@article{BaldNich95,
  title = {A method for quantifying differentiation between populations at multi-allelic loci and its implications for investigating identity and paternity},
  volume = {96},
  ISSN = {1573-6857},
  url = {http://dx.doi.org/10.1007/BF01441146},
  DOI = {10.1007/bf01441146},
  number = {1–2},
  journal = {Genetica},
  publisher = {Springer Science and Business Media LLC},
  author = {Balding,  David J. and Nichols,  Richard A.},
  year = {1995},
  month = jun,
  pages = {3–12}
}

@article{Lang92,
	ISSN = {00063444},
	URL = {http://www.jstor.org/stable/2336852},
	abstract = {We consider inferences about Poisson log linear models for
	            which only certain disjoint sums of the data are observable.
	            We derive an explicit formula for the observed information
	            matrix associated with the log linear parameters that is
	            intuitively appealing and simple to evaluate.},
	author = {Joseph B. Lang},
	journal = {Biometrika},
	number = {2},
	pages = {405--407},
	publisher = {[Oxford University Press, Biometrika Trust]},
	title = {Obtaining the Observed Information Matrix for the Poisson Log
	         Linear Model with Incomplete Data},
	urldate = {2025-04-21},
	volume = {79},
	year = {1992},
}


@article{GjesLie06,
	title = "Case-parent triads: estimating single- and double-dose effects
	         of fetal and maternal disease gene haplotypes",
	author = "H. K. Gjessing and Rolv T. Lie",
	abstract = "Case-parent triad data are considered a robust basis for
	            studying association between variants of a gene and a
	            disease. Methods evaluating statistical significance of
	            association, like the TDT-test and its extensions, are
	            frequently used. When there are prior hypotheses of a causal
	            effect of the gene under study, however, methods measuring
	            penetrance of alleles or haplotypes as relative risks will be
	            more informative. Log-linear models have been proposed as a
	            flexible tool for such relative risk estimation. We
	            demonstrate an extension of the log-linear model to a natural
	            framework for also estimating effects of multiple alleles or
	            haplotypes, incorporating both single- and double-dose
	            effects. The model also incorporates effects of single- and
	            double-dose maternal haplotypes on a fetus during pregnancy.
	            Unknown phase of haplotypes as well as missing parents are
	            accounted for by the EM algorithm. A number of numerical
	            improvements to maximum likelihood estimation are also
	            implemented to facilitate a larger number of haplotypes.
	            Software for these analyses, HAPLIN, is publicly available
	            through our web site. As an illustration we have re-analyzed
	            data on the MSX1 homeobox-gene on chromosome 4 to show how
	            haplotypes may influence the risk of oral clefts.",
	journal = "Annals of Human Genetics",
	publisher = "Wiley",
	volume = 70,
	number = "Pt 3",
	pages = "382--396",
	month = may,
	year = 2006,
	copyright = "http://onlinelibrary.wiley.com/termsAndConditions\#vor",
	language = "en",
}

@article{Rase+25,
	AUTHOR = {Rasevic, Nikola and Bastasic, Joseph and Rubini, Michele and
	          Rakesh, Mohan R. and Burkett, Kelly M. and Ray, Debashree and
	          Mossey, Peter A. and Peterlin, Borut and Khan, Mohammad Faisal
	          J. and Ravaei, Amin and Autelitano, Luca and Meazzini, Maria C.
	          and Little, Julian and Roy-Gagnon, Marie-Hélène},
	TITLE = {Maternal and Parent-of-Origin Gene–Environment Effects on the
	         Etiology of Orofacial Clefting},
	JOURNAL = {Genes},
	VOLUME = {16},
	YEAR = {2025},
	NUMBER = {2},
	ARTICLE-NUMBER = {195},
	URL = {https://www.mdpi.com/2073-4425/16/2/195},
	PubMedID = {40004524},
	ISSN = {2073-4425},
	ABSTRACT = {Background/Objectives: We investigated maternal and
	            parent-of-origin (PoO) gene-environment interaction effects
	            on the risk of nonsyndromic orofacial clefts for two maternal
	            environmental factors: periconceptional smoking and folic
	            acid supplementation. Methods: Genome-wide single nucleotide
	            polymorphisms (SNPs) genotypes and TopMed-imputed genotypes
	            were obtained for case-parent triads from the EUROCRAN and
	            ITALCLEFT studies. Candidate regions were selected around
	            target SNPs from a previous genome-wide association study,
	            resulting in 12 (726 SNPs) and 11 regions (730 SNPs) for
	            maternal and PoO effects, respectively. Log-linear models
	            were used to analyze 404 case-parent triads and 40
	            case-parent dyads. p-values were combined across regions.
	            Results: None of the interactions reached statistical
	            significance after correction for the number of regions
	            tested. Nominally significant (pooled p-values < 0.05)
	            interactions pointed to regions in or close to genes LRRC7
	            (maternal gene-folate interaction), NCKAP5 (PoO-smoking
	            interaction), and IFT43 and GPATCH2L (PoO-folate
	            interaction). Conclusions: Our results suggested that the
	            genetic effects in or around these genes were heightened
	            under periconceptional exposure to tobacco or no folic acid
	            supplementation. The involvement of these genes in orofacial
	            cleft development, in conjunction with environmental
	            exposures, should be further studied.},
	DOI = {10.3390/genes16020195},
}

@article{Hell+17,
	author = {Hellwege, Jacklyn N. and Keaton, Jacob M. and Giri, Ayush and
	          Gao, Xiaoyi and Velez Edwards, Digna R. and Edwards, Todd L.},
	title = {Population Stratification in Genetic Association Studies},
	journal = {Current Protocols in Human Genetics},
	volume = {95},
	number = {1},
	pages = {1.22.1-1.22.23},
	keywords = {admixture, admixture mapping, association confounding,
	            global ancestry, local ancestry, population stratification},
	doi = {https://doi.org/10.1002/cphg.48},
	url = {
	       https://currentprotocols.onlinelibrary.wiley.com/doi/abs/10.1002/cphg.48
	       },
	eprint = {
	          https://currentprotocols.onlinelibrary.wiley.com/doi/pdf/10.1002/cphg.48
	          },
	abstract = {Abstract Population stratification (PS) is a primary
	            consideration in studies of genetic determinants of human
	            traits. Failure to control for PS may lead to confounding,
	            causing a study to fail for lack of significant results, or
	            resources to be wasted following false-positive signals. Here
	            , historical and current approaches for addressing PS when
	            performing genetic association studies in human populations
	            are reviewed. Methods for detecting the presence of PS,
	            including global and local ancestry methods, are described.
	            Also described are approaches for accounting for PS when
	            calculating association statistics, such that measures of
	            association are not confounded. Many traits are being
	            examined for the first time in minority populations, which
	            may inherently feature PS. © 2017 by John Wiley \& Sons, Inc.
	            },
	year = {2017},
}

@article{Hobbs+14,
	author = {Hobbs, Charlotte A. and Cleves, Mario A. and MacLeod, Stewart
	          L. and Erickson, Stephen W. and Tang, Xinyu and Li, Jingyun and
	          Li, Ming and Nick, Todd and Malik, Sadia and the National Birth
	          Defects Prevention Study},
	title = {Conotruncal heart defects and common variants in maternal and
	         fetal genes in folate, homocysteine, and transsulfuration
	         pathways},
	journal = {Birth Defects Research Part A: Clinical and Molecular
	           Teratology},
	volume = {100},
	number = {2},
	pages = {116-126},
	keywords = {conotruncal heart defects, single nucleotide polymorphisms,
	            oxidative stress, genetics, folic acid, gene X environment
	            interaction},
	doi = {https://doi.org/10.1002/bdra.23225},
	url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/bdra.23225},
	eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/bdra.23225},
	abstract = {Background We investigated the association between
	            conotruncal heart defects (CTDs) and maternal and fetal
	            single nucleotide polymorphisms (SNPs) in 60 genes in the
	            folate, homocysteine, and transsulfuration pathways. We also
	            investigated whether periconceptional maternal folic acid
	            supplementation modified associations between CTDs and SNPs
	            Methods Participants were enrolled in the National Birth
	            Defects Prevention Study between 1997 and 2008. DNA samples
	            from 616 case-parental triads affected by CTDs and 1645
	            control-parental triads were genotyped using an Illumina®
	            Golden Gate custom SNP panel. A hybrid design analysis,
	            optimizing data from case and control trios, was used to
	            identify maternal and fetal SNPs associated with CTDs Results
	            Among 921 SNPs , 17 maternal and 17 fetal SNPs had a Bayesian
	            false-discovery probability of <0.8. Ten of the 17 maternal
	            SNPs and 2 of the 17 fetal SNPs were found within the
	            glutamate-cysteine ligase, catalytic subunit (GCLC) gene.
	            Fetal SNPs with the lowest Bayesian false-discovery
	            probability (rs2612101, rs2847607, rs2847326, rs2847324) were
	            found within the thymidylate synthetase (TYMS) gene.
	            Additional analyses indicated that the risk of CTDs
	            associated with candidate SNPs was modified by
	            periconceptional folic acid supplementation. Nineteen
	            maternal and nine fetal SNPs had a Bayesian false-discovery
	            probability <0.8 for gene-by-environment (G × E) interactions
	            with maternal folic acid supplementation. Conclusion These
	            results support previous studies suggesting that maternal and
	            fetal SNPs within folate, homocysteine , and transsulfuration
	            pathways are associated with CTD risk. Maternal use of
	            supplements containing folic acid may modify the impact of
	            SNPs on the developing heart. Birth Defects Research (Part A)
	            100:116–126, 2014. © 2014 Wiley Periodicals, Inc.},
	year = {2014},
}


@article{Heal+10,
	author = {Healy, Jasmine and Bourgey, Mathieu and Richer, Chantal and
	          Sinnett, Daniel and Roy-Gagnon, Marie-Helene},
	title = {Detection of Fetomaternal Genotype Associations in Early-Onset
	         Disorders: Evaluation of Different Methods and Their Application
	         to Childhood Leukemia},
	journal = {BioMed Research International},
	volume = {2010},
	number = {1},
	pages = {369534},
	doi = {https://doi.org/10.1155/2010/369534},
	url = {https://onlinelibrary.wiley.com/doi/abs/10.1155/2010/369534},
	eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1155/2010/369534},
	abstract = {Several designs and analytical approaches have been proposed
	            to dissect offspring from maternal genetic contributions to
	            early-onset diseases. However, lack of parental controls
	            halts the direct verification of the assumption of mating
	            symmetry (MS) required to assess maternally-mediated effects.
	            In this study, we used simulations to investigate the
	            performance of existing methods under mating asymmetry (MA)
	            when parents of controls are missing. Our results show that
	            the log-linear, likelihood-based framework using a
	            case-triad/case-control hybrid design provides valid tests
	            for maternal genetic effects even under MA. Using this
	            approach, we examined fetomaternal associations between 29
	            SNPs in 12 cell-cycle genes and childhood pre-B acute
	            lymphoblastic leukemia (ALL). We identified putative
	            fetomaternal effects at loci CDKN2A rs36228834 (P = .017) and
	            CDKN2B rs36229158 (P = .022) that modulate the risk of
	            childhood ALL. These data further corroborate the importance
	            of the mother′s genotype on the susceptibility to early-onset
	            diseases.},
	year = {2010},
}


@article{Ains+11,
	author = {Ainsworth, Holly F. and Unwin, Jennifer and Jamison, Deborah
	          L. and Cordell, Heather J.},
	title = {Investigation of maternal effects, maternal-fetal interactions
	         and parent-of-origin effects (imprinting), using mothers and
	         their offspring},
	journal = {Genetic Epidemiology},
	volume = {35},
	number = {1},
	pages = {19-45},
	keywords = {epigenetic, log-linear model, case/parent trio},
	doi = {https://doi.org/10.1002/gepi.20547},
	url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/gepi.20547},
	eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/gepi.20547},
	abstract = {Abstract 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. ©
	            2010 Wiley-Liss, Inc.},
	year = {2011},
}


@manual{R21,
	title = {R: A language and environment for statistical computing},
	author = {{R Core Team}},
	organization = {R Foundation for Statistical Computing},
	address = {Vienna, Austria},
	year = {2021},
	url = {https://www.R-project.org/},
}


@article{Gjer+18,
	author = {Gjerdevik, Miriam and Haaland, {\O}ystein A. and Romanowska,
	          Julia and Lie, Rolv T. and Jugessur, Astanand and Gjessing, H.
	          K.},
	title = {Parent-of-origin-environment interactions in case-parent triads
	         with or without independent controls},
	journal = {Annals of Human Genetics},
	volume = {82},
	number = {2},
	pages = {60-73},
	keywords = {case–parent triad, gene–environment interaction, hybrid
	            design, imprinting, parent-of-origin, power and sample size
	            calculation, trios},
	doi = {https://doi.org/10.1111/ahg.12224},
	url = {https://onlinelibrary.wiley.com/doi/abs/10.1111/ahg.12224},
	eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1111/ahg.12224},
	abstract = {Abstract With case–parent triad data, one can frequently
	            deduce parent of origin of the child's alleles. This allows a
	            parent-of-origin (PoO) effect to be estimated as the ratio of
	            relative risks associated with the alleles inherited from the
	            mother and the father, respectively. A possible cause of PoO
	            effects is DNA methylation, leading to genomic imprinting.
	            Because environmental exposures may influence methylation
	            patterns, gene–environment interaction studies should be
	            extended to allow for interactions between PoO effects and
	            environmental exposures (i.e., PoOxE). One should thus search
	            for loci where the environmental exposure modifies the PoO
	            effect. We have developed an extensive framework to analyze
	            PoOxE effects in genome-wide association studies (GWAS),
	            based on complete or incomplete case–parent triads with or
	            without independent control triads. The interaction approach
	            is based on analyzing triads in each exposure stratum using
	            maximum likelihood estimation in a log-linear model.
	            Interactions are then tested applying a Wald-based posttest
	            of parameters across strata. Our framework includes a
	            complete setup for power calculations. We have implemented
	            the models in the R software package Haplin. To illustrate
	            our PoOxE test, we applied the new methodology to top hits
	            from our previous GWAS, assessing whether smoking during the
	            periconceptional period modifies PoO effects on cleft palate
	            only.},
	year = {2018},
}


@article{Gjer+19,
	title = {Haplin power analysis: a software module for power and sample
	         size calculations in genetic association analyses of family
	         triads and unrelated controls},
	volume = {20},
	ISSN = {1471-2105},
	url = {http://dx.doi.org/10.1186/s12859-019-2727-3},
	DOI = {10.1186/s12859-019-2727-3},
	number = {1},
	journal = {BMC Bioinformatics},
	publisher = {Springer Science and Business Media LLC},
	author = {Gjerdevik, Miriam and Jugessur, Astanand and Haaland, {\O}
	          ystein A. and Romanowska, Julia and Lie, Rolv T. and Cordell,
	          Heather J. and Gjessing, Håkon K.},
	year = {2019},
	month = apr,
}


@article{Juge+12,
	title = {Using offspring-parent triads to study complex traits: A
	         tutorial based on orofacial clefts},
	volume = {21},
	url = {https://www.ntnu.no/ojs/index.php/norepid/article/view/1503},
	DOI = {10.5324/nje.v21i2.1503},
	abstractNote = {Health investigators routinely collect DNA and
	                environmental data from study participants in order to
	                assess the impact of genetic and environmental risk
	                factors on an outcome of interest. When planning a study,
	                alternate study designs are evaluated to minimize bias
	                and achieve a large enough sample size from available
	                resources. With the enormous volumes of high-quality
	                biomedical data housed within its numerous biobanks,
	                Norway is particularly well-suited to spearhead the
	                investigation of a wide array of exposures and outcomes
	                in a systematic manner. The rich array of longitudinal
	                phenotypic data also permits an assessment of
	                geneenvironment- timing interactions. Maximizing the
	                research potential inherent in Norwegian biobanks is the
	                overarching aim of Biobank Norway, an infrastructure
	                project recently funded by the Norwegian Research
	                Council. The development of advanced statistical tools
	                for the analysis of high-throughput genomic data is
	                critical to fulfill this aim and biostatistics platforms
	                have been key elements of major biobank harmonization
	                initiatives. However, many of these approaches have
	                focused on traditional case-control designs. To exploit
	                the particular advantages inherent in the Norwegian
	                Mother and Child Cohort Study (MoBa), we describe here
	                models to analyze the special data configurations
	                available with offspring-parent designs. These models and
	                the statistical tools outlined in this review were
	                developed through the support of Biohealth Norway, a
	                biobank platform funded by the Norwegian Functional
	                Genomics Research Program (FUGE).},
	number = {2},
	journal = {Norsk Epidemiologi},
	author = {Jugessur, Astanand and Skare, Øivind and Harris, Jennifer Ruth
	          and Lie, Rolv Terje and Gjessing, Håkon Kristian},
	year = {2012},
	month = {Apr.},
}


@article{Wein99,
	title = {Methods for Detection of Parent-of-Origin Effects in Genetic
	         Studies of Case-Parents Triads},
	volume = {65},
	ISSN = {0002-9297},
	url = {http://dx.doi.org/10.1086/302466},
	DOI = {10.1086/302466},
	number = {1},
	journal = {The American Journal of Human Genetics},
	publisher = {Elsevier BV},
	author = {Weinberg, Clarice R.},
	year = {1999},
	month = jul,
	pages = {229–235},
}


@article{HoweCord12,
	title = {{PREMIM} and {EMIM}: tools for estimation of maternal,
	         imprinting and interaction effects using multinomial modelling},
	volume = {13},
	ISSN = {1471-2105},
	url = {http://dx.doi.org/10.1186/1471-2105-13-149},
	DOI = {10.1186/1471-2105-13-149},
	number = {1},
	journal = {BMC Bioinformatics},
	publisher = {Springer Science and Business Media LLC},
	author = {Howey, Richard and Cordell, Heather J.},
	year = {2012},
	month = jun,
}

@manual{Verm97,
	author = {Vermunt, Jeroen},
	year = {1997},
	month = {01},
	pages = {},
	title = {{LEM}: A General Program for the Analysis of Categorical Data},
}

@article{Garl+20,
	title = {Role of epigenetics and {miRNAs} in orofacial clefts},
	volume = {112},
	ISSN = {2472-1727},
	url = {http://dx.doi.org/10.1002/bdr2.1802},
	DOI = {10.1002/bdr2.1802},
	number = {19},
	journal = {Birth Defects Research},
	publisher = {Wiley},
	author = {Garland, Michael A. and Sun, Bo and Zhang, Shuwen and Reynolds
	          , Kurt and Ji, Yu and Zhou, Chengji J.},
	year = {2020},
	month = sep,
	pages = {1635–1659},
}

@article{WeinUmba05,
	title = {A Hybrid Design for Studying Genetic Influences on Risk of
	         Diseases with Onset Early in Life},
	volume = {77},
	ISSN = {0002-9297},
	url = {http://dx.doi.org/10.1086/496900},
	DOI = {10.1086/496900},
	number = {4},
	journal = {The American Journal of Human Genetics},
	publisher = {Elsevier BV},
	author = {Weinberg, C.R. and Umbach, D.M.},
	year = {2005},
	month = oct,
	pages = {627–636},
}

@article{CardPalm03,
	title = {Population stratification and spurious allelic association},
	journal = {The Lancet},
	volume = {361},
	number = {9357},
	pages = {598-604},
	year = {2003},
	issn = {0140-6736},
	doi = {https://doi.org/10.1016/S0140-6736(03)12520-2},
	url = {
	       https://www.sciencedirect.com/science/article/pii/S0140673603125202
	       },
	author = {Lon R. Cardon and Lyle J. Palmer},
	abstract = {Summary Great efforts and expense have been expended in
	            attempts to detect genetic polymorphisms contributing to
	            susceptibility to complex human disease. Concomitantly,
	            technology for detection and scoring of single nucleotide
	            polymorphisms (SNPs) has undergone rapid development,
	            extensive catalogues of SNPs across the genome have been
	            constructed, and SNPs have been increasingly used as a means
	            for investigation of the genetic causes of complex human
	            diseases. For many diseases, population-based studies of
	            unrelated individuals—in which case-control and cohort
	            studies serve as standard designs for genetic association
	            analysis—can be the most practical and powerful approach.
	            However, extensive debate has arisen about optimum study
	            design, and considerable concern has been expressed that
	            these approaches are prone to population stratification,
	            which can lead to biased or spurious results. Over the past
	            decade, a great shift has been noted, away from case-control
	            and cohort studies, towards family-based association designs.
	            These designs have fewer problems with population
	            stratification but have greater genotyping and sampling
	            requirements, and data can be difficult or impossible to
	            gather. We discuss past evidence for population
	            stratification on genotype-phenotype association studies,
	            review methods to detect and account for it, and present
	            suggestions for future study design and analysis.},
}

@article{Bour+11,
	author = {Bourgey, Mathieu and Healy, Jasmine and Saint-Onge, Pascal and
	          Massé , Hugues and Sinnett, Daniel and Roy-Gagnon, Marie-Hélène
	          },
	title = {Genome-wide detection and characterization of mating asymmetry
	         in human populations},
	journal = {Genetic Epidemiology},
	volume = {35},
	number = {6},
	pages = {526-535},
	keywords = {mating asymmetry, confounding, maternal effects, HapMap,
	            simulation study},
	doi = {https://doi.org/10.1002/gepi.20602},
	url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/gepi.20602},
	eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/gepi.20602},
	abstract = {Abstract The study of the genetic component of early-onset
	            diseases requires investigation into parental genetic effects
	            , particularly those mediated by the mother who can influence
	            the offspring's risk of disease through the effects of her
	            genes acting directly on the intrauterine milieu or
	            indirectly through maternal-gene child-gene interaction
	            effects. An important source of bias that can arise in
	            feto-maternal association testing is the possibility of
	            confounding due to mating asymmetry (MA). However, there is
	            little information on the levels of MA present in human
	            populations and the impact on maternal association testing.
	            In this study, we developed a novel approach to measuring MA
	            and, using HapMap mate-pairs of European and African descent,
	            carried out a genome-wide investigation and characterization
	            of MA. We further investigated the impact of observed levels
	            of MA on maternal association tests through simulation
	            experiments. For the first time, we showed that
	            non-negligible levels of MA are detected in human populations
	            , such that subtle genotype frequency differences between
	            individuals mating in the population are sufficient to induce
	            spurious maternal genotype associations. Though the
	            underlying mechanisms driving the asymmetry within these
	            populations remain elusive, our findings provide
	            consequential evidence for the occurrence of MA in humans and
	            highlight the importance of controlling for MA in maternal
	            association testing. Genet. Epidemiol. 2011. © 2011
	            Wiley-Liss, Inc. 35: 526-535, 2011},
	year = {2011},
}

@article{Lee+05,
	author = {Lee, P.J. and Ridout, D. and Walter, J.H. and Cockburn, F.},
	title = {Maternal phenylketonuria: report from the United Kingdom
	         Registry 1978{\textendash}97},
	volume = {90},
	number = {2},
	pages = {143--146},
	year = {2005},
	doi = {10.1136/adc.2003.037762},
	publisher = {BMJ Publishing Group Ltd},
	abstract = {Background: The effects of maternal phenylalanine on the
	            fetus include facial dysmorphism, microcephaly, intrauterine
	            growth retardation, developmental delay, and congenital heart
	            disease.Aims: To evaluate the impact of phenylalanine
	            restricted diet in pregnant women with phenylketonuria (PKU)
	            on their offspring.Methods: Data on virtually all pregnancies
	            of women with PKU in the United Kingdom between 1978 and 1997
	            were reported to the United Kingdom PKU Registry. The effect
	            of the use and timing in relation to pregnancy of a
	            phenylalanine restricted diet on birth weight, birth head
	            circumference, the presence or absence of congenital heart
	            disease (CHD), 4 year developmental quotient, and 8 year
	            intelligence quotient were examined.Results: A total of 228
	            pregnancies resulted in live births (seven twin pregnancies
	            were excluded). In 110 (50\%), diet started before
	            conception. For this group mean (SD) birth weight was 3160
	            (612) g, birth head circumference 33.6 (1.9) cm, 4 year DQ
	            108.9 (13.2), 8 year IQ 103.4 (15.6), and incidence of CHD
	            was 2.4\%. In comparison, for those born where treatment was
	            started during pregnancy (n = 91), birth weight was 2818
	            (711) g, birth head circumference 32.7 (2.0) cm, 4 year DQ
	            96.8 (15.0), 8 year IQ 86.5 (13.0), and incidence of CHD was
	            17\%. Month-by-month regression analyses suggested that
	            metabolic control by 12{\textendash}16 weeks gestation had
	            most influence on outcome.Conclusions: Many features of the
	            maternal PKU syndrome are preventable by starting a
	            phenylalanine restricted diet. Women with PKU and their
	            carers must be aware of the risks and should start the diet
	            before conception, or as soon after as possible.},
	issn = {0003-9888},
	URL = {https://adc.bmj.com/content/90/2/143},
	eprint = {https://adc.bmj.com/content/90/2/143.full.pdf},
	journal = {Archives of Disease in Childhood},
}

@article{Wilc+98,
	author = {Wilcox, Allen J. and Weinberg, Clarice R. and Lie, Rolv Terje},
	title = {Distinguishing the Effects of Maternal and Offspring Genes
	         through Studies of “Case-Parent Triads”},
	journal = {American Journal of Epidemiology},
	volume = {148},
	number = {9},
	pages = {893-901},
	year = {1998},
	month = {11},
	abstract = {A gene variant that increases disease risk will be
	            overrepresented among diseased persons, even compared with
	            their own biologic parents. This insight has led to tests
	            based solely on the asymmetric distribution of a variant
	            allele among cases and their parents (e.g., the
	            transmission/disequilibrium test). Existing methods focus on
	            effects of alleles that operate through the offspring
	            genotype. Alleles can also operate through the mother's
	            genotype, particularly for conditions such as birth defects
	            that have their origins in fetal life. An allele working
	            through the mother would have higher frequency in
	            case-mothers than in case-fathers. The authors develop a
	            log-linear method for estimating relative risks for alleles
	            in the context of case-parent triads. This method is able to
	            detect the effects of genes working through the offspring,
	            the mother, or both. The authors assume Mendelian inheritance
	            , but Hardy-Weinberg equilibrium is unnecessary. Their
	            approach uses standard software, and simulations demonstrate
	            satisfactory power and confidence interval coverage. This
	            method is valid with a self-selected or hospital-based series
	            of cases and helps to protect against misleading inference
	            that can result when cases and controls are randomly sampled
	            from a population not in Hardy-Weinberg equilibrium. Am J
	            Epidemiol 1998; 148:893–901.},
	issn = {0002-9262},
	doi = {10.1093/oxfordjournals.aje.a009715},
	url = {https://doi.org/10.1093/oxfordjournals.aje.a009715},
	eprint = {
	          https://academic.oup.com/aje/article-pdf/148/9/893/291154/148-9-893.pdf
	          },
}
@article{Shin+10,
	author = {Shin, Ji-Hyung and McNeney, Brad and Graham, Jinko},
	title = {On the Use of Allelic Transmission Rates for Assessing
	         Gene-by-Environment Interaction in Case-Parent Trios},
	journal = {Annals of Human Genetics},
	volume = {74},
	number = {5},
	pages = {439-451},
	keywords = {Case-parent trios, gene-environment interaction, genetic
	            association, genotype relative risks, population
	            stratification, transmission probability},
	doi = {https://doi.org/10.1111/j.1469-1809.2010.00599.x},
	url = {
	       https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1469-1809.2010.00599.x
	       },
	eprint = {
	          https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1469-1809.2010.00599.x
	          },
	abstract = {Summary Allelic transmission rates from parents to cases are
	            frequently stratified by an environmental risk factor E and
	            compared, with heterogeneity interpreted as gene-environment
	            interaction or G×E. Though generally invalid, such analyses
	            continue to appear. We revisit why heterogeneity is not
	            equivalent to G×E in a range of settings not considered
	            previously. The objective is a fuller understanding of the
	            bias in transmission rates and what is driving it. Extending
	            previously published findings, we derive parental mating-type
	            probabilities in cases and use them to obtain transmission
	            rates, which we then compare to G×E. Through simulation, we
	            investigate the practical implications of the bias for a
	            transmission-based test of G×E. We find that general
	            population characteristics distort the picture of G×E
	            obtained from transmission rates: the stratum-specific
	            mating-type probabilities under G − E dependence and the
	            allele frequency under independence. Furthermore, the
	            transmission-based test has inflated error rates relative to
	            a likelihood-based test. Our investigation provides further
	            insight into how and why transmission-based tests and
	            descriptive summaries can mislead about G×E. For exploring
	            G×E, we suggest graphical displays of the transmission rates
	            within parental mating types, as they are robust to
	            population stratification and the penetrance model.},
	year = {2010},
}



@software{Sage21,
	title = {{Statistical Analysis for Genetic Epidemiology}},
	year = 2021,
	author = {{S.A.G.E.}},
	url = {http://darwin.cwru.edu},
	note = {Release 6.4.2: \href{http://darwin.cwru.edu}{
	        http://darwin.cwru.edu}},
}

@article{UmbaWein00,
	title = {The Use of Case-Parent Triads to Study Joint Effects of
	         Genotype and Exposure},
	volume = {66},
	ISSN = {0002-9297},
	url = {http://dx.doi.org/10.1086/302707},
	DOI = {10.1086/302707},
	number = {1},
	journal = {The American Journal of Human Genetics},
	publisher = {Elsevier BV},
	author = {Umbach, David M. and Weinberg, Clarice R.},
	year = {2000},
	month = jan,
	pages = {251–261},
}
@phdthesis{Huds19,
	title = {Maternal gene-environment effects: An evaluation of statistical
	         approaches to detect effects and an investigation of the effect
	         of violations of model assumptions},
	author = "Julie Hudson",
	year = 2019,
	month = sep,
	address = {Ottawa, ON},
	note = {Available at \url{http://dx.doi.org/10.20381/ruor-23880}},
	school = {University of Ottawa},
	type = {{MSc.} thesis},
}

@article{Demp+77,
	author = {Arthur P. Dempster and Nathan M. Laird and Donald B. Rubin},
	title = {Maximum Likelihood from Incomplete Data Via the EM Algorithm},
	journal = {Journal of the Royal Statistical Society: Series B
	           (Methodological) },
	volume = {39},
	number = {1},
	pages = {1-22},
	year = {1977},
	month = sep,
	abstract = {A broadly applicable algorithm for computing maximum
	            likelihood estimates from incomplete data is presented at
	            various levels of generality. Theory showing the monotone
	            behaviour of the likelihood and convergence of the algorithm
	            is derived. Many examples are sketched, including missing
	            value situations, applications to grouped, censored or
	            truncated data, finite mixture models, variance component
	            estimation, hyperparameter estimation, iteratively reweighted
	            least squares and factor analysis.},
	issn = {0035-9246},
	doi = {10.1111/j.2517-6161.1977.tb01600.x},
	url = {https://doi.org/10.1111/j.2517-6161.1977.tb01600.x},
	eprint = {
	          https://academic.oup.com/jrsssb/article-pdf/39/1/1/49117094/jrsssb
	          \_ 39\_1\_1.pdf},
}

@article{Loui82,
	ISSN = {00359246},
	URL = {http://www.jstor.org/stable/2345828},
	abstract = {A procedure is derived for extracting the observed
	            information matrix when the EM algorithm is used to find
	            maximum likelihood estimates in incomplete data problems. The
	            technique requires computation of a complete-data gradient
	            vector or second derivative matrix, but not those associated
	            with the incomplete data likelihood. In addition, a method
	            useful in speeding up the convergence of the EM algorithm is
	            developed. Two examples are presented.},
	author = {Thomas A. Louis},
	journal = {Journal of the Royal Statistical Society. Series B
	           (Methodological) },
	number = {2},
	pages = {226--233},
	publisher = {[Royal Statistical Society, Oxford University Press]},
	title = {Finding the Observed Information Matrix when Using the EM
	         Algorithm},
	urldate = {2025-05-16},
	volume = {44},
	year = {1982},
}

@article{Wein+98,
	title = "A log-linear approach to case-parent-triad data: assessing
	         effects of disease genes that act either directly or through
	         maternal effects and that may be subject to parental imprinting",
	author = "Clarice R. Weinberg and Allen J. Wilcox and Rolv T. Lie",
	abstract = "We describe a log-linear method for analysis of
	            case-parent-triad data, based on maximum likelihood with
	            stratification on parental mating type. The method leads to
	            estimates of association parameters, such as relative risks,
	            for a single allele, and also to likelihood ratio chi2 tests
	            (LRTs) of linkage disequilibrium. Hardy-Weinberg equilibrium
	            need not be assumed. Our simulations suggest that the LRT has
	            power similar to that of the chi2 ``score'' test proposed by
	            Schaid and Sommer and that both can outperform the
	            transmission/disequilibrium test (TDT), although the TDT can
	            perform better under an additive model of inheritance.
	            Because a restricted version of the LRT is asymptotically
	            equivalent to the TDT, the proposed test can be regarded as a
	            generalization of the TDT. The method that we describe
	            generalizes easily to accommodate maternal effects on risk
	            and, in fact, produces powerful and orthogonal tests of the
	            contribution of fetal versus maternal genetic factors. We
	            further generalize the model to allow for effects of parental
	            imprinting. Imprinting effects can be fitted by a simple,
	            iterative procedure that relies on the
	            expectation-maximization algorithm and that uses standard
	            statistical software for the maximization steps. Simulations
	            reveal that LRT tests for detection of imprinting have very
	            good operating characteristics. When a single allele is under
	            study, the proposed method can yield powerful tests for
	            detection of linkage disequilibrium and is applicable to a
	            broader array of causal scenarios than is the TDT.",
	journal = "American Journal of Human Genetics",
	publisher = "Elsevier BV",
	volume = 62,
	number = 4,
	pages = "969--978",
	month = apr,
	year = 1998,
	copyright = "https://www.elsevier.com/open-access/userlicense/1.0/",
	language = "en",
}

@book{Stra99,
	publisher = {BIOS Scientific},
	isbn = {1859962025},
	year = {1999},
	title = {Human molecular genetics 2},
	edition = {2nd ed.},
	language = {eng},
	author = {Tom Strachan and Andrew P. Read},
	keywords = {Human molecular genetics},
}

@article{Port14,
	title = "The birth and development of the {DNA} theory of inheritance:
	         sixty years since the discovery of the structure of {DNA}",
	author = "Portin, Petter",
	abstract = "The development of the DNA theory of inheritance culminated
	            in the publication of the molecular structure of DNA 60 years
	            ago. This paper describes this development, beginning with
	            the discovery of DNA as a chemical substance by Friedrich
	            Miescher in 1869, followed by its basic chemical analysis and
	            demonstration of its participation in the structure of
	            chromosomes. Subsequently it was discovered by Oswald Avery
	            in 1944 that DNA was the genetic material, and then Erwin
	            Chargaff showed that the proportions of the bases included in
	            the structure of DNA followed a certain law. These findings,
	            in association with the biophysical studies of Maurice
	            Wilkins and Rosalind Franklin with Raymond Gosling, led James
	            Watson and Francis Crick to the discovery of the
	            double-helical structure of DNA in 1953. The paper ends with
	            a short description of the development of the DNA theory of
	            inheritance after the discovery of the double helix.",
	journal = "J. Genet.",
	publisher = "Springer Science and Business Media LLC",
	volume = 93,
	number = 1,
	pages = "293--302",
	month = apr,
	year = 2014,
	language = "en",
}
