Correlated Poisson models for age-period-cohort analysis

Age-period-cohort (APC) models are widely used to analyze population-level rates, particularly cancer incidence and mortality. These models are used for descriptive epidemiology, comparative risk analysis, and extrapolating future disease burden. Traditional APC models have 2 major limitations: (1) they lack parsimony because they require estimation of deviations from linear trends for each level of age, period, and cohort; and (2) rates observed at similar ages, periods, and cohorts are treated as independent, ignoring any correlations between them that may lead to biased parameter estimates and inefficient standard errors. We propose a novel approach to estimation of APC models using a spatially correlated Poisson model that accounts for over-dispersion and correlations in age, period, and cohort, simultaneously. We treat the outcome of interest as event rates occurring over a grid defined by values of age, period, and cohort. Rates defined in this manner lend themselves to well-established approaches from spatial statistics in which correlation among proximate observations may be modeled using a spatial random effect. Through simulations, we show that in the presence of spatial dependence and over-dispersion: (1) the correlated Poisson model attains lower AIC; (2) the traditional APC model produces biased trend parameter estimates; and (3) the correlated Poisson model corrects most of this bias. We illustrate our approach using brain and breast cancer incidence rates from the Surveillance Epidemiology and End Results Program of the United States. Our approach can be easily extended to accommodate comparative risk analyses and interpolation of cells in the Lexis with sparse data.