A Method for Using Incomplete Triads to Test Maternally Mediated Genetic
Effects and Parent-of-Origin Effects in Relation to a Quantitative Trait
Emily O. Kistner1, Claire Infante-Rivard2, and Clarice R. Weinberg1
1Biostatistics Branch, National Institute of Environmental Health Sciences, Research Triangle Park, NC.
2Department of Epidemiology, Biostatistics and Occupational Health, Faculty of Medicine, McGill University, Montre ´al,
Que ´bec, Canada.
Received for publication May 16, 2005; accepted for publication September 13, 2005.
Theauthorsrecentlydevelopedasemiparametric family-based testforlinkageandassociationbetweenmarkers
and quantitative traits. This quantitative polytomous logistic regression test allows for analysis of families with
incomplete information on parental genotype. In addition, it is not necessary to assume normality of the quantitative
trait. Previous simulations have shown that the new test is as powerful as the other widely used tests for linkage
disequilibrium in relation to a quantitative trait. Here the authors propose an extension to quantitative polytomous
logistic regression that allows testing for maternally mediated effects and parent-of-origin effects in the same
framework. Missing data on parental genotype are accommodated through an expectation-maximization algorithm
approach. Simulations show robustness of the new tests and good power for detecting effects in the presence or
absence of offspring effects. Methods are illustrated with birth weight and gestational length, two quantitative
outcomes for which data were collected in a Montreal, Canada, study of intrauterine growth restriction between
May 1998 and June 2000.
association; cytochrome P-450 enzyme system; epidemiologic methods; genomic imprinting; linkage (genetics);
logistic models; polymorphism, single nucleotide
Abbreviation: CYP, cytochrome P-450.
Family-based tests of linkage and association between
markers and quantitative traits are popular in part because
the tests are valid in the presence of genetic stratification,
whereas straightforward case-control designs do not allow
valid testing with admixed populations. Some tests accom-
modate data from incomplete nuclear families. Some meth-
ods, such asthe quantitativetransmission disequilibrium test
and the Family Genotype Analysis Program, assume that the
trait has, or has been transformed to have, a normal distribu-
tion (1, 2). Other methods, such as the family-based associ-
ation test, are nonparametric and rely on covariance between
a function of the trait and the genotype (3). For our methods,
we consider a design in which a diallelic gene is studied in
triads consisting of individuals and their parents and a quan-
titative trait is measured in the offspring. In a previous paper
(4), we proposed a semiparametric test, using a polytomous
logistic regression and expectation-maximization approach,
In addition to testing for effects of the inherited allele in-
which can influence the offspring through the intrauterine
environment, or parent-of-origin effects, in which an inher-
ited allele can influence the offspring differently depending
on whether it was maternal or paternal in origin. The latter
anism called ‘‘imprinting’’ (5).
Correspondence to Dr. Clarice Weinberg, Biostatistics Branch, National Institute of Environmental Health Sciences, Research Triangle Park,
NC 27709 (e-mail: email@example.com).
American Journal of Epidemiology
Copyright ª 2005 by the Johns Hopkins Bloomberg School of Public Health
All rights reserved; printed in U.S.A.
American Journal of Epidemiology Advance Access published December 7, 2005
by guest on May 30, 2013
separate genetic mechanisms act additively on the quanti-
tative trait under study. If instead the maternal effect and
the offspring-mediated effect are not additive, departures
from additivity can be mistaken for parent-of-origin effects,
because the maternal coefficient may depend in complex
ways on the offspring genotype and the trait value. For ex-
ample, consider the following possible interaction between
maternal and offspring genotype. Suppose a given level of
obesity in a child can be produced by the child’s inheriting
a copy of the allelic variant or by the mother’s carrying a
copy, which influences her own phenotype and hence the
fetal development of her child. For an obese child who does
not carry a copy of the variant allele, the mother will be at
increased likelihood of carrying a copy herself, compared
with the mother of a similarly obese child who does carry a
copy. In this way, the interpretation of apparent parent-of-
origin effects can become problematic.
In this paper, we have illustrated that the proposed
method is valid and powerful for tests to detect maternal
effects or parent-of-origin effects between a quantitative
trait and a diallelic marker, with complete or incomplete
triads. Readers may be interested in estimating power for
scenarios other than those described here. Power can also be
approximated by assuming normality of the trait, estimating
the frequencies for specific strata using Hardy-Weinberg
equilibrium and the assumed prevalence of the allele, and
using new SAS power software available in version 9 (19).
The power of the binary logistic model may be estimated by
computing the power of a two-way analysis of variance,
treating the parental mating type strata as blocking factors.
Because the methods are based on likelihood ratio tests,
available software makes them easily programmable and
the analyses quick to execute. SAS macros for carrying
out such analyses are available at a National Institute of
Environmental Health Sciences website (http://dir.niehs.nih.
Dr. Claire Infante-Rivard’s work was funded by the
Canadian Institutes of Health Research (grants MA-14705
and MOP 53069). Dr. Infante-Rivard holds a Canada Re-
search Chair (James McGill Professorship from McGill
The authors thank Drs. Norman Kaplan and David
Umbach for their helpful comments.
Conflict of interest: none declared.
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