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The Stata Journal
Volume 10 Number 4: pp. 606-627



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Age-period-cohort modeling

Mark J. Rutherford
Department of Health Sciences
University of Leicester, UK
mjr40@le.ac.uk
Paul C. Lambert
Department of Health Sciences
University of Leicester, UK
paul.lambert@le.ac.uk
John R. Thompson
Department of Health Sciences
University of Leicester, UK
john.thompson@le.ac.uk
Abstract.  Age–period–cohort models provide a useful method for modeling incidence and mortality rates. It is well known that age–period–cohort models suffer from an identifiability problem due to the exact relationship between the variables (cohort = period − age). In 2007, Carstensen published an article advocating the use of an analysis that models age, period, and cohort as continuous variables through the use of spline functions (Carstensen, 2007, Statistics in Medicine 26: 3018–3045). Carstensen implemented his method for age–period–cohort models in the Epi package for R. In this article, a new command is introduced, apcfit, that performs the methods in Stata. The identifiability problem is overcome by forcing constraints on either the period or cohort effects. The use of the command is illustrated through an example relating to the incidence of colon cancer in Finland. The example shows how to include covariates in the analysis.
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