Confounding and misrounding in age-period-cohort models

A natural starting point for an age-period-cohort analysis is to assess the suitability of an independence model. If necessary, modifications are then made to the independence model to account for the effects of period and cohort. Data are usually made available for analysis in a two-way contingency table categorised in terms of rounded age and rounded period. The linear relationship age=period-cohort does not hold exactly under rounding and the observation in a cell rounded age-by-period is not necessarily the same as an observation in a cell rounded age-by-cohort. In practice, independence models are discretised incorrectly such that the age-by-period data are used for model fitting as if the data are rounded age-by-cohort. The independence model is often deemed to be unsuitable as a description of the data and modifications are made to the independence model according to a proportional hazards assumption. We investigate whether the need for modifications is only apparent due to the misrounded treatment of the data. The case of Bovine Spongiform Encephalopathy is used as an illustrative example.