Approaches to fitting age‐period‐cohort models with unequal intervals

Age-period-cohort models have provided useful insights into the analysis of time trends for disease rates, in spite of the well known identifiability problem. Unique parameter estimates that avoid arbitrary constraints are provided by estimable functions of the parameter estimates. For data that are generated using equal interval widths for age and period, the identifiability issue may be expressed in terms of the age, period and cohort slopes. However, when the interval widths are not the same for age and period, additional identifiability problems arise. These may be represented in terms of macro-trends, which have the identical identifiability problem seen in the equal interval case, and micro-trends, which are the source of the additional problems. A framework for testing estimability is presented, and a variety of potentially interesting functions of the parameters considered. Unlike the equal interval case, drift is not estimable for unequal intervals, but local drift may be. In addition, the available functions for forecasting are much more restrictive in the latter case. This estimability problem induces cyclical patterns in the estimates of trend as is demonstrated using data on leukaemia in Connecticut males, but this can be avoided through the use of smoothing splines. These methods of are illustrated for three-year period and five-year age intervals using data on lung cancer mortality in Californian women.