provide examples of historical uses of age–period–cohort analysis; (3) illustrate the statistical problem in simultaneously estimating age, period, and cohort effects; (4) offer an example of a multi-phased method for quantifying cohort effects using data on suicide mortality in the USA; and (5) summarize and describe new directions and innovations in age–period–cohort analysis. The prevalence and incidence of fatal and nonfatal injuries have exhibited substantial trends over time (Martinez-Schnell and Zaidi, Statistics in Medicine 13(8):823–838, 1989). By examining these trends, we can gain insight into the causes of injury at the population level, for example: the effectiveness of public health prevention and intervention efforts for gun control, or the magnitude of change in social norms regarding driving practices, and can forecast the future burden of injury outcomes in the population. Quantitative evaluation trends over time in injury is aided by a comprehensive approach to age–period–cohort analysis, an analytic tool to partition trends into components that are associated with changes over time within a given age structure of the population, time period, and birth cohort. In this chapter, we review essential concepts and definitions in age–period–cohort analysis, provide examples of historical uses of age–period–cohort analysis, illustrate the statistical problem in simultaneously estimating age, period, and cohort effects, offer an example of a multi-phased method for quantifying cohort effects using data on suicide in the USA from 1910 to 2004, and summarize and describe new directions and innovations in age–period–cohort analysis. The prevalence and incidence of fatal and non-fatal injuries have exhibited substantial trends over time (Martinez-Schnell and Zaidi 1989). By examining these trends we can gain insight into the causes of injury at the population level, for example: the effectiveness of public health prevention and intervention efforts for gun control, or the magnitude of change in social norms regarding driving practices, and can forecast the future burden of injury outcomes in the population. Quantitative evaluation of trends over time in injury is aided by a comprehensive approach to age-period-cohort analysis, an analytic tool to partition trends into components that are associated with changes over time within a given age structure of the population, time period, and birth cohort. In this chapter we will review essential concepts and definitions in age-period-cohort analysis, provide examples of historical uses of age-period-cohort analysis, illustrate the statistical problem in simultaneously estimating age, period, and cohort effects, offer an example of a multi-phase method for quantifying cohort effects using data on suicide in the United States from 1910–2004, and summarize and describe new directions and innovations in age-period-cohort analysis.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Ajdacic-Gross, V., Bopp, M., Gostynski, M., Lauber, C., Gutzwiller, F., & Rössler, W. (2006). Age-period-cohort analysis of Swiss suicide data, 1881–2000. European Archives of Psychiatry and Clinical Neuroscience, 256(4), 207–14.
Ajdacic-Gross, V., Weiss, M. G., et al. (2008). Methods of suicide: International suicide patterns derived from the WHO mortality database. Bulletin of the World Health Organization, 86(9), 726–32.
Berzuini, C., & Clayton, D. (1994). Bayesian analysis of survival on multiple time scales. Statistics in Medicine, 13(8), 823–38.
Ben-Shlomo, Y., D. Kuh (2002). A life course approach to chronic disease epidemiology: Conceptual models, empirical challenges and interdisciplinary perspectives. International Journal of Epidemiology, 31(2), 285–293.
Bills, C. B., & Li, G. (2005). Correlating homicide and suicide. International Journal of Epidemiology, 34(4), 837–45.
Bullman, T. A., & Kang, H. K. (1996). The risk of suicide among wounded Vietnam veterans. American Journal of Public Health, 86(5), 662–7.
Carstensen, B. (2007). Age-period-cohort models for the Lexis diagram. Statistics in Medicine, 26(15), 3018–45.
Case, R. A. M. (1956). Cohort analysis of mortality rates as an historical or narrative technique. British Journal of Preventative and Social Medicine, 10, 159–171.
Clayton, D., & Schifflers, E. (1987). Models for temporal variation in cancer rates. I: Age-period and age-cohort models. Statistics in Medicine, 6(4), 449–67.
Cleries, R., Ribes, J., et al. (2006). Time trends of breast cancer mortality in Spain during the period 1977–2001 and Bayesian approach for projections during 2002–2016. Annals of Oncology, 17(12), 1783–91.
Cook, P., & Laub, J. (1998). The unprecedented epidemic in youth violence. Chicago: University of Chicago Press.
Derrick, V. P. A. (1927). Observations on (1) errors of age in the population statistics of England and Wales, and (2) the changes in mortality indicated by the national records. Journal of the Institute of Actuaries, LVIII, 117–159.
Doll, R. (1971). The age distribution of cancer: Implications for models of carcinogenesis. Journal of the Royal Statistical Society, 134, 133–155.
Evans, J. G., Seagroatt, V., et al. (1997). Secular trends in proximal femoral fracture, Oxford record linkage study area and England 1968–1986. Journal of Epidemiology and Community Health, 51(4), 424–9.
Fienberg, S. E., & Mason, W. M. (1979). Identification and estimation of age-period-cohort models in the analysis of discrete archival data. Sociological Methodology, 10(1), 1–67.
Frost, W. H. (1939). The age selection of morality from tuberculosis in successive decades. American Journal of Hygiene, 30, 91–96.
Gibbons, R. D., Brown, C. H., et al. (2007). Early evidence on the effects of regulators’ suicidality warnings on SSRI prescriptions and suicide in children and adolescents. The American Journal of Psychiatry, 164(9), 1356–63.
Glenn, N. D. (1976). Cohort analysts’ futile quest: Statistical attempts to separate age, period, and cohort effects. American Sociological Review, 41, 900–905.
Granizo, J. J., Guallar, E., & Rodriguez-Artalejo, F. (1996). Age-period-cohort analysis of suicide mortality rates in Spain, 1959–1991. International journal of epidemiology, 25(4), 814–20.
Greenberg, B. G., Wright, J. J., et al. (1950). A technique for analyzing some factors affecting the incidence of syphilis. American Statistical Association Journal, 45(251), 373–399.
Gunnell, D., Middleton, N., et al. (2003). Influence of cohort effects on patterns of suicide in England and Wales, 1950–1999. The British Journal of Psychiatry, 182, 164–70.
Hall, A. J., Yee, L. J., et al. (2002). Life course epidemiology and infectious diseases. International Journal of Epidemiology, 31(2), 300–301.
Hobcraft, J., Menken, J., et al. (1982). Age, period, and cohort effects in demography: A review. Population Index, 48(1), 4–43.
Holford, T. R. (1991). Understanding the effects of age, period, and cohort on incidence and mortality rates. Annual Review of Public Health, 12, 425–57.
Holford, T. R. (1992). Analysing the temporal effects of age, period and cohort. Statistical Methods in Medical Research, 1(3), 317–37.
Joe, S. (2006). Explaining changes in the patterns of black suicide in the United States from 1981 to 2002: An age, cohort, and period analysis. Journal of Black Psychology, 32(3), 262–284.
Johnston, L. D., O’Malley, P. M., et al. (2007). Monitoring the Future national survey results on drug use, 1975–2006: Volume I, Secondary school students. Bethesda, MD: National Institute on Drug Abuse.
Kang, H. K., & Bullman, T. A. (2008). Risk of suicide among US veterans after returning from the Iraq or Afghanistan war zones. The Journal of the American Medical Association, 300(6), 652–3.
Kannus, P., Niemi, S., et al. (1999). Hip fractures in Finland between 1970 and 1997 and predictions for the future. Lancet, 353(9155), 802–5.
Kermack, W. O., McKendrick, A. G., et al. (1934). Death-rates in great Britain and Sweden. Some general regularities and their significance. Lancet, 31, 698–703.
Keyes, K. M., & Li, G. (2010). A multiphase method for estimating cohort effects in age-period contingency table data. Annals of Epidemiology, 20(10), 779–85.
Keyes, K. M., Utz, R. L., et al. (2010). What is a cohort effect? Comparison of three statistical methods for modeling cohort effects in obesity prevalence in the United States, 1971–2006. Social Science and Medicine, 70(7), 1100–8.
Korteweg, R. (1951). The age curve in lung cancer. British Journal of Cancer, 5, 21–27.
Kupper, L. L., Janis, J. M., et al. (1985). Statistical age-period-cohort analysis: A review and critique. Journal of Chronic Disease, 38(10), 811–30.
Last, J. M. (2001). A dictionary of epidemiology (4th ed.). New York, NY: Oxford University Press.
Lee, W. C., & Lin, R. S. (1996). Autoregressive age-period-cohort models. Statistics in Medicine, 15(3), 273–81.
Lester, D. (1996). Patterns of homicide and suicide in the World. Commack, NY: Nova Science Publishers, Inc.
Libby, A. M., Brent, D. A., et al. (2007). Decline in treatment of pediatric depression after FDA advisory on risk of suicidality with SSRIs. The American Journal of Psychiatry, 164(6), 884–91.
Lynch, J. & Smith, G. D., (2005). A life course approach to chronic disease epidemiology. Annual Review of Public Health, 26, 1–35.
Lynskey, M., Degenhardt, L., & Hall, W. (2000). Cohort trends in youth suicide in Australia 1964-1997. The Australian and New Zealand journal of psychiatry, 34(3), 408–12.
Macmahon, B. & Terry, W. D. (1958). Application of cohort analysis to the study of time trends in neoplastic disease. Journal of Chronic Diseases, 7(1), 24–35.
Martinez-Schnell, B., & Zaidi, A. (1989). Time series analysis of injuries. Statistics in Medicine, 8(12), 1497–508.
Mason, K. O., Mason, W. M., et al. (1973). Some methodological issues in cohort analysis of archival data. American Sociological Review, 38, 242–258.
McNally, R. J., Alexander, F. E., et al. (1997). A comparison of three methods of analysis for age-period-cohort models with application to incidence data on non-Hodgkin’s lymphoma. International Journal of Epidemiology, 26(1), 32–46.
Miech, R., Koester, S., et al. (2011). Increasing U.S. mortality due to accidental poisoning: The role of the baby boom cohort. Addiction. 106(4), 806–815.
Miller, M., & Hemenway, D. (2008). Guns and suicide in the United States. The New England Journal of Medicine, 359(10), 989–91.
Murphy, G. E., & Wetzel, R. D. (1980). Suicide risk by birth cohort in the United States, 1949 to 1974. Archives of General Psychiatry, 37(5), 519–23.
Nakamura, T. (1986). Bayesian cohort models for general cohort table analysis. Annals of the Institute of Statistical Mathematics, 38((Part B)), 353–70.
O’Brien, R. M. (2000). Age period cohort characteristic models. Social Science Research, 29, 123–139.
Odagiri, Y., Uchida, H., et al. (2011). Gender differences in age, period, and birth-cohort effect on suicide mortality rate in Japan 1985-2006. Asia-pacific Journal of public Health, 23(4), 581–7.
Pampel, F. C. (1996). Cohort size and age-specific suicide rates: A contingent relationship. Demography, 33(3), 341–355.
Paulozzi, L., Crosby, A., et al. (2007). Increases in age-group – specific injury mortality – United States, 1999–2004. Morbidity and Mortality Weekly Report, 56(49), 1281–1284.
Preston, S. H., & Wang, H. (2006). Sex mortality differences in the United States: The role of cohort smoking patterns. Demography, 43(4), 631–46.
Riggs, J. E., McGraw, R. L., et al. (1996). Suicide in the United States, 1951–1988: Constant age-period-cohort rates in 40- to 44-year-old men. Comprehensive Psychiatry, 37(3), 222–5.
Robertson, C., & Boyle, P. (1986). Age, period and cohort models: The use of individual records’. Statistics in Medicine, 5, 527–538.
Robertson, C., Gandini, S., et al. (1999). Age-period-cohort models: A comparative study of available methodologies. Journal of Clinical Epidemiology, 52, 569–583.
Rodrigues, N. C., & Werneck, G. L. (2005). Age-period-cohort analysis of suicide rates in Rio de Janeiro, Brazil, 1979–1998. Social Psychiatry and Psychiatric Epidemiology, 40(3), 192–6.
Rosenbauer, J., & Strassburger, K. (2007). Letter to the Editor: Comments on “Age-period-cohort models for the Lexis diagram”. Statistics in Medicine, 26, 3018–3045.
Ryder, N. B. (1965). The cohort as a concept in the study of social change. American Sociological Review, 30(6), 843–61.
Samelson, E. J., Zhang, Y., et al. (2002). Effect of birth cohort on risk of hip fracture: Age-specific incidence rates in the Framingham Study. American Journal of Public Health, 92(5), 858–62.
Selvin, S. (1996). Statistical analysis of epidemiologic data. New York: Oxford University Press.
Shahpar, C., & Li, G. (1999). Homicide mortality in the United States, 1935–1994: Age, period, and cohort effects. American Journal of Epidemiology, 150(11), 1213–22.
Stockard, J., & O’Brien, R. M. (2002a). Cohort effects on suicide rates: International variations. American Sociological Review, 67, 854–872.
Stockard, J., & O’Brien, R. M. (2002b). Cohort variations and changes in age-specific suicide rates over time: Explaining variations in youth suicide. Social Forces, 81(2), 605–642.
Susser, M. (1961). Environmental factors and peptic ulcer. Practitioner, 186(302–311).
Susser, M. (2001). Commentary: The longitudinal perspective and cohort analysis. International Journal of Epidemiology, 30(4), 684–7.
Tarone, R. E., & Chu, K. C. (1992). Implications of birth cohort patterns in interpreting trends in breast cancer rates. Journal of the National Cancer Institute, 84(18), 1402–10.
Tukey, J. W. (1977). Exploratory data analysis. Reading, MS: Addison-Wesley Publishing Company.
US Public Health Service. (1999). The surgeon general’s call to action to prevent suicide. Washington, DC: U. S. P. H. Service.
Valuck, R. J., Libby, A. M., et al. (2007). Spillover effects on treatment of adult depression in primary care after FDA advisory on risk of pediatric suicidality with SSRIs. The American Journal of Psychiatry, 164(8), 1198–205.
Wickramaratne, P. J., Weissman, M. M., et al. (1989). Age, period and cohort effects on the risk of major depression: Results from five United States communities. Journal of Clinical Epidemiology, 42(4), 333–43.
Winship, C., & Harding, D. J. (2008). A general strategy for the identification of age, period, cohort models: A mechanism based approach. Sociological Methods and Research, 36(3), 362–401.
Yang, Y., Fu, W. J., et al. (2004). A methodological comparison of age-period-cohort models: The intrinsic estimator and conventional generalized linear models. Sociological Methodology, 34, 75–110.
Yang, Y., & Land, K. C. (2006). A mixed models approach to age-period-cohort analysis of repeated cross-section surveys: Trends in verbal test scores. Sociological Methodology. R. M. Stolzenberg. Boston: Blackwell Publishing. 36.
Zheng, T., Holford, T. R., et al. (1995). Time trend in pancreatic cancer incidence in Connecticut, 1935–1990. International Journal of Cancer, 61(5), 622–7.
Zheng, T., Holford, T. R., et al. (1996). Time trend and age-period-cohort effect on incidence of bladder cancer in Connecticut, 1935–1992. International Journal of Cancer, 68(2), 172–6.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Keyes, K.M., Li, G. (2012). Age–Period–Cohort Modeling. In: Li, G., Baker, S. (eds) Injury Research. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-1599-2_22
Download citation
DOI: https://doi.org/10.1007/978-1-4614-1599-2_22
Published:
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4614-1598-5
Online ISBN: 978-1-4614-1599-2
eBook Packages: MedicineMedicine (R0)