A varying-coefficient Cox model for the effect of age at a marker event on age at menopause

It is of recent interest in reproductive health research to investigate the validity of a marker event for the onset of menopausal transition and to estimate age at menopause using age at the marker event. We propose a varying-coefficient Cox model to investigate the association between age at a marker event, defined as a specific bleeding pattern change, and age at menopause, where both events are subject to censoring and their association varies with age at the marker event. Estimation proceeds using the regression spline method. The proposed method is applied to the Tremin Trust data to evaluate the association between age at onset of the 60-day menstrual cycle and age at menopause. The performance of the proposed method is evaluated using a simulation study.