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Spatially varying age-period-cohort analysis with application to US mortality, 2002-2016.

Many public health databases index disease counts by age groups and calendar periods within geographic regions (e.g., states, districts, or counties). Issues around relative risk estimation in small areas are well-studied; however, estimating trend parameters that vary across geographic regions has received less attention. Additionally, small counts (e.g., $<10$) in most publicly accessible databases are censored, further complicating age-period-cohort (APC) analysis in small areas. Here, we present a novel APC model with left-censoring and spatially varying intercept and trends, estimated with correlations among contiguous geographic regions. Like traditional models, our model captures population-scale trends, but it can also be used to characterize geographic disparities in relative risk and age-adjusted trends over time. To specify the joint distribution of our three spatially varying parameters, we adapt the generalized multivariate conditional autoregressive prior, previously used for multivariate disease mapping. Specified in this manner, region-specific parameters are correlated spatially, and also to one another. Estimation is performed using the No-U-Turn Hamiltonian Monte Carlo sampler in Stan. We conduct a simulation study to assess the performance of the proposed model relative to the standard model, and conclude with an application to US state-level opioid overdose mortality in men and women aged 15-64 years.