Statistical Science

A Review and Comparison of Age–Period–Cohort Models for Cancer Incidence

Theresa R. Smith and Jon Wakefield

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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.

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Statist. Sci., Volume 31, Number 4 (2016), 591-610.

First available in Project Euclid: 19 January 2017

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Age–period–cohort models identifiability random walk priors


Smith, Theresa R.; Wakefield, Jon. A Review and Comparison of Age–Period–Cohort Models for Cancer Incidence. Statist. Sci. 31 (2016), no. 4, 591--610. doi:10.1214/16-STS580.

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Supplemental materials

  • Supplement A: Supplementary Material. Additional figures and details: A. Additional figures, B. Design matrices, C. Code, D. Forecasting details, E. Sensitivity analysis.
  • Supplement B: R Code. APC_Models_LungDK.R: Contains code for running the four models, comparing estimates of the double differences, forecasts, and priors using the Danish lung cancer data from Carstensen (2007). Functions.R: Helper functions for the MNN parameterization. MCMC_Functions.R: functions for running the MCMC.