Mortality from opioid use is not only increasing, but the age structure of the affected population is changing. A model able to quantify the changing age distribution requires an age effect, a time effect, and an interaction between the two. A two-dimensional Markov random field model is used for the age-time interaction, which assumes only that the mortality risk changes slowly by age and calendar year. Information in the data are weak, and strong Penalized Complexity priors and judicious use of constraints are required. Data are modelled monthly in time by single-year age group, and a Poisson model fit with Bayes and INLA is used to accommodate the low counts.
Deaths in Ontario up until the end of 2016 are modelled, and the age distribution has shifted from unimodal to bimodal in recent years.