Genetic epidemiology of breast cancer: interest of survival analysis methods

In an attempt to explain the controversy resulting from the analysis of the breast cancer data collected by Jacobsen, a segregation analysis was performed using successively the unified mixed model (UM) and the logistic hazard function model (LHM) (Abel & Bonney, 1990). Under the UM, age of onset of the disease cannot be taken into account, each individual being assigned to a liability class according to his age at examination, whereas, in the LHM, variable age of onset is modelled using survival analysis methods. Under the UM, we confirmed the results of Demenais et al. (1986b), i.e. the transmission probabilities are significantly different from Mendelian expectations. The same results were obtained when taking into account the specific mortality for the computation of the morbid risk observed in a given liability class. Under the LHM, the analysis provides evidence for a monogenic autosomal model with a rare dominant allele responsible for the disease, and transmission probabilities compatible with Mendelian expectations. This study shows that the rejection of the Mendelian transmission under the UM can be due to a violation of a constraint of this model (i.e. the probability of being and not being affected in a given liability class should sum to 1) when a specific mortality is induced by the disease as in breast cancer. Survival analysis methods avoid these problems by taking into account the onset of the disease as the failure time event and are more suitable when studying a complex trait such as breast cancer.