Piecewise Constant Cross-ratio Estimation for Bivariate Survival Data: Association Between Ages at Onset of a Marker Event and Menopause

• Activity Number: 289
• Type: Invited
• Date/Time: Wednesday, August 11, 2004 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Xihong Lin*+ and Bin Nan and Lynda Lisabeth and Sioban Harlow
• Companies: University of Michigan and University of Michigan and University of Michigan and University of Michigan
• Keywords: bivariate failure time ; Clayton model ; cross-ratio function ; marker event ; menopausal transition ; reproductive health

Abstract

This article provides an analysis for the association between ages at onset of a marker and menopause using the Tremin Trust data, a long-term cohort study following women through the whole reproductive life span. Although various marker events based on bleeding pattern change have been proposed for early and late transition to menopause clinically, formal statistical analysis for evaluating their associations with age at onset of menopause appears to be complicated. Such an analysis is challenged by the fact that both a marker event and menopause are subject to right-censoring and their association depends on the age at the marker event. We propose to model their association using a cross-ratio model, which is assumed to be a piecewise constant function of the marker event time. Two estimation procedures using the direct and sequential two-stage methods are proposed, and are extended to allow for covariates in marginal survival functions. The proposed methods are applied to the analysis of the Tremin Trust data, and their performance is evaluated using simulations.