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 .

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