Sankhya: The Indian Journal of Statistics

2001, Volume 63, Series B, Pt. 1, pp. 56--68

A GENERALIZED LIKELIHOOD RATIO APPROACH FOR CLUSTER-CORRELATED DATA FROM HUMAN FERTILITY STUDIES

By

HAIBO ZHOU, *University of North Carolina, Chapel Hill, U.S.A.*

MINGE XIE, *Rutgers University Piscataway, U.S.A.*

DOUGLAS G. SIMPSON, *University of Illinois, Champaign, U.S.A.*

and

CLARICE R. WEINBERG, *National Institute of Environmental Health Sciences, U.S.A.*

SUMMARY. Data from fertility studies are naturally cluster-correlated due to the fact that menstrual cycles belonging to the same couple are biologically related. We discuss a generalized likelihood ratio approach for a fertility model for the probability of conception, where the mean structure is given as the product of two independent components, and each of the components can be modeled as a function of a generalized linear model. We use the proposed method to construct confidence intervals for parameters that are restricted on [0,1]. The proposed approach provides range-preserving, asymmetric confidence intervals for the fertility parameters. Analysis of a data set from a North Carolina fertility study reveals some interesting findings that can not be observed with the traditional methods. The analysis suggests that prenatal exposure to maternal smoking has a deleterious effect on cycle viability while late menarche has a beneficial effect. The data do not support the existence of a negative effect of frequent ejaculation on sperm potency.

*AMS (1991) subject classification.* Primary 62J12;
secondary 62F99, 62P10.

*Key words and phrases. *Fertility, generalized likelihood ratio,
latent variables, quantile, weighted *X ^{2} *.