A review and comparison of age-period-cohort models for cancer incidence. (English) Zbl 1437.92041

Summary: Age-period-cohort models have been used to examine and forecast cancer incidence and mortality for over three decades. However, the fitting and interpretation of these models requires great care because of the well-known identifiability problem that exists; given any two of age, period, and cohort, the third is determined. In this paper, we review the identifiability problem and models that have been proposed for analysis, from both frequentist and Bayesian standpoints. A number of recent analyses that use age-period-cohort models are described and critiqued before data on cancer incidence in Washington State are analyzed with various models, including a new Bayesian approach based on an identifiable parameterization.


92C32 Pathology, pathophysiology
62P10 Applications of statistics to biology and medical sciences; meta analysis
60G50 Sums of independent random variables; random walks
92-02 Research exposition (monographs, survey articles) pertaining to biology
Full Text: DOI Euclid


[1] Ahmad, A. S., Ormiston-Smith, N. and Sasieni, P. D. (2015). Trends in the lifetime risk of developing cancer in Great Britain: Comparison of risk for those born from 1930 to 1960. Br. J. Cancer112 943-947.
[2] Ananth, C. V., Keyes, K. M., Hamilton, A., Gissler, M., Wu, C., Liu, S., Luque-Fernandez, M. A., Skjærven, R., Williams, M. A. and Tikkanen, M. (2014). An international contrast of rates of placental abruption: An age-period-cohort analysis. PLoS ONE10 e0125246.
[3] Berzuini, C. and Clayton, D. (1994). Bayesian analysis of survival on multiple time scales. Stat. Med.13 823-838.
[4] Besag, J., Green, P., Higdon, D. and Mengersen, K. (1995). Bayesian computation and stochastic systems. Statist. Sci.10 3-66. · Zbl 0955.62552
[5] Brown, C. C. and Kessler, L. G. (1988). Projections of lung cancer mortality in the United States: 1985-2025. J. Natl. Cancer Inst.80 43-51.
[6] Carstensen, B. (2007). Age-period-cohort models for the Lexis diagram. Stat. Med.26 3018-3045.
[7] Carstensen, B., Plummer, M., Laara, E. and Hills, M. (2014). Epi: A package for statistical analysis in epidemiology. Available at http://CRAN.R-project.org/package=Epi, R package version 1.1.67.
[8] Cervantes-Amat, M., López-Abente, G., Aragonés, N., Pollán, M., Pastor-Barriuso, R. and Pérez-Gómez, B. (2015). The end of the decline in cervical cancer mortality in Spain: Trends across the period 1981-2012. BMC Cancer15 287.
[9] Clayton, D. and Schifflers, E. (1987a). Models for temporal variation in cancer rates. I: Age-period and age-cohort models. Stat. Med.6 449-467.
[10] Clayton, D. and Schifflers, E. (1987b). Models for temporal variation in cancer rates. II: Age-period-cohort models. Stat. Med.6 469-481.
[11] Escedy, J. and Hunter, D. (2008). The origin of cancer. In Textbook of Cancer Epidemiology, 2nd ed. (H. O. Adami, D. Hunter and D. Trichopoulos, eds.). Oxford Univ. Press, Oxford.
[12] Ferkingstad, E. and Rue, H. (2015). Improving the INLA approach for approximate Bayesian inference for latent Gaussian models. Electron. J. Stat.9 2706-2731. · Zbl 1329.62127
[13] Fienberg, S. E. and Mason, W. M. (1979). Identification and estimation of age-period-cohort models in the analysis of discrete archival data. Sociol. Method.10 1-67.
[14] Fong, Y., Rue, H. and Wakefield, J. C. (2010). Bayesian inference for generalized linear mixed models. Biostatistics11 397-412. · Zbl 1437.62460
[15] Frost, W. H. (1939). The age selection of mortality from tuberculosis in successive decades. American Journal of Hygiene30 91-96. Reprinted in American Journal of Epidemiology141 (1995) 4-9.
[16] Ghosh, K., Tiwari, R. C., Feuer, E. J., Cronin, K. and Jemal, A. (2007). Predicting US cancer mortality counts using state space models. In Computational Methods in Biomedical Research (R. Khattree and D. N. Naik, eds.) 131-151.
[17] Greenberg, B. G., Wright, J. J. and Sheps, C. G. (1950). A technique for analyzing some factors affecting the incidence of syphilis. J. Amer. Statist. Assoc.45 373-399.
[18] Heuer, C. (1997). Modeling of time trends and interactions in vital rates using restricted regression splines. Biometrics53 161-177. · Zbl 0883.62118
[19] Ho, M.-L., Hsiao, Y.-H., Su, S.-Y., Chou, M.-C. and Liaw, Y.-P. (2015). Mortality of breast cancer in Taiwan, 1971-2010: Temporal changes and an age-period-cohort analysis. Journal of Obstetrics & Gynaecology35 60-63.
[20] Holford, T. R. (1983). The estimation of age, period and cohort effects for vital rates. Biometrics39 311-324.
[21] Holford, T. R. (1991). Understanding the effects of age, period, and cohort on incidence and mortality rates. Annu. Rev. Public Health12 425-457.
[22] Holford, T. R. (2006). Approaches to fitting age-period-cohort models with unequal intervals. Stat. Med.25 977-993.
[23] Keiding, N. (1990). Statistical inference in the Lexis diagram. Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci.332 487-509. · Zbl 0714.62102
[24] Keiding, N. (2011). Age-period-cohort analysis in the 1870s: Diagrams, stereograms, and the basic differential equation. Canad. J. Statist.39 405-420. · Zbl 1349.62010
[25] Knorr-Held, L. and Rainer, E. (2001). Projections of lung cancer mortality in West Germany: A case study in Bayesian prediction. Biostatistics2 109-129.
[26] Kuang, D., Nielsen, B. and Nielsen, J. P. (2008a). Forecasting with the age-period-cohort model and the extended chain-ladder model. Biometrika95 987-991. · Zbl 1437.62516
[27] Kuang, D., Nielsen, B. and Nielsen, J. P. (2008b). Identification of the age-period-cohort model and the extended chain-ladder model. Biometrika95 979-986. · Zbl 1437.62515
[28] Lee, R. D. and Carter, L. R. (1992). Modeling and forecasting US mortality. J. Amer. Statist. Assoc.87 659-671. · Zbl 1351.62186
[29] Lexis, W. H. R. A. (1875). Einleitung in die Theorie der Bevölkerungsstatistik. KJ Trübner.
[30] Lindgren, F. and Rue, H. (2008). On the second-order random walk model for irregular locations. Scand. J. Stat.35 691-700. · Zbl 1199.60276
[31] Louie, K. S., Mehanna, H. and Sasieni, P. (2015). Trends in head and neck cancers in England from 1995 to 2011 and projections up to 2025. Oral Oncology51 341-348.
[32] Lunn, D. J., Thomas, A., Best, N. and Spiegelhalter, D. (2000). WinBUGS—a Bayesian modelling framework: Concepts, structure, and extensibility. Stat. Comput.10 325-337.
[33] Luo, L. (2013). Assessing validity and application scope of the intrinsic estimator approach to the age-period-cohort problem. Demography50 1945-1967.
[34] Martínez Miranda, M. D., Nielsen, B. and Nielsen, J. P. (2015). Inference and forecasting in the age-period-cohort model with unknown exposure with an application to mesothelioma mortality. J. Roy. Statist. Soc. Ser. A178 29-55.
[35] Mason, K. O., Mason, W. M., Winsborough, H. H. and Poole, W. K. (1973). Some methodological issues in cohort analysis of archival data. Am. Sociol. Rev.38 242-258.
[36] Møller, B., Fekjær, H., Hakulinen, T., Sigvaldason, H., Storm, H. H., Talbäck, M. and Haldorsen, T. (2003). Prediction of cancer incidence in the Nordic countries: Empirical comparison of different approaches. Stat. Med.22 2751-2766.
[37] Nielsen, B. (2014). apc: A package for age-period-cohort analysis. Available at http://CRAN.R-project.org/package=apc, R package version 1.0.
[38] Nielsen, B. and Nielsen, J. P. (2014). Identification and forecasting in mortality models. Sci. World J.2014 347043. · Zbl 1328.62575
[39] O’Brien, R. M. (2000). Age period cohort characteristic models. Soc. Sci. Res.29 123-139.
[40] O’Brien, R. (2014). Age-Period-Cohort Models: Approaches and Analyses with Aggregate Data. Chapman & Hall/CRC Press, London.
[41] Osmond, C. and Gardner, M. J. (1982). Age, period and cohort models applied to cancer mortality rates. Stat. Med.1 245-259.
[42] Papoila, A. L., Riebler, A., Amaral-Turkman, A., São-João, R., Ribeiro, C., Geraldes, C. and Miranda, A. (2014). Stomach cancer incidence in Southern Portugal 1998-2006: A spatio-temporal analysis. Biom. J.56 403-415. · Zbl 1441.62455
[43] Renshaw, A. E. and Haberman, S. (2006). A cohort-based extension to the Lee-Carter model for mortality reduction factors. Insurance Math. Econom.38 556-570. · Zbl 1168.91418
[44] Riebler, A. and Held, L. (2010). The analysis of heterogeneous time trends in multivariate age-period-cohort models. Biostatistics11 57-69. · Zbl 1437.62591
[45] Riebler, A. and Held, L. (2016). Projecting the future burden of cancer: Bayesian age-period-cohort analysis with integrated nested Laplace approximations. Biom. J. To appear. · Zbl 1422.62332
[46] Riebler, A., Held, L. and Rue, H. (2012). Estimation and extrapolation of time trends in registry data—borrowing strength from related populations. Ann. Appl. Stat.6 304-333. · Zbl 1235.62030
[47] Riebler, A., Held, L., Rue, H. and Bopp, M. (2012). Gender-specific differences and the impact of family integration on time trends in age-stratified Swiss suicide rates. J. Roy. Statist. Soc. Ser. A175 473-490.
[48] Roberts, G. O. and Tweedie, R. L. (1996). Exponential convergence of Langevin distributions and their discrete approximations. Bernoulli2 341-363. · Zbl 0870.60027
[49] Robertson, C. and Boyle, P. (1986). Age, period and cohort models: The use of individual records. Stat. Med.5 527-538.
[50] Rodgers, W. L. (1982). Estimable functions of age, period, and cohort effects. Am. Sociol. Rev.47 774-787.
[51] Rosenberg, P. S. and Anderson, W. F. (2011). Age-period-cohort models in cancer surveillance research: Ready for prime time? Cancer Epidemiol. Biomark. Prev.20 1263-1268.
[52] Rosenberg, P. S., Check, D. P. and Anderson, W. F. (2014). A web tool for age-period-cohort analysis of cancer incidence and mortality rates. Cancer Epidemiol. Biomark. Prev.23 2296-2302.
[53] Rue, H. and Held, L. (2005). Gaussian Markov Random Fields: Theory and Applications. Monographs on Statistics and Applied Probability104. Chapman & Hall/CRC, Boca Raton, FL. · Zbl 1093.60003
[54] Rue, H., Martino, S. and Chopin, N. (2009). Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations. J. R. Stat. Soc. Ser. B. Stat. Methodol.71 319-392. · Zbl 1248.62156
[55] Rutherford, M. J., Lambert, P. C. and Thompson, J. R. (2010). Age-period-cohort modeling. Stata J.10 606-627.
[56] Sasieni, P. D. (2012). Age-period-cohort models in Stata. Stata J.12 45-60.
[57] Schmid, V. J. and Held, L. (2007). Bayesian age-period-cohort modeling and prediction—BAMP. J. Stat. Softw.21 1-15.
[58] Seoane-Mato, D., Aragonés, N., Ferreras, E., García-Pérez, J., Cervantes-Amat, M., Fernández-Navarro, P., Pastor-Barriuso, R. and López-Abente, G. (2014). Trends in oral cavity, pharyngeal, oesophageal and gastric cancer mortality rates in Spain, 1952-2006: An age-period-cohort analysis. BMC Cancer14 254.
[59] Smith, T. R. and Wakefield, J. (2016). Supplement to “A review and comparison of age-period-cohort models for cancer incidence.” DOI:10.1214/16-STS580SUPPA, DOI:10.1214/16-STS580SUPPB. · Zbl 1437.92041
[60] Springett, V. H. (1950). A comparative study of tuberculosis mortality rates. J. Hyg.48 361-395.
[61] Tzeng, I. S. and Lee, W. C. (2015). Forecasting hepatocellular carcinoma mortality in Taiwan using an age-period-cohort model. Asia-Pacific Journal of Public Health27 NP65-NP73.
[62] Vaccarella, S., Franceschi, S., Engholm, G., Lönnberg, S., Khan, S. and Bray, F. (2014). 50 years of screening in the Nordic countries: Quantifying the effects on cervical cancer incidence. Br. J. Cancer111 965-969.
[63] Valery, P. C., Laversanne, M. and Bray, F. (2015). Bone cancer incidence by morphological subtype: A global assessment. Cancer Causes Control26 1127-1139.
[64] Yang, Y., Fu, W. J. and Land, K. C. (2004). A methodological comparison of age-period-cohort models: The intrinsic estimator and conventional generalized linear models. Sociol. Method.34 75-110.
[65] Yang, Y. and Land, K. C. (2013). Age-Period-Cohort Analysis: New Models, Methods, and Empirical Applications. CRC Press, Boca Raton, FL.
[66] Zheng, R., Peng, X., Zeng, H., Zhang, S., Chen, T., Wang, H. and Chen, W. (2015). Incidence, mortality and survival of childhood cancer in China during 2000-2010 period: A population-based study. Cancer Letters363 176-180.
[67] Zhu, L., Pickle, L. W., Ghosh, K., Naishadham, D., Portier, K., Chen, H., Kim, H., Zou, J., Cucinelli, Z., Kohler, B., Edwards, B. K., King, J., Feuer, E. J. and Jemal, A. (2012). Predicting US- and state-level cancer counts for the current calendar year. Cancer118 1100-1109.
[68] Zhu, L., Pickle, L. W., Zou, Z. and Cucinelli, J. (2014). Trends and patterns of childhood cancer incidence in the United States, 1995-2010. Stat. Interface7 121-134.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.