Transmission disequilibrium test (TDT) when only one parent is available: the 1-TDT

Benchmarking statistical methods for analyzing parent-child dyads in genetic association studies

Genetic association studies of child health outcomes often employ family-based study designs. One of the most popular family-based designs is the case-parent trio design that considers the smallest possible nuclear family consisting of two parents and their affected child. This trio design is particularly advantageous for studying relatively rare disorders because it is less prone to type 1 error inflation due to population stratification compared to population-based study designs (e.g., case-control studies). However, obtaining genetic data from both parents is difficult, from a practical perspective, and many large studies predominantly measure genetic variants in mother-child dyads. While some statistical methods for analyzing parent-child dyad data (most commonly involving mother-child pairs) exist, it is not clear if they provide the same advantage as trio methods in protecting against population stratification, or if a specific dyad design (e.g., case-mother dyads vs. case-mother/control-mother dyads) is more advantageous. In this article, we review existing statistical methods for analyzing genome-wide marker data on dyads and perform extensive simulation experiments to benchmark their type I errors and statistical power under different scenarios. We extend our evaluation to existing methods for analyzing a combination of case-parent trios and dyads together. We apply these methods on genotyped and imputed data from multiethnic mother-child pairs only, case-parent trios only or combinations of both dyads and trios from the Gene, Environment Association Studies consortium (GENEVA), where each family was ascertained through a child affected by nonsyndromic cleft lip with or without cleft palate. Results from the GENEVA study corroborate the findings from our simulation experiments. Finally, we provide recommendations for using statistical genetic association methods for dyads.

Innovative approach to identify multigenomic and environmental interactions associated with birth defects in family-based hybrid designs

Genes, including those with transgenerational effects, work in concert with behavioral, environmental, and social factors via complex biological networks to determine human health. Understanding complex relationships between causal factors underlying human health is an essential step towards deciphering biological mechanisms. We propose a new analytical framework to investigate the interactions between maternal and offspring genetic variants or their surrogate single nucleotide polymorphisms (SNPs) and environmental factors using family-based hybrid study design. The proposed approach can analyze diverse genetic and environmental factors and accommodate samples from a variety of family units, including case/control-parental triads, and case/control-parental dyads, while minimizing potential bias introduced by population admixture. Comprehensive simulations demonstrated that our innovative approach outperformed the log-linear approach, the best available method for case-control family data. The proposed approach had greater statistical power and was capable to unbiasedly estimate the maternal and child genetic effects and the effects of environmental factors, while controlling the Type I error rate against population stratification. Using our newly developed approach, we analyzed the associations between maternal and fetal SNPs and obstructive and conotruncal heart defects, with adjustment for demographic and lifestyle factors and dietary supplements. Fourteen and 11 fetal SNPs were associated with obstructive and conotruncal heart defects, respectively. Twenty-seven and 17 maternal SNPs were associated with obstructive and conotruncal heart defects, respectively. In addition, maternal body mass index was a significant risk factor for obstructive defects. The proposed approach is a powerful tool for interrogating the etiological mechanism underlying complex traits.

A comparison of popular TDT-generalizations for family-based association analysis

The transmission disequilibrium test (TDT) is the gold standard for testing the association between a genetic variant and disease in samples consisting of affected individuals and their parents. In practice, more complex pedigree structures, that is siblings with no parents, or three-generational pedigrees with possibly missing genotypes, are common. There are several generalizations of the TDT that are suitable for use with arbitrary pedigree structures. We consider three such frequently used generalizations, family-based association test, pedigree disequilibrium test, and generalized disequilibrium test, that have accompanying software and compare them regarding validity and power in the single variant setting. We use simulations to study the effects of population admixture, populations whose genotypes are not in Hardy-Weinberg equilibrium (HWE), different pedigree structures, and the presence of linkage. Whereas our results show that some TDT generalizations can have a substantially increased Type 1 error, these tests are often used in substantive research without caveats about the validity of their Type 1 error. For the association analysis of rare variants in sequencing studies, region-based extensions of the TDT generalizations, that rely on the postulated robustness of the single variant tests, have been proposed. We discuss the implications of our results for these region-based extensions.

Transmission/disequilibrium tests incorporating unaffected offspring

We propose a new method for family-based tests of association and linkage called transmission/disequilibrium tests incorporating unaffected offspring (TDTU). This new approach, constructed based on transmission/disequilibrium tests for quantitative traits (QTDT), provides a natural extension of the transmission/disequilibrium test (TDT) to utilize transmission information from heterozygous parents to their unaffected offspring as well as the affected offspring from ascertained nuclear families. TDTU can be used in various study designs and can accommodate all types of independent nuclear families with at least one affected offspring. When the study sample contains only case-parent trios, the TDTU is equivalent to TDT. Informative-transmission disequilibrium test (i-TDT) and generalized disequilibrium test(GDT) are another two methods that can use information of both unaffected offspring and affected offspring. In contract to i-TDT and GDT, the test statistic of TDTU is simpler and more explicit, and can be implemented more easily. Through computer simulations, we demonstrate that power of the TDTU is slightly higher compared to i-TDT and GDT. All the three methods are more powerful than method that uses affected offspring only, suggesting that unaffected siblings also provide information about linkage and association.

Detecting rare variants in case-parents association studies

Despite the success of genome-wide association studies (GWASs) in detecting common variants (minor allele frequency ≥0.05) many suggested that rare variants also contribute to the genetic architecture of diseases. Recently, researchers demonstrated that rare variants can show a strong stratification which may not be corrected by using existing methods. In this paper, we focus on a case-parents study and consider methods for testing group-wise association between multiple rare (and common) variants in a gene region and a disease. All tests depend on the numbers of transmitted mutant alleles from parents to their diseased children across variants and hence they are robust to the effect of population stratification. We use extensive simulation studies to compare the performance of four competing tests: the largest single-variant transmission disequilibrium test (TDT), multivariable test, combined TDT, and a likelihood ratio test based on a random-effects model. We find that the likelihood ratio test is most powerful in a wide range of settings and there is no negative impact to its power performance when common variants are also included in the analysis. If deleterious and protective variants are simultaneously analyzed, the likelihood ratio test was generally insensitive to the effect directionality, unless the effects are extremely inconsistent in one direction.

Association analysis of complex diseases using triads, parent-child dyads and singleton monads

Background

Triad families are routinely used to test association between genetic variants and complex diseases. Triad studies are important and popular since they are robust in terms of being less prone to false positives due to population structure. In practice, one may collect not only complete triads, but also incomplete families such as dyads (affected child with one parent) and singleton monads (affected child without parents). Since there is a lack of convenient algorithms and software to analyze the incomplete data, dyads and monads are usually discarded. This may lead to loss of power and insufficient utilization of genetic information in a study.

Results

We develop likelihood-based statistical models and likelihood ratio tests to test for association between complex diseases and genetic markers by using combinations of full triads, parent-child dyads, and affected singleton monads for a unified analysis. A likelihood is calculated directly to facilitate the data analysis without imputation and to avoid computational complexity. This makes it easy to implement the models and to explain the results.

Conclusion

By simulation studies, we show that the proposed models and tests are very robust in terms of accurately controlling type I error evaluations, and are powerful by empirical power evaluations. The methods are applied to test for association between transforming growth factor alpha (TGFA) gene and cleft palate in an Irish study.

Power analysis of C-TDT for small sample size genome-wide association studies by the joint use of case-parent trios and pairs

In family-based genetic association studies, it is possible to encounter missing genotype information for one of the parents. This leads to a study consisting of both case-parent trios and case-parent pairs. One of the approaches to this problem is permutation-based combined transmission disequilibrium test statistic. However, it is still unknown how powerful this test statistic is with small sample sizes. In this paper, a simulation study is carried out to estimate the power and false positive rate of this test across different sample sizes for a family-based genome-wide association study. It is observed that a statistical power of over 80% and a reasonable false positive rate estimate can be achieved even with a combination of 50 trios and 30 pairs when 2% of the SNPs are assumed to be associated. Moreover, even smaller samples provide high power when smaller percentages of SNPs are associated with the disease.

Children's Oncology Group's 2013 blueprint for research: epidemiology

Investigators worldwide have for over 40 years conducted case-control studies aimed at determining the causes of childhood cancer. The central challenge to conducting such research is the rarity of childhood cancer, thus many studies aggregate cases through clinical trials organizations such as COG. Rarity also precludes the use of prospective study designs, which are less prone to recall and selection biases. Despite these challenges a substantial literature on childhood cancer etiology has emerged but few strong environmental risk factors have been identified. Genetic studies are thus now coming to the fore with some success. The ultimate aim of epidemiologic studies is to reduce the population burden of childhood cancer by suggesting preventive measures or possibly by enabling early detection. Pediatr Blood Cancer 2013; 60: 1059-1062. © 2012 Wiley Periodicals, Inc.

Dosage transmission disequilibrium test (dTDT) for linkage and association detection

Both linkage and association studies have been successfully applied to identify disease susceptibility genes with genetic markers such as microsatellites and Single Nucleotide Polymorphisms (SNPs). As one of the traditional family-based studies, the Transmission/Disequilibrium Test (TDT) measures the over-transmission of an allele in a trio from its heterozygous parents to the affected offspring and can be potentially useful to identify genetic determinants for complex disorders. However, there is reduced information when complete trio information is unavailable. In this study, we developed a novel approach to "infer" the transmission of SNPs by combining both the linkage and association data, which uses microsatellite markers from families informative for linkage together with SNP markers from the offspring who are genotyped for both linkage and a Genome-Wide Association Study (GWAS). We generalized the traditional TDT to process these inferred dosage probabilities, which we name as the dosage-TDT (dTDT). For evaluation purpose, we developed a simulation procedure to assess its operating characteristics. We applied the dTDT to the simulated data and documented the power of the dTDT under a number of different realistic scenarios. Finally, we applied our methods to a family study of alcohol dependence (COGA) and performed individual genotyping on complete families for the top signals. One SNP (rs4903712 on chromosome 14) remained significant after correcting for multiple testing Methods developed in this study can be adapted to other platforms and will have widespread applicability in genomic research when case-control GWAS data are collected in families with existing linkage data.

Structural and population-based evaluations of TBC1D1 p.Arg125Trp

Obesity is now a leading cause of preventable death in the industrialised world. Understanding its genetic influences can enhance insight into molecular pathogenesis and potential therapeutic targets. A non-synonymous polymorphism (rs35859249, p.Arg125Trp) in the N-terminal TBC1D1 phosphotyrosine-binding (PTB) domain has shown a replicated association with familial obesity in women. We investigated these findings in the Avon Longitudinal Study of Parents and Children (ALSPAC), a large European birth cohort of mothers and offspring, and by generating a predicted model of the structure of this domain. Structural prediction involved the use of three separate algorithms; Robetta, HHpred/MODELLER and I-TASSER. We used the transmission disequilibrium test (TDT) to investigate familial association in the ALSPAC study cohort (N = 2,292 mother-offspring pairs). Linear regression models were used to examine the association of genotype with mean measurements of adiposity (Body Mass Index (BMI), waist circumference and Dual-energy X-ray absorptiometry (DXA) assessed fat mass), and logistic regression was used to examine the association with odds of obesity. Modelling showed that the R125W mutation occurs in a location of the TBC1D1 PTB domain that is predicted to have a function in a putative protein:protein interaction. We did not detect an association between R125W and BMI (mean per allele difference 0.27 kg/m² (95% Confidence Interval: 0.00, 0.53) P = 0.05) or obesity (odds ratio 1.01 (95% Confidence Interval: 0.77, 1.31, P = 0.96) in offspring after adjusting for multiple comparisons. Furthermore, there was no evidence to suggest that there was familial association between R125W and obesity (χ² = 0.06, P = 0.80). Our analysis suggests that R125W in TBC1D1 plays a role in the binding of an effector protein, but we find no evidence that the R125W variant is related to mean BMI or odds of obesity in a general population sample.

A novel test of informative missingness using inconsistent linkage disequilibrium signals between case-parent triads and incomplete data

In general, multiple issues are examined before the analysis of genetic data such as Hardy-Weinberg Equilibrium and Mendelian errors. Although missing genotypes are commonly observed in genetic studies, potential bias due to informative missingness is usually overlooked. Therefore, the Test of Informative Missingness (TIM) was the first attempt to determine whether or not parental genotypes are missing informatively. The TIM is a useful tool for genetic data cleaning. For example, excluding single-nucleotide polymorphisms that appear to be missing informatively may further improve the quality of genetic data. Although the TIM has decent power, its performance is discernibly weaker when the minor allele/genotype introduces informative missingness. In an effort to avoid such reduced power, the newly proposed strategy detects informative missingness by comparing inconsistent linkage disequilibrium signals between intact case-parent triads and incomplete data. Computer simulations revealed that the new method was robust to population stratifications and more powerful than the TIM in most situations. In addition, the new method demonstrated decent power in the genome-wide association study, even if the most conservative correction for multiple testing was adopted.

A powerful approach for association analysis incorporating imprinting effects

MOTIVATION

For a diallelic marker locus, the transmission disequilibrium test (TDT) is a simple and powerful design for genetic studies. The TDT was originally proposed for use in families with both parents available (complete nuclear families) and has further been extended to 1-TDT for use in families with only one of the parents available (incomplete nuclear families). Currently, the increasing interest of the influence of parental imprinting on heritability indicates the importance of incorporating imprinting effects into the mapping of association variants.

RESULTS

In this article, we extend the TDT-type statistics to incorporate imprinting effects and develop a series of new test statistics in a general two-stage framework for association studies. Our test statistics enjoy the nature of family-based designs that need no assumption of Hardy-Weinberg equilibrium. Also, the proposed methods accommodate complete and incomplete nuclear families with one or more affected children. In the simulation study, we verify the validity of the proposed test statistics under various scenarios, and compare the powers of the proposed statistics with some existing test statistics. It is shown that our methods greatly improve the power for detecting association in the presence of imprinting effects. We further demonstrate the advantage of our methods by the application of the proposed test statistics to a rheumatoid arthritis dataset.

CONTACT

wingfung@hku.hk

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Joint analysis for genome-wide association studies in family-based designs

In family-based data, association information can be partitioned into the between-family information and the within-family information. Based on this observation, Steen et al. (Nature Genetics. 2005, 683-691) proposed an interesting two-stage test for genome-wide association (GWA) studies under family-based designs which performs genomic screening and replication using the same data set. In the first stage, a screening test based on the between-family information is used to select markers. In the second stage, an association test based on the within-family information is used to test association at the selected markers. However, we learn from the results of case-control studies (Skol et al. Nature Genetics. 2006, 209-213) that this two-stage approach may be not optimal. In this article, we propose a novel two-stage joint analysis for GWA studies under family-based designs. For this joint analysis, we first propose a new screening test that is based on the between-family information and is robust to population stratification. This new screening test is used in the first stage to select markers. Then, a joint test that combines the between-family information and within-family information is used in the second stage to test association at the selected markers. By extensive simulation studies, we demonstrate that the joint analysis always results in increased power to detect genetic association and is robust to population stratification.

A robust TDT-type association test under informative parental missingness

Many family-based association tests rely on the random transmission of alleles from parents to offspring. Among them, the transmission/disequilibrium test (TDT) may be considered to be the most popular statistical test. The TDT statistic and its variations were proposed to evaluate nonrandom transmission of alleles from parents to the diseased children. However, in family studies, parental genotypes may be missing due to parental death, loss, divorce, or other reasons. Under some missingness conditions, nonrandom transmission of alleles may still occur even when the gene and disease are not associated. As a consequence, the usual TDT-type tests would produce excessive false positive conclusions in association studies. In this paper, we propose a novel TDT-type association test which is not only simple in computation but also robust to the joint effect of population stratification and informative parental missingness. Our test is model-free and allows for different mechanisms of parental missingness across subpopulations. We use a simulation study to compare the performance of the new test with TDT and point out the advantage of the new method.

Application of association mapping to understanding the genetic diversity of plant germplasm resources

Compared to the conventional linkage mapping, linkage disequilibrium (LD)-mapping, using the nonrandom associations of loci in haplotypes, is a powerful high-resolution mapping tool for complex quantitative traits. The recent advances in the development of unbiased association mapping approaches for plant population with their successful applications in dissecting a number of simple to complex traits in many crop species demonstrate a flourish of the approach as a “powerful gene tagging” tool for crops in the plant genomics era of 21st century. The goal of this review is to provide nonexpert readers of crop breeding community with (1) the basic concept, merits, and simple description of existing methodologies for an association mapping with the recent improvements for plant populations, and (2) the details of some of pioneer and recent studies on association mapping in various crop species to demonstrate the feasibility, success, problems, and future perspectives of the efforts in plants. This should be helpful for interested readers of international plant research community as a guideline for the basic understanding, choosing the appropriate methods, and its application.

Current findings, challenges and novel approaches in human genetic susceptibility to tuberculosis

The evidence for a human genetic component in susceptibility to tuberculosis (TB) is incontrovertible. Quite apart from studies of rare disease events illustrating the importance of key genes in humans and animals, TB at the population level is also influenced by the genetics of the host. Heritability of disease concordance and immune responses to mycobacterial antigens has been clearly shown, and ranges up to 71%. Linkage studies, designed to identify major susceptibility genes in a disease, have produced a number of candidate loci but few, except for regions on chromosome 5p15, 20p and 20q, have been replicated. The region on 5p15 regulates the intensity of the response to the tuberculin skin test, and another locus on 11p14 appears to control resistance to the bacterium. In addition, numerous genes and pathways have been implicated in candidate gene association studies, with validation of polymorphisms in IFNG, NRAMP1, and NOS2A and equivocal results for IL10, CCL2, DC-SIGN, P2RX7, VDR, TLR2, TLR9 and SP110. Other more recently researched candidate genes such as TNFRSF1B remain to be validated, preferably in meta-analyses. New approaches have provided early evidence for the importance of gene-gene interactions in regulating resistance to disease, and also the prospect that applying host genetics in the field of vaccinomics could lead to a more targeted approach in designing interventions to aid the human immune system in combating mycobacteria. Genome-wide association studies and admixture mapping are approaches that remain to be applied to TB, and it is not clear, as is the case with other complex diseases, how much of the heritability of the TB susceptibility phenotype will be determined by multiple genes of small effect versus rare variants with disproportionately large effects.

A generalized family-based association test for dichotomous traits

Recent advances in genotyping technology make it possible to utilize large-scale association analysis for disease-gene mapping. Powerful and robust family-based association methods are crucial for successful gene mapping. We propose a family-based association method, the generalized disequilibrium test (GDT), in which the genotype differences of all discordant relative pairs are utilized in assessing association within a family. The improvement of the GDT over existing methods is threefold: (1) information beyond first-degree relatives is incorporated efficiently, yielding substantial gains in power in comparison to existing tests; (2) the GDT statistic is implemented via a robust technique that does not rely on large sample theory, resulting in further power gains, especially at high levels of significance; and (3) covariates and weights based on family size are incorporated. Advantages of the GDT over existing methods are demonstrated by extensive computer simulations and by application to recently published large-scale genome-wide linkage data from the Type 1 Diabetes Genetics Consortium (T1DGC). In our simulations, the GDT consistently outperforms other tests for a common disease and frequently outperforms other tests for a rare disease; the power improvement is > 13% in 6 out of 8 extended pedigree scenarios. All of the six strongest associations identified by the GDT have been reported by other studies, whereas only three or four of these associations can be identified by existing methods. For the T1D association at gene UBASH3A, the GDT resulted in a genome-wide significance (p = 4.3 x 10(-6)), much stronger than the published significance (p = 10(-4)).

A hybrid design: case-parent triads supplemented by control-mother dyads

Hybrid designs arose from an effort to combine the benefits of family-based and population-based study designs. A recently proposed hybrid approach augments case-parent triads with population-based control-parent triads, genotyping everyone except the control offspring. Including parents of controls substantially improves statistical efficiency for testing and estimating both offspring and maternal genetic relative risk parameters relative to using case-parent triads alone. Moreover, it allows testing of required assumptions. Nevertheless, control fathers can be hard to recruit, whereas control offspring and their mothers may be readily available. Consequently, we propose an alternative hybrid design where offspring-mother pairs, instead of parents, serve as population-based controls. We compare the power of our proposed method with several competitors and show that it performs well in various scenarios, though it is slightly less powerful than the hybrid design that uses control parents. We describe approaches for checking whether population stratification will bias inferences that use controls and whether the mating-symmetry assumption holds. Surprisingly, if mating symmetry is violated, even though mating-type parameters cannot be directly estimated using control-mother dyads alone, and maternal effects cannot be estimated using case-parent triads alone, combining both sources of data allows estimation of all the parameters. This hybrid design can also be used to study environmental influences on disease risk and gene-by-environment interactions.

Detection of parent-of-origin effects based on complete and incomplete nuclear families with multiple affected children

Parent-of-origin effects are important in studying genetic traits. More than 1% of all mammalian genes are believed to show parent-of-origin effects. Some statistical methods may be ineffective or fail to detect linkage or association for a gene with parent-of-origin effects. Based on case-parents trios, the parental-asymmetry test (PAT) is simple and powerful in detecting parent-of-origin effects. However, it is common in practice to collect nuclear families with both parents as well as nuclear families with only one parent. In this paper, when only one parent is available for each family with an arbitrary number of affected children, we firstly develop a new test statistic 1-PAT to test for parent-of-origin effects in the presence of association between an allele at the marker locus under study and a disease gene. Then we extend the PAT to accommodate complete nuclear families each with one or more affected children. Combining families with both parents and families with only one parent, the C-PAT is proposed to detect parent-of-origin effects. The validity of the test statistics is verified by simulation in various scenarios of parameter values. A power study shows that using the additional information from incomplete nuclear families in the analysis greatly improves the power of the tests, compared to that based on only complete nuclear families. Also, utilizing all affected children in each family, the proposed tests have a higher power than when only one affected child from each family is selected. Additional power comparison also demonstrates that the C-PAT is more powerful than a number of other tests for detecting parent-of-origin effects.

The impact of complex informative missingness on the validity of the transmission/disequilibrium test (TDT)

The transmission/disequilibrium test was introduced to test for linkage and association between a marker and a putative disease locus using case-parent triads. Several extensions have been proposed to accommodate incomplete triads. Some strategies assumed that parental genotypes were missing completely at random and some methods allowed informative missingness for parental genotypes. However, the above tests assumed that offspring genotypes were missing completely at random and concluded that the transmission/disequilibrium test remained a valid test by excluding incomplete triads from the analysis. In this article, the conditional distribution of ascertained triads allowing informative missingness for offspring genotypes, as well as their parental genotypes, was derived and several tests under such scenarios were evaluated. In simulations, independent triads from the Genetic Analysis Workshop 15 simulated data (Problem 3) was ascertained. When offspring genotypes were missing informatively, simulation results revealed inflated type I error and/or reduced power for the transmission/disequilibrium test excluding incomplete triads.

Family study designs in the age of genome-wide association studies: experience from the Framingham Heart Study

PURPOSE OF REVIEW

The past year has seen the publication of many genome-wide association studies, most of which are case-control studies. These publications are at the forefront of current research into the examination of genetic effects for numerous diseases, including diabetes, heart disease and cancer. Over the past 25 years the tour de force of genetics research has been in family studies, using segregation, linkage and association analyses. Are these approaches now passé? Here we discuss the role of family studies in modern genetics research, using results from the Framingham Heart Study as examples.

RECENT FINDINGS

Family studies permit both linkage and association analyses. Importantly, family-based association tests that consider transmission of genetic variants within a family provide important information on the genetic etiology of disease traits and avoid the potential of false-positive findings due to population substructure.

SUMMARY

Family-based study designs continue to contribute much to the modern era of genome-wide association studies.

Review and evaluation of methods correcting for population stratification with a focus on underlying statistical principles

When two or more populations have been separated by geographic or cultural boundaries for many generations, drift, spontaneous mutations, differential selection pressures and other factors may lead to allele frequency differences among populations. If these 'parental' populations subsequently come together and begin inter-mating, disequilibrium among linked markers may span a greater genetic distance than it typically does among populations under panmixia [see glossary]. This extended disequilibrium can make association studies highly effective and more economical than disequilibrium mapping in panmictic populations since less marker loci are needed to detect regions of the genome that harbor phenotype-influencing loci. However, under some circumstances, this process of intermating (as well as other processes) can produce disequilibrium between pairs of unlinked loci and thus create the possibility of confounding or spurious associations due to this population stratification. Accordingly, researchers are advised to employ valid statistical tests for linkage disequilibrium mapping allowing conduct of genetic association studies that control for such confounding. Many recent papers have addressed this need. We provide a comprehensive review of advances made in recent years in correcting for population stratification and then evaluate and synthesize these methods based on statistical principles such as (1) randomization, (2) conditioning on sufficient statistics, and (3) identifying whether the method is based on testing the genotype-phenotype covariance (conditional upon familial information) and/or testing departures of the marginal distribution from the expected genotypic frequencies.

A family-based likelihood ratio test for general pedigree structures that allows for genotyping error and missing data

The purpose of this work is the development of a family-based association test that allows for random genotyping errors and missing data and makes use of information on affected and unaffected pedigree members. We derive the conditional likelihood functions of the general nuclear family for the following scenarios: complete parental genotype data and no genotyping errors; only one genotyped parent and no genotyping errors; no parental genotype data and no genotyping errors; and no parental genotype data with genotyping errors. We find maximum likelihood estimates of the marker locus parameters, including the penetrances and population genotype frequencies under the null hypothesis that all penetrance values are equal and under the alternative hypothesis. We then compute the likelihood ratio test. We perform simulations to assess the adequacy of the central chi-square distribution approximation when the null hypothesis is true. We also perform simulations to compare the power of the TDT and this likelihood-based method. Finally, we apply our method to 23 SNPs genotyped in nuclear families from a recently published study of idiopathic scoliosis (IS). Our simulations suggest that this likelihood ratio test statistic follows a central chi-square distribution with 1 degree of freedom under the null hypothesis, even in the presence of missing data and genotyping errors. The power comparison shows that this likelihood ratio test is more powerful than the original TDT for the simulations considered. For the IS data, the marker rs7843033 shows the most significant evidence for our method (p = 0.0003), which is consistent with a previous report, which found rs7843033 to be the 2nd most significant TDTae p value among a set of 23 SNPs.

Testing informative missingness in genetic studies using case-parent triads

In genetic studies, the transmission/disequilibrium test (TDT) using case-parent triads has gained popularity attributable to its robustness to population admixture. Several extensions have been proposed to accommodate incomplete triads. Some strategies assume that parental genotypes are missing completely at random (MCAR) to insure an unbiased conclusion and some methods allow parental genotypes to be missing informatively, resulting in reduced power when the missing data pattern is indeed MCAR. However, these tests assumed that offspring genotypes were MCAR. Recently, Guo indicated that when offspring genotypes were missing informatively, an occurrence that can be considered as ascertainment bias, inflated type-I error and/or reduced power may occur using the TDT when incomplete triads are excluded. In an effort to avoid an erroneous conclusion, we propose a strategy called testing informative missingness (TIM) that compares conditional distributions of parental genotypes among complete triads and incomplete data with only one parent to examine the missing data pattern. Through computer simulations, TIM has decent power to detect informative missingness and is robust to population admixture. In addition, we illustrate TIM with an application to the Framingham Heart Study.

Haplotype-association analysis

Association methods based on linkage disequilibrium (LD) offer a promising approach for detecting genetic variations that are responsible for complex human diseases. Although methods based on individual single nucleotide polymorphisms (SNPs) may lead to significant findings, methods based on haplotypes comprising multiple SNPs on the same inherited chromosome may provide additional power for mapping disease genes and also provide insight on factors influencing the dependency among genetic markers. Such insights may provide information essential for understanding human evolution and also for identifying cis-interactions between two or more causal variants. Because obtaining haplotype information directly from experiments can be cost prohibitive in most studies, especially in large scale studies, haplotype analysis presents many unique challenges. In this chapter, we focus on two main issues: haplotype inference and haplotype-association analysis. We first provide a detailed review of methods for haplotype inference using unrelated individuals as well as related individuals from pedigrees. We then cover a number of statistical methods that employ haplotype information in association analysis. In addition, we discuss the advantages and limitations of different methods.

Two-stage association tests for genome-wide association studies based on family data with arbitrary family structure

Recently, Steen et al proposed a two-stage approach for genome-wide family-based association studies. In the first stage, a screening test is used to select markers, and in the second stage, a family-based association test is performed on a much smaller set of the selected markers. The two-stage method can be much more powerful than the traditional family-based association tests. In this article, we extend the approach so that it can incorporate parental information and can be applied to an arbitrary pedigree structure. We use simulation studies to evaluate the type I error rates and the power of the proposed methods. Our results show that the two-stage approach that incorporates founders' phenotypes has the correct type I error rates, and is much more powerful than the two-stage approach that uses children's phenotypes only. Also, by carefully choosing the number of markers retained in the first stage, the power of a two-stage approach can be much more than that of the corresponding one-stage approach.

Genetic diversity of the IL-4, IL-4 receptor and IL-13 loci in mestizos in the general population and in patients with asthma from three subpopulations in Mexico

Asthma is an inflammatory airway disease characterized by increased serum IgE levels, mucus hypersecretion and infiltration of inflammatory cells, and is a multifactorial disease that exhibits genetic heterogeneity. Polymorphisms in the interleukin-4 (C-590T), interleukin-4 receptor (ile50val and gln576arg), and interleukin-13 (arg130gln) genes have been described as susceptibility alleles for asthma. This study was designed to determine whether asthma susceptibility is influenced by genotypic and allelic distribution of the above polymorphisms in three Mexican subpopulations. Four hundred and thirty-seven subjects from three Mexican subpopulations were classified into two groups: general population and affected/unaffected and genotyped for the above polymorphisms. We compared the distributions of the loci in the groups. In addition, we undertook association analysis between these loci and asthma phenotype in each affected/unaffected group, and determined Nei's genetic distance between the three subpopulations. The allelic and genotypic distributions of the polymorphisms differed between the three subpopulations. There was no association between any of the polymorphisms and asthma phenotype. However, there was a differential distribution of haplogroups (P < 0.0001) between the affected and the unaffected groups from the subpopulations of Jalisco and Guerrero. The genetic distribution of the four polymorphisms in the subpopulations did not influence susceptibility to asthma. Furthermore, the difference in the prevalence of asthma in these subpopulations is not attributable to the genetic background for the four polymorphisms analysed. However, haplogroup analysis suggests that the interaction of the polymorphisms and other predisposing alleles leads to the expression of the clinical phenotype.

The transmission disequilibrium test and imprinting effects test based on case-parent pairs

The transmission disequilibrium test (TDT) based on case-parents trios is a powerful tool in linkage analysis and association studies. When only one parent is available, the 1-TDT is applicable in the absence of imprinting. In the presence of imprinting, a statistic is proposed, based on case-mother pairs and case-father pairs to test for linkage when association is present as well as to test for association when linkage is present. The recombination fractions are allowed to be sex-specific in this test statistic. Meanwhile, a statistic based on case-parent pairs is proposed to test for imprinting. Both test statistics can be extended to include families with more than one affected offspring. A number of simulation studies are conducted to investigate the validity of the proposed tests. The effects of different ratios of the numbers of case-mother pairs and case-father pairs on the powers of the proposed tests are studied through simulation. The results show that the optimal ratio is 1:1. How to combine case-parents, case-mother pairs, and case-father pairs jointly in testing for linkage, association, and imprinting is addressed.

Genetic studies of a cluster of acute lymphoblastic leukemia cases in Churchill County, Nevada

OBJECTIVE

In a study to identify exposures associated with 15 cases of childhood leukemia, we found levels of tungsten, arsenic, and dichlorodiphenyldichloroethylene in participants to be higher than mean values reported in the National Report on Human Exposure to Environmental Chemicals. Because case and comparison families had similar levels of these contaminants, we conducted genetic studies to identify gene polymorphisms that might have made case children more susceptible than comparison children to effects of the exposures.

DESIGN

We compared case with comparison children to determine whether differences existed in the frequency of polymorphic genes, including genes that code for enzymes in the folate and purine pathways. We also included discovery of polymorphic forms of genes that code for enzymes that are inhibited by tungsten: xanthine dehydrogenase, sulfite oxidase (SUOXgene), and aldehyde oxidase.

PARTICIPANTS

Eleven case children were age- and sex-matched with 42 community comparison children for genetic analyses. Twenty parents of case children also contributed to the analyses.

RESULTS

One bilalleleic gene locus in SUOX was significantly associated with either case or comparison status, depending on which alleles the child carried (without adjusting for multiple comparisons).

CONCLUSIONS

Although genetic studies did not provide evidence that a common agent or genetic susceptibility factor caused the leukemias, the association between a SUOXgene locus and disease status in the presence of high tungsten and arsenic levels warrants further investigation.

RELEVANCE

Although analyses of community clusters of cancer have rarely identified causes, these findings have generated hypotheses to be tested in subsequent studies.

An extension of the transmission disequilibrium test incorporating imprinting

The recombination rates in meioses of females and males are often different. Some genes that affect development and behavior in mammals are known to be imprinted, and >1% of all mammalian genes are believed to be imprinted. When the gene is imprinted and the recombination fractions are sex specific, the conventional transmission disequilibrium test (TDT) is shown to be still valid for testing for linkage. The power function of the TDT is derived, and the effect of the degree of imprinting on the power of the TDT is investigated. It is learned that imprinting has little effect on the power when the female and male recombination rates are equal. On the basis of case-parents trios, the transmissions from the heterozygous fathers/mothers to their affected children are separated as paternal and maternal, and two TDT-like statistics, TDT(p) and TDT(m), are consequently constructed. It is found that the TDT(p) possesses a higher power than the TDT for maternal imprinting genes, and the TDT(m) is more powerful than the TDT for paternal imprinting genes. On the basis of the parent-of-origin effects test statistic (POET), a novel statistic, TDT incorporating imprinting (TDTI) is proposed to test for linkage in the presence of linkage disequilibrium, which is shown to be more powerful than the TDT when parent-of-origin effects are significant but slightly less powerful than the TDT when parent-of-origin effects are negligible. The validity of the TDT and TDTI is assessed by simulation. The power approximation formulas for the TDT and TDTI are derived and the simulation results show that they are accurate. The simulation study on power comparison shows that the TDTI outperforms the TDT for imprinted genes. The improvement can be substantial in the case of complete paternal/maternal imprinting.

Candidate-gene association study of mothers with pre-eclampsia, and their infants, analyzing 775 SNPs in 190 genes

Pre-eclampsia (PE) affects 5-7% of pregnancies in the US, and is a leading cause of maternal death and perinatal morbidity and mortality worldwide. To identify genes with a role in PE, we conducted a large-scale association study evaluating 775 SNPs in 190 candidate genes selected for a potential role in obstetrical complications. SNP discovery was performed by DNA sequencing, and genotyping was carried out in a high-throughput facility using the MassARRAY(TM) System. Women with PE (n = 394) and their offspring (n = 324) were compared with control women (n = 602) and their offspring (n = 631) from the same hospital-based population. Haplotypes were estimated for each gene using the EM algorithm, and empirical p values were obtained for a logistic regression-based score test, adjusted for significant covariates. An interaction model between maternal and offspring genotypes was also evaluated. The most significant findings for association with PE were COL1A1 (p = 0.0011) and IL1A (p = 0.0014) for the maternal genotype, and PLAUR (p = 0.0008) for the offspring genotype. Common candidate genes for PE, including MTHFR and NOS3, were not significantly associated with PE. For the interaction model, SNPs within IGF1 (p = 0.0035) and IL4R (p = 0.0036) gave the most significant results. This study is one of the most comprehensive genetic association studies of PE to date, including an evaluation of offspring genotypes that have rarely been considered in previous studies. Although we did not identify statistically significant evidence of association for any of the candidate loci evaluated here after adjusting for multiple testing using the false discovery rate, additional compelling evidence exists, including multiple SNPs with nominally significant p values in COL1A1 and the IL1A region, and previous reports of association for IL1A, to support continued interest in these genes as candidates for PE. Identification of the genetic regulators of PE may have broader implications, since women with PE are at increased risk of death from cardiovascular diseases later in life.

Approaches to handling incomplete data in family-based association testing

The high throughput of data arising from the complete sequence of the human genome has left statistical geneticists with a rich and extensive information source. The wide availability of software and the increase in computing power has improved the possibilities to access and process such data. One problem is incompleteness of the data: unobserved or partially observed data points due to technical reasons or reasons associated with the patient's status or erroneous measurements of phenotype or genotype, to name a few. When not properly accounted for, these sources of incompleteness may seriously jeopardize the credibility of results from analyses. In this paper we provide some perspectives on the occurrence and analysis of different forms of incomplete data in family-based genetic association testing.

Integrating molecular genetics analyses into clinical research

The integration of molecular genetics approaches into the study of complex health phenomena is an increasingly important and available strategy for researchers across the health science disciplines. Pain sensation and response to painful stimuli are examples of complex health phenomena that are particularly amenable to molecular genetics approaches. Both human and animal model research suggests that differences in these responses may be related, in part, to variation in the genes that modulate sensation and behavior. The authors are currently managing a large cross-disciplinary research effort to identify child characteristics, including genotypes, that predict the degree of distress displayed by children following a painful medical procedure (i.e., IV insertion). The purpose of this article is to describe the strategies used to integrate molecular genetics methods into this project. The authors discuss the steps needed to complete this process, including (a) establishing a collaboration with genetics researchers and laboratory facilities, (b) developing and implementing a plan to manage biologic samples, and (c) incorporating genetics into the informed consent process.

Transmission disequilibrium test for quantitative trait loci detection in livestock populations

The performance of several transmission disequilibrium tests (TDT) for detection of quantitative trait loci (QTL) in data structures typical of outbred livestock populations were investigated. Factorial mating designs were simulated with 10 sires mated to either 50 or 200 dams, each family having five or eight full sibs. A single marker and QTL, both bi-allelic, were simulated using a disequilibrium coefficient based on complete initial disequilibrium and 50 generations of recombination [i.e. D = D(0)(1 - theta)50], where theta is the recombination fraction between marker and QTL. The QTL explained either 10% (small QTL) or 30% (large QTL) of the genetic variance for a trait with heritability of 0.3. Methods were: TDT for QTL (Q-TDT; both parents known), 1-TDT (only one parent known) and sibling-based TDT (S-TDT; neither parent known, but sibs available). All were found to be effective tests for association and linkage between the QTL and a tightly linked marker (theta < 0.02) in these designs. For a large QTL, theta = 0.01, and five full sibs per family, the empirical power for Q-TDT, 1-TDT and S-TDT was 0.966, 0.602 and 0.974, respectively, in a large population, versus 0.700, 0.414 and 0.654, respectively, in a small population. For a small QTL effect, theta = 0.01, large population the empirical power of these tests were 0.709, 0.287 and 0.634. The power of Q-TDT, 1-TDT and S-TDT was satisfactory for large populations, for QTL with large effects and for five full sibs per family. The 1-TDT based on a linear model was more powerful than the normal 1-TDT. The empirical power for Q-TDT and 1-TDT with a linear model was 0.978 and 0.995 respectively. TDT based on analogous linear models, incorporating the polygenic covariance structure, provided only small increases in power compared with the usual TDT for QTL.

Advances in statistical human genetics over the last 25 years

The past 25 years has seen an explosion in the number of genetic markers that can be measured on DNA samples at an ever decreasing cost. Although basic statistical methods for analysing such data gathered on samples of either independent individuals or family members, one or two markers at a time, were already well developed before this explosion occurred, there has been a corresponding burst in activity to develop multiple marker models to find disease-causing gene variants, capitalizing on the data that have become available, to increase the power of such methods. This has required the concomitant development of faster algorithms to speed up the computation of various likelihoods. For linkage analysis, to obtain the approximate locations for genes of interest, Mendelian segregation models have been extended to be more realistic and statistical models that do not assume specific modes of inheritance have been extended to allow for the analysis of larger pedigree structures. For association analysis, to obtain more precise locations for genes of interest, the recent completion of the first stage of the HapMap project has spurred the development, still underway, of novel experimental designs and analytical methods to combat the curse of dimensionality and the resulting multiple testing problem. Perhaps the greatest current challenge concerns how best to gather and synthesize the many lines of evidence possible in order to discover the genetic determinants underlying complex diseases.

Xenobiotic-Metabolizing Genes and Small-for-Gestational-Age Births

BACKGROUND

Little is known about the role of xenobiotic-metabolizing gene variants as risk factors for small-for-gestational-age (SGA) births or as modifiers for the effects of exposures such as maternal smoking.

METHODS

We conducted 2 joint studies: a case-control design including 493 cases (birth weight below the 10th percentile according to gestational age and sex) and 472 controls (at or above the 10th percentile) and a family-based study (mother, father, and newborn) with approximately 250 case trios and a similar number of control trios. Logistic regression and a log-linear model were used to analyze the association between genetic variants such as CYP1A1*2A, CYP1A1*2B, CYP1A1*4, GSTT1, GSTM1, and XRCC3 and SGA. The interaction between genetic variants and maternal smoking was also studied.

RESULTS

The odds ratio (OR) for the association of complete maternal GSTT1 deletion with SGA was 0.63 (95% confidence interval = 0.41-0.97), and that for the complete newborn GSTM1 deletion was 0.74 (0.55-0.98). Newborns with the partial GSTT1 deletion had an OR of 1.40 (1.01-1.95), and newborns homozygous for CYP1A1*2A had an OR of 4.28 (1.02-18.0). These results were coherent with the trio-based results. Significant interactions were observed between maternal smoking in the third trimester and CYP1A1*2A (P = 0.03), XRCC3 (P = 0.03), and newborn GSTT1 (P = 0.01).

CONCLUSIONS

Certain genetic variants involved in the metabolism of xenobiotics increase the risk of SGA, as well as modify the effects of maternal smoking by increasing or decreasing its risk.

Impact of non-ignorable missingness on genetic tests of linkage and/or association using case-parent trios

The transmission/disequilibrium test was introduced to test for linkage disequilibrium between a marker and a putative disease locus using case-parent trios. However, parental genotypes may be incomplete in such a study. When parental information is non-randomly missing, due, for example, to death from the disease under study, the impact on type I error and power under dominant and recessive disease models has been reported. In this paper, we examine non-ignorable missingness by assigning missing values to the genotypes of affected parents. We used unrelated case-parent trios in the Genetic Analysis Workshop 14 simulated data for the Danacaa population. Our computer simulations revealed that the type I error of these tests using incomplete trios was not inflated over the nominal level under either recessive or dominant disease models. However, the power of these tests appears to be inflated over the complete information case due to an excess of heterozygous parents in dyads.

Evaluation of a methylenetetrahydrofolate-dehydrogenase 1958G>A polymorphism for neural tube defect risk

Genetic variants of enzymes involved in the folate pathway might be expected to have an impact on neural tube defect (NTD) risk. Given its key role in folate metabolism, the methylenetetrahydrofolate dehydrogenase 1 (MTHFD1) gene could represent an attractive candidate in NTD aetiology. In this study, the impact of the MTHFD1 1958G > A polymorphism on NTD risk in the Italian population was examined both by hospital-based case-control and family-based studies. The MTHFD1 1958G > A polymorphism was genotyped in 142 NTD cases, 125 mothers, 108 fathers and 523 controls. An increased risk was found for the heterozygous 1958G/A (OR = 1.69; P = 0.04) and homozygous 1958A/A (OR = 1.91; P = 0.02) genotypes in the children. Significant association was also found when combined 1958G/A and 1958A/A genotypes of cases were compared with the 1958G/G genotype (OR = 1.76; P = 0.02). The risk of an NTD-affected pregnancy of the mothers was increased 1.67-fold (P = 0.04) only when a dominant effect (1958G/A or 1958A/A vs 1958G/G) of the 1958A allele was analysed. The combined TDT/1-TDT (Z = 2.11; P = 0.03) and FBAT (Z = 2.4; P = 0.01) demonstrated a significant excess of transmission of the 1958A allele to affected individuals. In summary, our results indicate that heterozygosity and homozygosity for the MTHFD1 1958G > A polymorphism are genetic determinants of NTD risk in the cases examined.

Factors affecting statistical power in the detection of genetic association

The mapping of disease genes to specific loci has received a great deal of attention in the last decade, and many advances in therapeutics have resulted. Here we review family-based and population-based methods for association analysis. We define the factors that determine statistical power and show how study design and analysis should be designed to maximize the probability of localizing disease genes.

Applications of whole-genome high-density SNP genotyping

The technology to simultaneously genotype hundreds of thousands of single nucleotide polymorphisms in a single assay has only recently been developed. These advances have the potential to revolutionize our ability to identify disease-associated proteins and their corresponding pathways as drugable targets. Several strategies that can take advantage of extremely high-density, genome-wide single nucleotide polymorphism genotyping to hone in on pathogenic genetic variants will be discussed. In familial linkage studies, high-density single nucleotide polymorphism genotyping has already been proven to speed up mutation identification of Mendelian traits several fold. Many studies now report examining loss of heterozygosity and genomic amplifications on a whole-genome level. Genotyping hundreds of thousands of single nucleotide polymorphisms in a single set of assays now also allows for whole-genome association studies in complex, multigenic diseases. The technology of high-density single nucleotide polymorphism genotyping has emerged rapidly, leaving data analysis and bioinformatic challenges only partially met. In this review, the immediate applications and implications of the rapidly changing high-density, whole-genome single nucleotide polymorphism genotyping field on translational research will be described.

Robust transmission/disequilibrium test for incomplete family genotypes

Several solutions have been proposed to extend the transmission disequilibrium test (TDT) to include cases with missing parental genotype. However, completion of the missing parental genotype may bias the test if the underlying missing data mechanism is informative. Furthermore, all these solutions resolve the problem of missing parental genotype, while offspring with missing genotypes are typically ignored. We propose here an extension to the TDT, called robust TDT (rTDT), able to handle incomplete genotypes on both parents and children and that does not rest on any assumption about the missing data mechanism. rTDT returns minimum and maximum values of TDT that are consistent with all the possible completions of the missing data. We also show that, in some situations, rTDT can achieve both greater power and greater significance than the popular TDT analysis of incomplete data. rTDT is applied to a database of markers of susceptibility to Crohn's disease and it shows that only 2 of the 11 markers originally associated with the phenotype do not depend on assumptions about the missing data mechanism.

Expectation Maximization Algorithm Based Haplotype Relative Risk (EM-HRR): Test of Linkage Disequilibrium Using Incomplete Case-Parents Trios

The Haplotype Relative Risk (HRR) was first proposed [Falk et al., Ann Hum Genet 1987] to test for Linkage Disequilibrium (LD) between a marker and a putative disease locus using case-parent trios. Spurious association does not appear in such family-based studies under population admixture. In this paper, we extend the HRR to accommodate incomplete trios via the Expectation-Maximization (EM) algorithm [Dempster et al., J R Stat Soc Ser B, 1977]. In addition to triads and dyads (parent-offspring pair), the EM-HRR easily incorporates individuals with no parental genotype information available, which is excluded from the one parent Transmission/Disequilibrium Test (1-TDT) [Sun et al., Am J Epidemiol 1999]. Due to the data structure of EM-HRR, transmitted alleles are always available regardless of the number of missing parental genotypes. As a result of having a larger sample size, computer simulations reveal that the EM-HRR is more powerful in detecting LD than the 1-TDT in a population under Hardy-Weinberg Equilibirum (HWE). If admixture is not extreme, the EM-HRR remains more powerful. When a large degree of admixture exists, the EM-HRR performs better the 1-TDT when the association is strong, though not as well when the association is weak. We illustrate the proposed method with an application to the Framingham Heart Study.