AbstractAge-period-cohort (APC) models are used to analyse a variety of different health and demographic related outcomes. When including all three temporal trends into one model, there arises the well-known identification problem due to the structural link between the temporal trends (given two, the third can be calculated). Previous methods to resolve this problem focus on defining a model based off identifiable quantities. Most of the literature focusses on the case when APC models are fit to data aggregated in equal intervals (age and period widths). This may be, in part, due to the added complication that arises when fitting APC models to data in unequal intervals which causes a cyclic pattern in any estimates of the temporal trends.
We first show that when an APC model is fit to data in unequal intervals, the previously identifiable terms, used to define a model that resolves the problem created by the structural link, are no longer identifiable. Using penalised smoothing splines, we show how the novel inclusion of a penalty on the previously identifiable terms resolves any problems that arise when fitting an APC model to data aggregated in unequal intervals and conclude the necessity of a penalty to provide a suitable solution. We demonstrate the suitability of our proposed model using theoretical and empirical results.
Subsequently, we highlight the key information that links our proposed method to a class of APC models that utilise smoothing priors in a Bayesian paradigm. We give a full consideration of the problems that arise when fitting APC models to unequal interval data and how smoothing priors can be used to resolve them. Using theoretical and empirical results, we show that the smoothing prior models are performing a similar penalisation to that of a penalised smoothing spline, which we had previously shown to be a suitable solution, concluding their suitability is due to this penalty.
We conclude with a novel application of an APC model to under-five mortality rates (U5MR) in Kenya 2006 to 2014. Previous methods to model U5MR include temporal terms for age and period, but not cohort. We extend the APC model to be suitable for the application by including spatial, spatio-temporal and strata specific terms alongside the terms for age, period, and cohort. The results indicate the inclusion of cohort is important to producing smooth fitting subnational estimates, an important goal for U5MR modelling which suffers from unstable estimates due to sparse data.
|Date of Award
|2 Nov 2022
|Theresa Smith (Supervisor) & Karim Anaya-Izquierdo (Supervisor)