Empirical Bayes age-period-cohort analysis of retrospective incidence data (Q2742757)

The authors analyse the (age, time) specific incidence of diabetes based on retrospective data obtained from a prevalent cohort only including survivors to a particular data. Let \(\alpha (a, t)\) denote the incidence of some chronic disease at age \(a\) and time \(t\) proportional to the probability that a healthy individual at \((a, t)\) will become ill in the next infinitesimal time interval. A central task in chronic disease epidemiology is to decompose \(\alpha (a, t)\) into effects explained by age \(a\), calendar time (``period'') \(t\) and birth time (``cohort'') \(c =t-a.\) For the incidence of diabetes the authors consider a log-linear model for the intensity \(\alpha (a, t)\) of the underlying events such that \(\log \alpha (a, t) = \mu + f_A (a) +f_T(t) + f_C(t-a)\), where \(\mu\) is a constant, and \(f_A (a)\), \(f_T(t)\) and \(f_C(c)\) are continuous functions with some constraints. They implement the age-period-cohort models by postulating spline decompositions of \(f_A (a)\), \(f_T(t)\) and \(f_C(c).\) The authors suppose that they can observe a bivariate Poisson point process which intensity function depends on \(\alpha (a, t).\) A Bayesian procedure is carried out for the optimal adjustment and comparison of isotropic and anisotropic smoothing priors for the intensity functions. The results apply for observations on insulin-dependent diabetic patients carried out in Fyn county, Denmark (population approximately 450.000).