Smooth predictions for age-period-cohort models: a comparison between splines and random process

Area of Science:

• Epidemiology
• Biostatistics
• Demography

Background:

• Age-Period-Cohort (APC) models are crucial for analyzing health and demographic trends.
• Two primary approaches exist: frequentist penalized splines and Bayesian random processes.
• These methods have historically seen limited integration.

Purpose of the Study:

• To compare the predictive performance of frequentist and Bayesian Age-Period-Cohort models.
• To elucidate the theoretical relationship between penalized splines and random processes.
• To evaluate model accuracy for both estimation and forecasting.

Main Methods:

• Theoretical comparison of frequentist (penalized splines) and Bayesian (random processes) APC models.
• Analysis of simulated data to assess estimation and forecasting accuracy.
• Evaluation using two real-world mental ill-health datasets for in-sample and out-of-sample prediction.

Main Results:

• Simulation studies showed nearly identical estimation results for both methods.
• Bayesian random processes demonstrated superior forecasting performance in simulations.
• Real-world data analysis confirmed close estimation results, with Bayesian methods slightly better.
• Bayesian random processes significantly improved forecasting accuracy on real-world data.

Conclusions:

• A clear theoretical link exists between penalized splines and random processes.
• Bayesian random process models exhibit superior predictive properties for forecasting compared to frequentist penalized splines.
• This research provides accessible insights into APC modeling for improved health trend prediction.