Incorporation of Inter‐individual Heterogeneity into the Multistage Carcinogenesis Model: Approach to the Analysis of Cancer Incidence Data

Abstract

We investigate a multistage carcinogenesis frailty model to incorporate inter-individual heterogeneity into carcinogenic response. Attention is focused on inference concerning the effects of different sources of population heterogeneity on cancer rates. The authors consider unobserved variability arising from either carcinogen exposure or background characteristics. Gamma and Inverse-Gaussian distributions are selected for frailty models, and the baseline hazard function is the generalized Armitage-Doll model (i.e. non-frailty model) in which exposure effects shift the age scale instead of acting multiplicatively on cancer rates. For illustration, we apply the method to solid cancer data from a cohort of atomic bomb survivors to examine some features of proposed models. The results show that the Gamma frailty model for the heterogeneity of baseline rates provides the best goodness-of-fit of the model and a non-zero frailty variance. Parameter estimates are, for the most part, comparable between the Gamma and Inverse-Gaussian frailty models. In a heterogeneous population the exposure effects on young adulthood cancer rates might be underestimated for the non-frailty model. Meaningful information regarding each source of heterogeneity has been provided by the proposed method. Therefore, the multistage carcinogenesis frailty model approach is useful for analyses of epidemiological cancer data to assess population heterogeneity and heterogeneity-influenced exposure effects.