Penalized smoothing splines resolve the curvature identifiability problem in age-period-cohort models with unequal intervals

Connor Gascoigne, Theresa Smith

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Abstract

Age-period-cohort (APC) models are frequently used in a variety of health and demographic-related outcomes. Fitting and interpreting APC models to data in equal intervals (equal age and period widths) is nontrivial due to the structural link between the three temporal effects (given two, the third can always be found) causing the well-known identification problem. The usual method for resolving the structural link identification problem is to base a model on identifiable quantities. It is common to find health and demographic data in unequal intervals, this creates further identification problems on top of the structural link. We highlight the new issues by showing that curvatures which were identifiable for equal intervals are no longer identifiable for unequal data. Furthermore, through extensive simulation studies, we show how previous methods for unequal APC models are not always appropriate due to their sensitivity to the choice of functions used to approximate the true temporal functions. We propose a new method for modeling unequal APC data using penalized smoothing splines. Our proposal effectively resolves the curvature identification issue that arises and is robust to the choice of the approximating function. To demonstrate the effectiveness of our proposal, we conclude with an application to UK all-cause mortality data from the Human mortality database.

Original languageEnglish
Pages (from-to)1888-1908
Number of pages21
JournalStatistics in Medicine
Volume42
Issue number12
Early online date12 Mar 2023
DOIs
Publication statusPublished - 30 May 2023

Keywords

  • age-period-cohort models
  • identifiability
  • penalized smoothing splines
  • unequal intervals

ASJC Scopus subject areas

  • Epidemiology
  • Statistics and Probability

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