Smooth predictions for age-period-cohort models: a comparison between splines and random process
File(s)
Published version
Author(s)
Gascoigne, Connor
Riebler, Andrea
Smith, Theresa
Type
Journal Article
Abstract
Background
Age-Period-Cohort (APC) models are well used in the context of modelling health and demographic data to produce smooth predictions of each time trend. When producing smooth predictions in the context of APC models, there are two main schools, frequentist using penalised splines, and Bayesian using random processes with little crossover between them.
Methods
We compared prediction using APC models in either a frequentist or Bayesian paradigm using theory, simulated data, and two separate real-world data examples for mental ill-health outcomes. For the theoretical comparison, we describe each method and give an accessible description highlighting how the two methods are equivalent. For the simulated and real-world data, we compared the results for both in-sample (estimation) and out-of-sample (forecasting) prediction.
Results
During the simulation study, the estimation results for both the penalised splines and random processes were almost identical. For the forecasting results, the random processes performed better. For the real-world examples, the estimation results for both were extremely close with random processes proving slightly better. For the real-world data forecasting results, the random processes provided a significant improvement over penalised splines.
Conclusions
The combination of theory and data examples we presented here make the relationship between splines and random processes both accessible and interpretable. Whilst there is a theoretical link between both penalised splines and random processes, when forecasting is the goal, a Bayesian random process approach displayed better predictive properties in comparison to the frequentist penalised spline approach.
Age-Period-Cohort (APC) models are well used in the context of modelling health and demographic data to produce smooth predictions of each time trend. When producing smooth predictions in the context of APC models, there are two main schools, frequentist using penalised splines, and Bayesian using random processes with little crossover between them.
Methods
We compared prediction using APC models in either a frequentist or Bayesian paradigm using theory, simulated data, and two separate real-world data examples for mental ill-health outcomes. For the theoretical comparison, we describe each method and give an accessible description highlighting how the two methods are equivalent. For the simulated and real-world data, we compared the results for both in-sample (estimation) and out-of-sample (forecasting) prediction.
Results
During the simulation study, the estimation results for both the penalised splines and random processes were almost identical. For the forecasting results, the random processes performed better. For the real-world examples, the estimation results for both were extremely close with random processes proving slightly better. For the real-world data forecasting results, the random processes provided a significant improvement over penalised splines.
Conclusions
The combination of theory and data examples we presented here make the relationship between splines and random processes both accessible and interpretable. Whilst there is a theoretical link between both penalised splines and random processes, when forecasting is the goal, a Bayesian random process approach displayed better predictive properties in comparison to the frequentist penalised spline approach.
Date Issued
2025-07-28
Date Acceptance
2025-07-01
Citation
BMC Medical Research Methodology, 2025, 25
ISSN
1471-2288
Publisher
BMC
Journal / Book Title
BMC Medical Research Methodology
Volume
25
Copyright Statement
© The Author(s) 2025. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
License URL
Publication Status
Published
Article Number
177
Date Publish Online
2025-07-28