Regularized Age-Period-Cohort Modeling of Opioid Mortality Rates

Abstract

Opioid mortality rates have been increasing sharply, but not uniformly by age. Peak ages have recently dropped from the mid-40s to the mid-30s. There are two age peaks that have been moving up diagonally, with years of birth around 1960 and 1980 staying near the tops, and those around 1970 generally lower. We model this history with the Lee-Carter plus cohorts mortality model, which includes variable trends by age, and a generalization of it. This can be fit by maximum likelihood estimation (MLE) but statistical methods that shrink parameters towards zero (regularization) give lower predictive variances than MLE does. We address how to apply regularization to age-period-cohort models. Frequentist and Bayesian regularization are explored. The latter has some practical advantages.