Likelihood ratio tests for maternal and fetal genetic effects on obstetric complications

It is well recognized that both maternal and fetal genes could contribute to susceptibility for obstetric complications. Logistic regression models are usually adopted to model the separate or joint action of maternal and fetal loci with case‐control data. The standard likelihood ratio tests (LRTs) can be used to test the significance of appropriate odds ratio parameters. This method, although simple to implement, fails to exploit a unique feature of genetic epidemiology studies of obstetric complications. Specifically, it does not take into consideration the correlation between the maternal and offspring genomes. We propose novel LRT that take advantage of this information by incorporating the fact that half of a child's genome is inherited from the mother. Our methods have substantially improved power for detecting marginal, main, and interactive maternal and fetal genotype effects, as evidenced by results from extensive simulation studies. We demonstrate our new methods by applying them to the analysis of data from a pilot study of preeclampsia. Genet. Epidemiol. 33:526–538, 2009. © 2009 Wiley‐Liss, Inc.     

A likelihood ratio test of population Hardy‐Weinberg equilibrium for case‐control studies

Testing Hardy‐Weinberg equilibrium (HWE) in the control group is commonly used to detect genotyping errors in genetic association studies. We propose a likelihood ratio test for testing HWE in the study population using both case and control samples. This test incorporates underlying association models. Another feature is that, when we infer the disease‐genotype association, we explicitly incorporate HWE or a possible departure from Hardy‐Weinberg equilibrium (DHWE) into the model. Our unified framework enables us to infer the disease‐genotype association when a detected DHWE needs to be part of the model after causes for the DHWE are explored. Real data sets are used to illustrate the application of the methodology and its implication in genetic association studies. Our analysis and interpretation touch on issues such as genotyping errors, population selection, population stratification, or the study sampling plan, that all could be the cause of DHWE. Genet. Epidemiol. 2009. Published 2008 Wiley‐Liss, Inc.     

Shrinkage estimation for robust and efficient screening of single‐SNP association from case‐control genome‐wide association studies

Population‐based case‐control design has become one of the most popular approaches for conducting genome‐wide association scans for rare diseases like cancer. In this article, we propose a novel method for improving the power of the widely used single‐single‐nucleotide polymorphism (SNP) two‐degrees‐of‐freedom (2 d.f.) association test for case‐control studies by exploiting the common assumption of Hardy‐Weinberg Equilibrium (HWE) for the underlying population. A key feature of the method is that it can relax the assumed model constraints via a completely data‐adaptive shrinkage estimation approach so that the number of false‐positive results due to the departure of HWE is controlled. The method is computationally simple and is easily scalable to association tests involving hundreds of thousands or millions of genetic markers. Simulation studies as well as an application involving data from a real genome‐wide association study illustrate that the proposed method is very robust for large‐scale association studies and can improve the power for detecting susceptibility SNPs with recessive effects, when compared to existing methods. Implications of the general estimation strategy beyond the simple 2 d.f. association test are discussed. Genet. Epidemiol. 33:740–750, 2009. Published 2009 Wiley‐Liss, Inc.     

Adapting the logical basis of tests for Hardy‐Weinberg Equilibrium to the real needs of association studies in human and medical genetics

The standard procedure to assess genetic equilibrium is a χ² test of goodness‐of‐fit. As is the case with any statistical procedure of that type, the null hypothesis is that the distribution underlying the data is in agreement with the model. Thus, a significant result indicates incompatibility of the observed data with the model, which is clearly at variance with the aim in the majority of applications: to exclude the existence of gross violations of the equilibrium condition. In current practice, we try to avoid this basic logical difficulty by increasing the significance bound to the P‐value (e.g. from 5 to 10%) and inferring compatibility of the data with Hardy Weinberg Equilibrium (HWE) from an insignificant result. Unfortunately, such direct inversion of a statistical testing procedure fails to produce a valid test of the hypothesis of interest, namely, that the data are in sufficiently good agreement with the model under which the P‐value is calculated. We present a logically unflawed solution to the problem of establishing (approximate) compatibility of an observed genotype distribution with HWE. The test is available in one‐ and two‐sided versions. For both versions, we provide tools for exact power calculation. We demonstrate the merits of the new approach through comparison with the traditional χ² goodness‐of‐fit test in 2×60 genotype distributions from 43 published genetic studies of complex diseases where departure from HWE was noted in either the case or control sample. In addition, we show that the new test is useful for the analysis of genome‐wide association studies. Genet. Epidemiol. 33:569–580, 2009. © 2009 Wiley‐Liss, Inc.     

Genotype‐based matching to correct for population stratification in large‐scale case‐control genetic association studies

Genome‐wide association studies are helping to dissect the etiology of complex diseases. Although case‐control association tests are generally more powerful than family‐based association tests, population stratification can lead to spurious disease‐marker association or mask a true association. Several methods have been proposed to match cases and controls prior to genotyping, using family information or epidemiological data, or using genotype data for a modest number of genetic markers. Here, we describe a genetic similarity score matching (GSM) method for efficient matched analysis of cases and controls in a genome‐wide or large‐scale candidate gene association study. GSM comprises three steps: (1) calculating similarity scores for pairs of individuals using the genotype data; (2) matching sets of cases and controls based on the similarity scores so that matched cases and controls have similar genetic background; and (3) using conditional logistic regression to perform association tests. Through computer simulation we show that GSM correctly controls false‐positive rates and improves power to detect true disease predisposing variants. We compare GSM to genomic control using computer simulations, and find improved power using GSM. We suggest that initial matching of cases and controls prior to genotyping combined with careful re‐matching after genotyping is a method of choice for genome‐wide association studies. Genet. Epidemiol. 33:508–517, 2009. © 2009 Wiley‐Liss, Inc.     

Oral facial clefts and gene polymorphisms in metabolism of folate/one‐carbon and vitamin A: a pathway‐wide association study

An increased risk of facial clefts has been observed among mothers with lower intake of folic acid or vitamin A around conception. We hypothesized that the risk of clefts may be further moderated by genes involved in metabolizing folate or vitamin A. We included 425 case‐parent triads in which the child had either cleft lip with or without cleft palate (CL/P) or cleft palate only (CPO), and no other major defects. We analyzed 108 SNPs and one insertion in 29 genes involved in folate/one‐carbon metabolism and 68 SNPs from 16 genes involved in vitamin A metabolism. Using the Triad Multi‐Marker (TRIMM) approach we performed SNP, gene, chromosomal region, and pathway‐wide association tests of child or maternal genetic effects for both CL/P and CPO. We stratified these analyses on maternal intake of folic acid or vitamin A during the periconceptional period. As expected with this high number of statistical tests, there were many associations with P‐values<0.05; although there were fewer than predicted by chance alone. The strongest association in our data (between fetal FOLH1 and CPO, P=0.0008) is not in agreement with epidemiologic evidence that folic acid reduces the risk of CL/P in these data, not CPO. Despite strong evidence for genetic causes of oral facial clefts and the protective effects of maternal vitamins, we found no convincing indication that polymorphisms in these vitamin metabolism genes play an etiologic role. Genet. Epidemiol. 2009. © 2008 Wiley Liss, Inc.     

A Multi‐Locus Likelihood Method for Assessing Parent‐of‐Origin Effects Using Case‐Control Mother‐Child Pairs

Parent‐of‐origin effects have been pointed out to be one plausible source of the heritability that was unexplained by genome‐wide association studies. Here, we consider a case‐control mother‐child pair design for studying parent‐of‐origin effects of offspring genes on neonatal/early‐life disorders or pregnancy‐related conditions. In contrast to the standard case‐control design, the case‐control mother‐child pair design contains valuable parental information and therefore permits powerful assessment of parent‐of‐origin effects. Suppose the region under study is in Hardy‐Weinberg equilibrium, inheritance is Mendelian at the diallelic locus under study, there is random mating in the source population, and the SNP under study is not related to risk for the phenotype under study because of linkage disequilibrium (LD) with other SNPs. Using a maximum likelihood method that simultaneously assesses likely parental sources and estimates effect sizes of the two offspring genotypes, we investigate the extent of power increase for testing parent‐of‐origin effects through the incorporation of genotype data for adjacent markers that are in LD with the test locus. Our method does not need to assume the outcome is rare because it exploits supplementary information on phenotype prevalence. Analysis with simulated SNP data indicates that incorporating genotype data for adjacent markers greatly help recover the parent‐of‐origin information. This recovery can sometimes substantially improve statistical power for detecting parent‐of‐origin effects. We demonstrate our method by examining parent‐of‐origin effects of the gene PPARGC1A on low birth weight using data from 636 mother‐child pairs in the Jerusalem Perinatal Study.     

A Shrinkage Method for Testing the Hardy–Weinberg Equilibrium in Case‐Control Studies

Testing for the Hardy–Weinberg equilibrium (HWE) is often used as an initial step for checking the quality of genotyping. When testing the HWE for case‐control data, the impact of a potential genetic association between the marker and the disease must be controlled for otherwise the results may be biased. Li and Li [2008] proposed a likelihood ratio test (LRT) that accounts for this potential genetic association and it is more powerful than the commonly used control‐only χ² test. However, the LRT is not efficient when the marker is independent of the disease, and also requires numerical optimization to calculate the test statistic. In this article, we propose a novel shrinkage test for assessing the HWE. The proposed shrinkage test yields higher statistical power than the LRT when the marker is independent of or weakly associated with the disease, and converges to the LRT when the marker is strongly associated with the disease. In addition, the proposed shrinkage test has a closed form and can be easily used to test the HWE for large datasets that result from genome‐wide association studies. We compare the performance of the shrinkage test with existing methods using simulation studies, and apply the shrinkage test to a genome‐wide association dataset for Alzheimer's disease.     

Methods for detecting interactions between genetic polymorphisms and prenatal environment exposure with a mother‐child design

Prenatal exposures such as polycyclic aromatic hydrocarbons and early postnatal environmental exposures are of particular concern because of the heightened susceptibility of the fetus and infant to diverse environmental pollutants. Marked inter‐individual variation in response to the same level of exposure was observed in both mothers and their newborns, indicating that susceptibility might be due to genetic factors. With the mother‐child pair design, existing methods developed for parent‐child trio data or random sample data are either not applicable or not designed to optimally use the information. To take full advantage of this unique design, which provides partial information on genetic transmission and has both maternal and newborn outcome status collected, we developed a likelihood‐based method that uses both the maternal and the newborn information together and jointly models gene‐environment interactions on maternal and newborn outcomes. Through intensive simulation studies, the proposed method has demonstrated much improved power in detecting gene‐environment interactions. The application on a real mother‐child pair data from a study conducted in Krakow, Poland, suggested four significant gene‐environment interactions after multiple comparisons adjustment. Genet. Epidemiol. 34: 125–132, 2010. © 2009 Wiley‐Liss, Inc.     

The Reduced Folate Carrier (RFC-1) 80A>G Polymorphism and Maternal Risk of Having a Child with Down Syndrome: A Meta-Analysis

A common polymorphism (c.80A>G) in the gene coding for the reduced folate carrier (SLC19A1, commonly known as RFC-1) has been associated with maternal risk of the birth of a child with Down Syndrome (DS), but results are controversial. We searched major online databases to identify available case-control studies, and performed a meta-analysis to summarize the data concerning this association. Nine independent case-control studies were identified for a total of 930 DS mothers (MDS) and 1240 control mothers. Odds ratios (OR) and 95% confidence intervals (CI) were calculated using both fixed and random effects models. An increase in the risk of having a birth with DS was observed for carriers of the homozygous GG genotype (OR 1.27, 95% CI 1.04–1.57; p = 0.02, fixed effects model), even after removal from the meta-analysis of published data with deviations from Hardy-Weinberg equilibrium (HWE) in controls (OR 1.26, 95% CI 1.02–1.55; p = 0.03, fixed effects model). Moreover, the pooled OR under the fixed effects model showed an increase in the maternal risk for the G allele (OR 1.14, 95% CI 1.01–1.30; p = 0.03). Present results suggest that the maternal RFC-1 80A>G polymorphism might be associated with an increased risk of having a birth with DS, particularly among carriers of the GG genotype.     

Approximate and exact tests of Hardy-Weinberg equilibrium using uncertain genotypes

Testing for Hardy-Weinberg equilibrium (HWE) is commonly used as a quality control filter in genome-wide scans for markers with experimentally determined genotypes. In contrast, for markers with imputed genotypes, there are post-imputation metrics of quality that can be used as screens but there are no formal tests of deviation from HWE. Similarly, there are no formal tests of deviation from HWE for probabilistic genotypes that are generated by sequencing projects. Here, I describe generalizations of the approximate χ(2) and exact tests of HWE for use with uncertain genotypes. The tests fully account for the probabilities of all possible genotypes at a marker for each individual. By computer simulation, the approximate and exact tests are shown to maintain valid control of the type I error rate. Calculations of the loss of power as the uncertainty in genotypes increases are illustrated. The tests are compatible with chip-based genotypes for single-nucleotide polymorphisms and copy number polymorphisms, imputed genotypes, and probabilistic assignments of genotype from variable-coverage sequence data.     

Single‐marker and two‐marker association tests for unphased case‐control genotype data,with a power comparison

In case‐control single nucleotide polymorphism (SNP) data, the allele frequency, Hardy Weinberg Disequilibrium, and linkage disequilibrium (LD) contrast tests are three distinct sources of information about genetic association. While all three tests are typically developed in a retrospective context, we show that prospective logistic regression models may be developed that correspond conceptually to the retrospective tests. This approach provides a flexible framework for conducting a systematic series of association analyses using unphased genotype data and any number of covariates. For a single stage study, two single‐marker tests and four two‐marker tests are discussed. The true association models are derived and they allow us to understand why a model with only a linear term will generally fit well for a SNP in weak LD with a causal SNP, whatever the disease model, but not for a SNP in high LD with a non‐additive disease SNP. We investigate the power of the association tests using real LD parameters from chromosome 11 in the HapMap CEU population data. Among the single‐marker tests, the allelic test has on average the most power in the case of an additive disease, but for dominant, recessive, and heterozygote disadvantage diseases, the genotypic test has the most power. Among the four two‐marker tests, the Allelic‐LD contrast test, which incorporates linear terms for two markers and their interaction term, provides the most reliable power overall for the cases studied. Therefore, our result supports incorporating an interaction term as well as linear terms in multi‐marker tests. Genet. Epidemiol. 34:67–77, 2010. © 2009 Wiley‐Liss, Inc.     

Multisample adjusted U‐statistics that account for confounding covariates

Multisample U‐statistics encompass a wide class of test statistics that allow the comparison of 2 or more distributions. U‐statistics are especially powerful because they can be applied to both numeric and nonnumeric data, eg, ordinal and categorical data where a pairwise similarity or distance‐like measure between categories is available. However, when comparing the distribution of a variable across 2 or more groups, observed differences may be due to confounding covariates. For example, in a case‐control study, the distribution of exposure in cases may differ from that in controls entirely because of variables that are related to both exposure and case status and are distributed differently among case and control participants. We propose to use individually reweighted data (ie, using the stratification score for retrospective data or the propensity score for prospective data) to construct adjusted U‐statistics that can test the equality of distributions across 2 (or more) groups in the presence of confounding covariates. Asymptotic normality of our adjusted U‐statistics is established and a closed form expression of their asymptotic variance is presented. The utility of our approach is demonstrated through simulation studies, as well as in an analysis of data from a case‐control study conducted among African‐Americans, comparing whether the similarity in haplotypes (ie, sets of adjacent genetic loci inherited from the same parent) occurring in a case and a control participant differs from the similarity in haplotypes occurring in 2 control participants.     

The health of children in sole‐parent families in New Zealand: results of a population‐based cross‐sectional survey

Objective: To investigate whether children in sole‐parent families in New Zealand bear excess risks of poor mental and physical health relative to children in two parent families. Data sources and statistical methods: The data source was the 2006/07 New Zealand Health Survey, a nationally representative household survey that sampled 502 children (5‐14 years) of sole mothers and 1,281 children of partnered mothers. Results: Children of sole mothers were 1.26 (0.94 – 2.69) times as likely as children of partnered mothers to return a low PhS score. Adjusting for maternal health and family socio‐economic disadvantage eliminated this weak association (which in any case was of borderline statistical significance). Children of sole mothers were more than twice as likely as children of partnered mothers to return a low PsS score, adjusting for demographic variables only. Conclusions: There is only a weak negative association (if any) between sole‐parenting and child physical health, but a stronger association with child mental health – consistent with most of the New Zealand and international literature. The association with child mental health is largely (but possibly not completely) ‘explained’ by the poorer mental health of sole‐parents and the poorer socio‐economic circumstances of single‐parent families (on average). Implications: These findings support policies aiming to improve access of sole‐parents and their children to community mental health services, and (more especially) policies aiming to ameliorate the disadvantaged economic circumstances of single parent families.     

Maternal control of child‐feeding during breast and formula feeding in the first 6 months post‐partum

Background: Mothers who breastfeed use lower levels of control over later child diet. The baby‐led nature of breastfeeding may encourage this low control to develop. Alternatively maternal desire for control may drive breastfeeding duration. The present study explored whether differences in maternal control are present during milk feeding and whether these stem from or drive breastfeeding duration. Methods: Five hundred and two mothers with an infant aged 6–12 months completed a modified retrospective version of the child‐feeding questionnaire adapted to reflect milk feeding during the first 6 months post‐partum. Participants were recruited from mother and baby groups and online parenting forums. Mothers recalled their use of encouraging intake and scheduling feeds in relation to their infant’s intake of milk. Attitudes towards breastfeeding were also measured, including views that breastfeeding is inconvenient, difficult and that formula‐fed infants were more content. Results: Compared to mothers who formula‐fed or ceased breastfeeding within 1 week, mothers who breastfed for at least 6 months recalled a lower use of scheduling and encouraging milk feeds. Mothers who initiated breastfeeding but ceased within 1 week reported lower control compared to exclusive formula feeders. A high level of scheduling feeds was associated with considering that breastfeeding was inconvenient and a greater perceived infant size, whereas encouraging feeds was associated with considering that breastfeeding was difficult, low maternal confidence and a smaller perceived infant size. Conclusions: Maternal desire for control may drive breastfeeding duration. A controlling maternal feeding style may therefore be dispositional and present much earlier than current studies suggest.     

Trends in Rural and Urban Deliveries and Vaginal Births: California 1998‐2002

ABSTRACT: Context: Pregnant women in rural areas may give birth in either rural or urban hospitals. Differences in outcomes between rural and urban hospitals may influence patient decision making. Purpose: Trends in rural and urban obstetric deliveries and neonatal and maternal mortality in California were compared to inform policy development and patient and provider decision making in rural health care settings. Methods: Deliveries in California hospitals identified by the California Department of Health Services, Birth Statistical Master Files for years 1998 through 2002 were analyzed. Three groups of interest were created: rural hospital births to all mothers, urban hospital births to rural mothers, and urban hospital births to urban mothers. Findings: Of 2,620,096 births analyzed, less than 4% were at rural hospitals. Neonatal death rates were significantly higher in babies born to rural mothers with no pregnancy complications who delivered a normal weight baby vaginally at an urban hospital compared to urban mothers delivering at an urban hospital (0.2 [CI 0.2‐0.4] deaths per 1,000 births versus 0.1 [CI 0.1‐0.1]). Logistic regression analysis showed that delivery in a rural hospital was a protective factor compared to urban mothers delivering in an urban hospital, with an odds ratio of 0.8 (CI 0.6‐0.9). Maternal death rates were not different. Conclusions: Rural obstetric services in this period showed favorable neonatal and maternal safety profiles. This information should reassure patients considering a rural hospital delivery, and aid policy makers and health care providers striving to ensure access to obstetric services for rural populations.     

What SNP genotyping errors are most costly for genetic association studies?

Which genotype misclassification errors are most costly, in terms of increased sample size necessary (SSN) to maintain constant asymptotic power and significance level, when performing case/control studies of genetic association? We answer this question for single‐nucleotide polymorphisms (SNPs), using the 2×3 χ² test of independence. Our strategy is to expand the noncentrality parameter of the asymptotic distribution of the χ² test under a specified alternative hypothesis to approximate SSN, using a linear Taylor series in the error parameters. We consider two scenarios: the first assumes Hardy‐Weinberg equilibrium (HWE) for the true genotypes in both cases and controls, and the second assumes HWE only in controls. The Taylor series approximation has a relative error of less than 1% when each error rate is less than 2%. The most costly error is recording the more common homozygote as the less common homozygote, with indefinitely increasing cost coefficient as minor SNP allele frequencies approach 0 in both scenarios. The cost of misclassifying the more common homozygote to the heterozygote also becomes indefinitely large as the minor SNP allele frequency goes to 0 under both scenarios. For the violation of HWE modeled here, the cost of misclassifying a heterozygote to the less common homozygote becomes large, although bounded. Therefore, the use of SNPs with a small minor allele frequency requires careful attention to the frequency of genotyping errors to ensure that power specifications are met. Furthermore, the design of automated genotyping should minimize those errors whose cost coefficients can become indefinitely large. Genet Epidemiol 26:132–141, 2004. © 2004 Wiley‐Liss, Inc.     

Assessing departure from Hardy-Weinberg equilibrium in the presence of disease association

Assessing Hardy-Weinberg equilibrium (HWE) is often employed as an important initial step for genotype data quality checking in genetics studies. Tests for HWE often assume that the genotypes are randomly sampled from the general population. However, in many human genetics studies, subjects are ascertained through their disease status, and affected individuals (and their relatives in family-based studies) are overly represented in the ascertained sample than in the general population. As a result, when a marker is associated with the disease, the type I error rate in the HWE tests can be inflated, leading to false exclusion of associated markers from future analysis. Here we develop a general likelihood framework that allows assessment of departure from HWE while taking into account potential association with the disease. Our method can differentiate HWE departure caused by disease association from departure caused by other reasons, such as genotyping errors. The framework can be used for various data structures, including unrelated cases and controls, nuclear families with one or more offspring, or a mixture of them. The type I error rate of our test is under control for a broad range of scenarios. For case-control data, compared to the traditional HWE test that uses only controls, our test is more powerful to detect HWE departure for common diseases and has comparable power for rare diseases. For case-parents trios, our test is more powerful than the traditional HWE test that uses parents only.     

Valid Monte Carlo Permutation Tests for Genetic Case‐Control Studies With Missing Genotypes

Monte Carlo permutation tests can be formally constructed by choosing a set of permutations of individual indices and a real‐valued test statistic measuring the association between genotypes and affection status. In this paper, we develop a rigorous theoretical framework for verifying the validity of these tests when there are missing genotypes. We begin by specifying a nonparametric probability model for the observed genotype data in a genetic case‐control study with unrelated subjects. Under this model and some minimal assumptions about the test statistic, we establish that the resulting Monte Carlo permutation test is exact level α if (1) the chosen set of permutations of individual indices is a group under composition and (2) the distribution of the observed genotype score matrix under the null hypothesis does not change if the assignment of individuals to rows is shuffled according to an arbitrary permutation in this set. We apply these conditions to show that frequently used Monte Carlo permutation tests based on the set of all permutations of individual indices are guaranteed to be exact level α only for missing data processes satisfying a rather restrictive additional assumption. However, if the missing data process depends on covariates that are all identified and recorded, we also show that Monte Carlo permutation tests based on the set of permutations within strata of individuals with identical covariate values are exact level α. Our theoretical results are verified and supplemented by simulations for a variety of missing data processes and test statistics.     

A novel haplotype‐sharing approach for genome‐wide case‐control association studies implicates the calpastatin gene in Parkinson's disease

The large number of markers considered in a genome‐wide association study (GWAS) has resulted in a simplification of analyses conducted. Most studies are analyzed one marker at a time using simple tests like the trend test. Methods that account for the special features of genetic association studies, yet remain computationally feasible for genome‐wide analysis, are desirable as they may lead to increased power to detect associations. Haplotype sharing attempts to translate between population genetics and genetic epidemiology. Near a recent mutation that increases disease risk, haplotypes of case participants should be more similar to each other than haplotypes of control participants; conversely, the opposite pattern may be found near a recent mutation that lowers disease risk. We give computationally simple association tests based on haplotype sharing that can be easily applied to GWASs while allowing use of fast (but not likelihood‐based) haplotyping algorithms and properly accounting for the uncertainty introduced by using inferred haplotypes. We also give haplotype‐sharing analyses that adjust for population stratification. Applying our methods to a GWAS of Parkinson's disease, we find a genome‐wide significant signal in the CAST gene that is not found by single‐SNP methods. Further, a missing‐data artifact that causes a spurious single‐SNP association on chromosome 9 does not impact our test. Genet. Epidemiol. 33:657–667, 2009. Published 2009 Wiley‐Liss, Inc.