Genetic Epidemiology 35 : 19–45 (2011)
Investigation of Maternal Effects, Maternal-Fetal Interactions
and Parent-of-Origin Effects (Imprinting), Using Mothers
and Their Offspring
Holly F. Ainsworth,1 Jennifer Unwin,1 Deborah L. Jamison,1 and Heather J. Cordell2
1School of Mathematics and Statistics, Newcastle University, Newcastle upon Tyne, United Kingdom
2Institute of Human Genetics, Newcastle University, Newcastle upon Tyne, United Kingdom
Many complex genetic effects, including epigenetic effects, may be expected to operate via mechanisms in the inter-uterine
environment. A popular design for the investigation of such effects, including effects of parent-of-origin (imprinting),
maternal genotype, and maternal-fetal genotype interactions, is to collect DNA from affected offspring and their mothers
(case/mother duos) and to compare with an appropriate control sample. An alternative design uses data from cases and
both parents (case/parent trios) but does not require controls. In this study, we describe a novel implementation of a
multinomial modeling approach that allows the estimation of such genetic effects using either case/mother duos or case/
parent trios. We investigate the performance of our approach using computer simulations and explore the sample sizes and
data structures required to provide high power for detection of effects and accurate estimation of the relative risks
conferred. Through the incorporation of additional assumptions (such as Hardy-Weinberg equilibrium, random mating and
known allele frequencies) and/or the incorporation of additional types of control sample (such as unrelated controls,
controls and their mothers, or both parents of controls), we show that the (relative risk) parameters of interest are
identifiable and well estimated. Nevertheless, parameter interpretation can be complex, as we illustrate by demonstrating
the mathematical equivalence between various different parameterizations. Our approach scales up easily to allow the
analysis of large-scale genome-wide association data, provided both mothers and affected offspring have been genotyped
at all variants of interest. Genet. Epidemiol. 35:19–45, 2011. r 2010 Wiley-Liss, Inc.
Key words: epigenetic; log-linear model; case/parent trio
Additional Supporting Information may be found in the online version of this article.
Contract grant sponsor: Wellcome Trust; Contract grant number: 087436; Contract grant sponsor: European Community’s 7th Framework
Programme contract (‘‘CHeartED’’); Contract grant number: HEALTH-F2-2008-223040.
Correspondence to: Heather J. Cordell, Institute of Human Genetics, Newcastle University, International Centre for Life, Central
Parkway, Newcastle upon Tyne NE1 3BZ, UK. E-mail: heather.cordell@newcastle.ac.uk
Received 13 April 2010; Revised 24 September 2010; Accepted 5 October 2010
Published online 10 December 2010 in Wiley Online Library (wileyonlinelibrary.com).
DOI: 10.1002/gepi.20547
INTRODUCTION
The current era of genome-wide association studies has
popularized the case/control design for the detection of
genetic variants predisposing to complex diseases. How-
ever, as recently pointed out by Buyske [2008], associations
detected in a case/control study can arise not only from
genetic effects operating in the cases but also from
alternative mechanisms that are statistically confounded
with case genotype effects, such as maternal genotype
effects, maternal-fetal interactions, or parent-of-origin
(imprinting) effects. A variety of diseases, particularly
those related to pregnancy outcomes or complications in
utero, have been hypothesized to operate via such
mechanisms. For example, both maternal and fetal genes,
either individually or in combination, have been impli-
cated in risk of pre-eclampsia [Goddard et al., 2007;
Schneider et al., 1994; Wilson et al., 2003], low birthweight
[Larizza et al., 2005; Ober et al., 1987], spina bifida [Jensen
et al., 2006], and schizophrenia [Palmer et al., 2006]. With
data collected only on cases and controls, these different
types of effect will be indistinguishable. For example, a
strong maternal genotype effect may present the same
pattern of risks as a weak offspring (case) genotype effect,
since cases and mothers of cases share an allele in
common. Given family rather than case/control data,
however—specifically given genotype data for cases plus
their mothers and/or fathers—it may be possible to
distinguish between these different mechanisms [Cordell
et al., 2004; Hsieh et al., 2006; Shi et al., 2008; Sinsheimer
et al., 2003; Weinberg, 1999b; Weinberg et al., 1998;
Weinberg and Shi, 2009].
A popular design for the investigation of maternal
effects and maternal-fetal interactions (operating perhaps
via the inter-uterine environment) is to collect DNA from
offspring and their mothers [Shi et al., 2008]. A compar-
ison of the genotype relative risks in cases (displaying
some disease of interest) vs. controls compared to the
relative risks in mothers of cases vs. mothers of controls
can allow one to investigate the merits of different
competing underlying models. For example, Jamieson
r 2010 Wiley-Liss, Inc.

et al. [2008] found unusual patterns of risk when analyzing
children affected with clinical signs of congenital toxo-
plasmosis vs. controls compared to when analyzing
mothers of affected children vs. mothers of controls, a
result that they interpreted as indicating the presence of a
maternal genotype and/or imprinting effect.
More formally, given genotype data from ‘‘duos’’
consisting of offspring (affected or unaffected) together
with their mothers, one may fit models (via logistic
regression, for example) that incorporate effects of off-
spring genotype, maternal genotype, maternal-fetal inter-
actions, and imprinting [Chen et al., 2009; Li et al., 2009;
Shi et al., 2008; Weinberg and Umbach, 2005]. By
examining the fit of the model with and without the
inclusion of specific terms, one may test formally for their
significance and estimate the magnitude of their effects.
However, collinearities between the parameters represent-
ing the various effects can complicate the interpretation of
such an analysis, as we shall discuss in more detail later.
A number of authors have considered the alternative
approach of using case/parent trios (i.e. affected offspring
and their parents) for the estimation of such effects [Chen
et al., 2009; Cordell et al., 2004; Hsieh et al., 2006;
Sinsheimer et al., 2003; Weinberg, 1999b; Weinberg et al.,
1998]. Case/parent trios are often used in genetic associa-
tion studies because of the robustness to population
stratification they can provide, via use of family-based
tests that examine the transmission of high-risk alleles
from parents to affected offspring [Spielman et al., 1993].
Recently, however, the case/control design has achieved
greater popularity owing to the larger sample size (and
thus greater power) that is achievable [WTCCC, 2007] and
the development of alternative methods to deal with
population stratification [Devlin and Roeder, 1999; Price
et al., 2006; Pritchard et al., 2000]. With case/parent trios,
we can test for association and estimate genotype and
haplotype relative risks using conditional logistic regres-
sion [Cordell and Clayton, 2002; Schaid, 1996; Schaid and
Sommer, 1993] or log-linear modeling [Shi et al., 2009].
More complex effects, such as maternal genotype effects,
maternal-fetal interactions and parent-of-origin effects,
may be estimated through an extension of the conditional
logistic regression approach [Cordell et al., 2004] or
through log-linear modeling [Sinsheimer et al., 2003;
Vermeulen et al., 2009; Weinberg, 1999b; Weinberg et al.,
1998]. One of the merits of the case/parent trio design is
the fact that it does not require control data: essentially the
untransmitted parental alleles or genotypes are used as
‘‘controls’’ for the transmitted alleles or genotypes.
However, greater efficiency can potentially be achieved
by incorporation of one or more additional separate
control samples consisting either of unrelated controls
[Epstein et al., 2005; Nagelkerke et al., 2000], the parents of
unrelated controls [Weinberg and Umbach, 2005], or of
control/mother duos [Vermeulen et al., 2009]. Regardless
of whether or not such additional control samples are
used, most approaches generally assume that both parents
(the mother and the father) of cases are available in at least
a subset of families [Weinberg, 1999a]. Shi et al. [2008],
however, extended their log-linear modeling approach to
apply to case/mother duos (for which no fathers’
genotypes are available), on the assumption that, in
common with logistic regression, there exists a sample of
control/mother duos that can be incorporated into the
analysis. Given such a sample, Chen et al. [2009]
developed an alternative constrained retrospective like-
lihood approach that exploits the Mendelian correlation
between mother’s and child’s genomes under a Hardy-
Weinberg equilibrium (HWE) assumption, allowing the
estimation of maternal and child effects and their
interactions, where the effects in the child and mother
could operate either at the same locus or at different
(separate) loci that are in linkage disequilibrium.
METHODS
NOTATION, PARAMETERIZATION, AND
RELATIONSHIP TO PREVIOUS MODELS
Before describing our approach in detail, we introduce
some notation. Without loss of generality, we denote the allele
(at a particular genetic locus) that is expected to confer high
risk as 2 and the low-risk allele as 1. (If, in fact, it is allele 1
that confers higher risk, the genotype relative risk estimates
associated with allele 2 will turn out to be less than, rather
than greater than, 1.0.) We parameterize the risks as follows: a
corresponds to the baseline probability of disease for an
individual (child) with the low-risk homozygote genotype
(i.e. 11) whose parents are also homozygous 11. The
parameters R1 and R2 correspond to multiplicative factors
by which the child’s probability of disease is multiplied if the
child has one or two copies of the high-risk allele (i.e. has
genotype 12 or 22, respectively). S1 and S2 correspond to
multiplicative factors by which the child’s probability of
disease is multiplied if their mother has one or two copies of
the high-risk allele, respectively. The parameters g11, g12, g21,
and g22 are standard statistical interaction terms for the
interaction between mother’s and child’s genotype (i.e. gij is
the (additional) factor by which the disease risk is multiplied
when the mother has i copies and the child has j copies of the
high-risk allele). The imprinting parameter Im corresponds to
a multiplicative factor by which the probability of disease is
multiplied if the child receives a (maternal) copy of the high-
risk allele from their mother, and the imprinting parameter Ip
corresponds to a multiplicative factor by which the prob-
ability of disease is multiplied if the child receives a (paternal)
copy of the high-risk allele from their father. Note that this
notation for the parent-of-origin effects Im and Ip corresponds
to notation used by Weinberg et al. [1998] rather than to a
later alternative parameterization used by Weinberg [1999b]
(discussed further later). Notation for the other effects
corresponds to the notation used by Weinberg et al. [1998]
and Cordell et al. [2004], except for the parameters gij, which
were not considered by Weinberg et al. [1998] or Weinberg
[1999b] and which were previously denoted aij by Cordell
et al. [2004].
The rationale for the above parameterization and its
relationship to some alternative proposed parameteriza-
tions can be seen by examination of Table I. The
quantitities given in each cell of Table I correspond to
the probability (or odds) of the child developing disease
given the genotype combination (gm, gc) for mother and
child, as might be estimated in a logistic regression
analysis of case/mother duos vs. control/mother duos.
Since only seven genotype combinations are allowable
under Mendelian inheritance, a maximum of seven
parameters will be estimable (in the absence of any
additional information e.g. concerning father’s genotype).
The first illustrative example (shown in the top three
rows of Table I) shows a parameterization where child
20 Ainsworth et al.
Genet. Epidemiol.