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Biostatistics Advance Access published online on July 14, 2005
Biostatistics, doi:10.1093/biostatistics/kxi043
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© The Author 2005. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oupjournals.org.
Received December 11, 2002
Revised June 29, 2005
Accepted July 13, 2005

Article

Modeling menstrual cycle length using a mixture distribution

Ying Guo 1, Amita K. Manatunga 1*, Shande Chen 2, and Michele Marcus 3

1 Department of Biostatistics, Emory University, Atlanta, GA, 30322, USA
2 Department of Biostatistics, University of North Texas Health Science Center at Fort Worth,TX, 76107,USA
3 Department of Epidemiology, Emory University, Atlanta, GA, 30322, USA

* To whom correspondence should be addressed.
Amita K. Manatunga, E-mail: amanatu{at}sph.emory.edu


  Abstract

In reproductive health studies, epidemiologists are often interested in examining the effects of covariates on menstrual cycle length which is a convenient, noninvasive measure of women's ovarian and reproductive function. Previous literature (Harlow and Zeger, 1991) suggests that the distribution of cycle length is a mixture of a major symmetric distribution and a component featuring a long right tail. Motivated by the shape of this marginal distribution, we propose a mixture distribution for cycle length, representing standard cycles from a Normal distribution and nonstandard cycles from a shifted Weibull distribution. The parameters are estimated using an estimating equation derived from the score function of an independence working model. The fitted mixture distribution agrees well with the distribution estimated using nonparametric approaches. We propose two measures to help determine whether a cycle is standard or nonstandard, developing tools necessary to identify characteristics of the menstrual cycles that are biologically indicative of ovarian dysfunction. We model the effect of a woman's age on the mean and variation of both standard and nonstandard cycle lengths using multiple measurements of women.

Keywords: Menstrual cycle length; Mixture distribution; Kernel density estimation; Optimum cutoff; Conditional probability; Estimating equation.
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