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.

[1]  R. Tibshirani,et al.  Generalized additive models for medical research , 1986, Statistical methods in medical research.

[2]  Jianhua Z. Huang.  Local asymptotics for polynomial spline regression , 2003 .

[3]  Daniel Commenges,et al.  A penalized likelihood approach for an illness-death model with interval-censored data: application to age-specific incidence of dementia. , 2002, Biostatistics.

[4]  Jian Huang.  Efficient estimation of the partly linear additive Cox model , 1999 .

[5]  M Zelen,et al.  Comparing the Survival of Two Groups with an Intermediate Clinical Event , 2001, Lifetime data analysis.

[6]  A. Treloar,et al.  Variation of the human menstrual cycle through reproductive life. , 1967, International journal of fertility.

[7]  Leszek Marzec,et al.  On fitting Cox's regression model with time-dependent coefficients , 1997 .

[8]  P. Sen,et al.  Time-dependent coefficients in a Cox-type regression model , 1991 .

[9]  Zongwu Cai,et al.  Local Linear Estimation for Time-Dependent Coefficients in Cox's Regression Models , 2003 .

[10]  J. Crowley,et al.  Covariance Analysis of Heart Transplant Survival Data , 1977 .

[11]  Xiaotong Shen,et al.  Local asymptotics for regression splines and confidence regions , 1998 .

[12]  J. Kalbfleisch,et al.  The Statistical Analysis of Failure Time Data: Kalbfleisch/The Statistical , 2002 .

[13]  J. Kalbfleisch,et al.  The Statistical Analysis of Failure Time Data , 1980 .

[14]  M. Soules,et al.  Executive summary: Stages of Reproductive Aging Workshop (STRAW). , 2001, Fertility and sterility.

[15]  Roderick J. A. Little,et al.  Statistical Analysis with Missing Data: Little/Statistical Analysis with Missing Data , 2002 .

[16]  F. O’Sullivan.  Nonparametric Estimation of Relative Risk Using Splines and Cross-Validation , 1988 .

[17]  R. Tibshirani,et al.  Varying‐Coefficient Models , 1993 .

[18]  Siobán D Harlow,et al.  Staging reproductive aging: a comparison of proposed bleeding criteria for the menopausal transition , 2004, Menopause.

[19]  Lorraine Dennerstein,et al.  Menstrual patterns leading to the final menstrual period , 2002, Menopause.

[20]  D. Rubin,et al.  Statistical Analysis with Missing Data. , 1989 .

[21]  W. Tsai,et al.  On using the Cox proportional hazards model with missing covariates , 1997 .

[22]  John D. Kalbfleisch,et al.  The Statistical Analysis of Failure Data , 1986, IEEE Transactions on Reliability.

[23]  N. Woods,et al.  Three stages of the menopausal transition from the Seattle Midlife Women's Health Study: toward a more precise definition , 2000, Menopause.