Background: Although interpretation of age-period-cohort analyses is complicated by the non-identifiability of maximum likelihood estimates, changes in the slope of the birth-cohort effect curve are identifiable and have potential aetiologic significance.
Methods: A nonparametric test for a change in the slope of the birth-cohort trend has been developed. The test is a generalisation of the sign test and is based on permutational distributions. A method for identifying interactions between age and calendar-period effects is also presented.
Results: The nonparametric method is shown to be powerful in detecting changes in the slope of the birth-cohort trend, although its power can be reduced considerably by calendar-period patterns of risk. The method identifies a previously unidentified decrease in the birth-cohort risk of lung-cancer mortality from 1912 to 1919, which appears to reflect a reduction in the initiation of smoking by young men at the beginning of the Great Depression (1930s). The method also detects an interaction between age and calendar period in leukemia mortality rates, reflecting the better response of children to chemotherapy.
Conclusion: The proposed nonparametric method provides a data analytic approach, which is a useful adjunct to log-linear Poisson analysis of age-period-cohort models, either in the initial model building stage, or in the final interpretation stage.