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In a recent genome-wide association study (GWAS) from an international consortium, evidence of linkage and association in chr8q24 was much stronger among nonsyndromic cleft lip/palate (CL/P) case-parent trios of European ancestry than among trios of Asian ancestry. We examined marker information content and haplotype diversity across 13 recruitment sites (from Europe, United States, and Asia) separately, and conducted principal components analysis (PCA) on parents. As expected, PCA revealed large genetic distances between Europeans and Asians, and a north-south cline from Korea to Singapore in Asia, with Filipino parents forming a somewhat distinct Southeast Asian cluster. Hierarchical clustering of SNP heterozygosity revealed two major clades consistent with PCA results. All genotyped SNPs giving P < 10−6 in the allelic transmission disequilibrium test (TDT) showed higher heterozygosity in Europeans than Asians. On average, European ancestry parents had higher haplotype diversity than Asians. Imputing additional variants across chr8q24 increased the strength of statistical evidence among Europeans and also revealed a significant signal among Asians (although it did not reach genome-wide significance). Tests for SNP-population interaction were negative, indicating the lack of strong signal for 8q24 in families of Asian ancestry was not due to any distinct genetic effect, but could simply reflect low power due to lower allele frequencies in Asians. Genet. Epidemiol. 36:392–399, 2012. © 2012 Wiley Periodicals, Inc.

We consider the problem of detection of modifier genes that lead to variations in a disease-related continuous variable (DRCV), such as the age of onset or a measure of disease severity, in a strategy of candidate genes. We propose a novel method, the ordered transmission disequilibrium test (OTDT), to test for a relation between the clinical heterogeneity expressed by a DRCV and marker genotypes of a candidate gene. The OTDT applies to trio families with one patients and his parents, all three genotyped at a bi-allelic marker M. The OTDT aims to find a critical value of the DRCV which separates the sample of families in two subsamples in which the transmission rates are significantly different. We investigate the power of the method by simulations under various genetic models and covariate distributions and compare it with a linear regression analysis.

The power of transmission/disequilibrium tests (TDTs) for detecting disease susceptibility loci is expected to be influenced by population admixture through its impact on the degree of linkage disequilibrium (LD) between the genetic marker and the DSL. However, few studies have been done to systematically examine this behavior of the TDTs in admixed populations. In the present study, extensive computer simulations were conducted to explore how population admixture affects the power of TDTs. It was found that (1) in newly admixed populations, the LD due to admixture makes no contribution to the power of TDTs, and it is the averaged background LD in the parental populations that determines the power of TDTs; but (2) after random mating between the admixed populations, the LD due to admixture becomes effective in increasing or decreasing the power of the tests, and (3) incomplete random mating can prolong the time for the LD due to admixture to become effective. This study clarifies the potential influence of population admixture on the performance of TDTs. Genet. Epidemiol. 2008. © 2008 Wiley-Liss, Inc.

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 casefather 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. Genet. Epidemiol. 31:273–287, 2007. r 2007 Wiley-Liss, Inc.

To date, there is no test valid for the composite null hypothesis of no linkage or no association that utilizes transmission information from heterozygous parents to their unaffected offspring as well as the affected offspring from ascertained nuclear families. Since the unaffected siblings also provide information about linkage and association, we introduce a new strategy called the informative-transmission disequilibrium test (i-TDT), which uses transmission information from heterozygous parents to all of the affected and unaffected offspring in ascertained nuclear families and provides a valid chi-square test for both linkage and association. The i-TDT can be used in various study designs and can accommodate all types of independent nuclear families with at least one affected offspring. We show that the transmission/disequilibrium test (TDT) (Spielman et al. [1993] Am. J. Hum. Genet. 52:506-516) is a special case of the i-TDT, if the study sample contains only case-parent trios. If the sample contains only affected and unaffected offspring without parental genotypes, the i-TDT is equivalent to the sibship disequilibrium test (SDT) (Horvath and Laird [1998] Am. J. Hum. Genet. 63:1886-1897. In addition, the test statistic of i-TDT is simple, explicit and can be implemented easily without intensive computing. Through computer simulations, we demonstrate that power of the i-TDT can be higher in many circumstances compared to a method that uses affected offspring only. Applying the i-TDT to the Framingham Heart Study data, we found that the apolipoprotein E (APOE) gene is significantly linked and associated with cross-sectional measures and longitudinal changes in total cholesterol.

Contributions to Group 17 of the Genetic Analysis Workshop 15 considered dense markers in linkage disequilibrium (LD) in the context of either linkage or association analysis. Three contributions reported on methods for modeling LD or selecting a subset of markers in linkage equilibrium to perform linkage analysis. When all markers were used without modeling LD, inflated evidence for linkage was observed when parental genotypes were missing. All methods for handling LD led to some decreased linkage evidence. Two groups performed a genome-wide association scan using either mixed models to account for known or unknown relatedness between individuals, trend tests or combination statistics. All methods failed to detect four of the eight simulated loci because of low LD in some regions. Three groups performed association analysis using simulated dense markers on chromosome 6, where a simulated HLA-DRB1 locus played a major role in disease susceptibility along with two additional loci of smaller effect. The overall conditional genotype method correctly identified both additional loci while a novel transmission disequilibrium test-statistic to combine studies with non-overlapping markers identified one HLA locus after stratifying on the parental HLA-DRB1 genotypes; LD mapping using the Malecot model mapped two loci in this region, even when using greatly reduced marker density. While LD between markers appears to be a nuisance that may cause spurious linkage results with missing parental genotypes in linkage analysis, association analysis thrives on LD, and disease genes fail to be detected in regions of low LD. Genet. Epidemiol. 31 (Suppl. 1):S139–S148, 2007. © 2007 Wiley-Liss, Inc.

Family-based tests of association between a candidate locus and a disease evaluate how often a variant allele at the locus is transmitted from parents to offspring. These tests assume that in the absence of association, an affected offspring is equally likely to have inherited either one of the two homologous alleles carried by a parent. However, transmission distortion was documented in families in which the offspring are unselected for phenotype. Moreover, if offspring genotypes are associated with a risk factor for the disease, transmission distortion to affected offspring can occur in the absence of a causal relation between gene and disease risk. We discuss the appropriateness of adjusting for established risk factors when evaluating association in family-based studies. We present methods for adjusting the transmission/disequilibrium test for risk factors when warranted, and we apply them to data on CYP19 (aromatase) genotypes in nuclear families with multiple cases of breast cancer. Simulations show that when genotypes are correlated with risk factors, the unadjusted test statistics have inflated size, while the adjusted ones do not. The covariate-adjusted tests are less powerful than the unadjusted ones, suggesting the need to check the relationship between genotypes and known risk factors to verify that adjustment is needed. The adjusted tests are most useful for data containing a large proportion of families that lack disease-discordant sibships, i.e., data for which multiple logistic regression of matched sibships would have little power. Software for performing the covariate-adjusted tests is available at http://www.stanford.edu/dept/HRP/epidemiology/COVTDT.

Case-control study has been and continues to be one of the most popular designs in epidemiology. More recently, this design has been adopted to test for candidate genes when searching for disease genetic etiology. In this report, we present a multipoint linkage disequilibrium (LD) mapping approach with the focus on estimating the location of the target trait locus. It builds upon a representation, which shows that the difference between a case and a control in probabilities of carrying the target allele of a marker is proportional to that of the trait locus and that the proportionality factor is simply a measure of LD between the trait locus and the marker. Our method has the desired properties that (1) there is no need to specify phases of genotypic data with multiple markers, (2) it provides an estimate of location of the disease locus along with sampling uncertainty to help investigators to narrow chromosomal regions, and (3) a single test statistic is provided to test for LD in the framed region rather than testing the hypothesis one marker at a time. Our simulation work suggests that the proposed method performs well in terms of bias and coverage probability. Extension of the proposed method to account for confounding and genetic heterogeneity is discussed. We apply the proposed method to a published case-control data set for cystic fibrosis.

This report summarizes the Genetic Analysis Workshop 14 contributions related to fine-mapping strategies, in which examining smaller regions by association with single-nucleotide polymorphisms (SNPs) can yield savings in genotyping and multiple-testing penalties. The aim of the analyses conducted in Group 7 contributions was to localize disease susceptibility loci from either the simulated or the Collaborative Study on the Genetics of Alcoholism (COGA) data within identified regions of linkage. Among the 10 contributions, most groups analyzed the simulated data, one group analyzed the COGA data only, and one group analyzed both data sets. The research questions included evaluation of new methods of analysis, as well as comparisons among alternative methods, analytic strategies, and study designs. Methods of interest included an algorithm for SNP marker ordering, a locally weighted transmission disequilibrium test statistic, a likelihood-ratio test statistic for family-based association in nuclear families, a robust test statistic for case-control association studies, and Bayesian spatial modeling methods for haplotype clustering and association. Evaluations included comparisons among confidence intervals for loci detected via linkage, effects of multiple testing adjustments and trade-offs between type I error and power, comparisons among haplotype-based (multilocus) and genotype-based (multilocus and single-locus) association analyses, and design of fine-mapping and replication studies. While several promising new approaches were identified, further development and evaluation of methods for multiple testing, regression modeling of association with multiple markers and haplotypes, and combined treatment of linkage and association data are necessary if we are to identify many of the genes that contribute to complex traits.

Most previous sample size calculations for case-control studies to detect genetic associations with disease assumed that the disease gene locus is known, whereas, in fact, markers are used. We calculated sample sizes for unmatched case-control and sibling case-control studies to detect an association between a biallelic marker and a disease governed by a putative biallelic disease locus. Required sample sizes increase with increasing discrepancy between the marker and disease allele frequencies, and with less-than-maximal linkage disequilibrium between the marker and disease alleles. Qualitatively similar results were found for studies of parent offspring triads based on the transmission disequilibrium test (Abel and Müller-Myhsok, 1998, Am. J. Hum. Genet. 63:664-667; Tu and Whittemore, 1999, Am. J. Hum. Genet. 64:641-649). We also studied other factors affecting required sample size, including attributable risk for the disease allele, inheritance mechanism, disease prevalence, and for sibling case-control designs, extragenetic familial aggregation of disease and recombination. The large sample-size requirements represent a formidable challenge to studies of this type.

Gene mapping for complex diseases is still a challenge in genetic studies. For family-based studies, the single-locus methods for detecting linkage and linkage disequilibrium (LD) one at a time may not capture the assumed interaction between multiple causal genes efficiently. We propose a multipoint LD approach for assessing the evidence of linkage and LD in a targeted chromosomal region by incorporating evidence from an unlinked region using the case-parent trio design. The paternal and maternal preferential transmission statistics defined in Liang et al. ([2001] Am. J. Hum. Genet. 68:937–950) are the primary statistics for this approach. Our generalized estimating equation (GEE) method builds on a model using the expected preferential transmission statistic from the targeted region conditional on this same statistic from the unlinked region. The major assumption is that there is no more than one trait locus in both the targeted region and unlinked region. The map position of an unobserved trait locus and its confidence interval can be calculated. Finally, we apply this approach to the African-American families drawn from the Collaborative Study on the Genetics of Asthma (CSGA). Previous analysis using this GEE approach developed by Liang et al. ([2001] Am. J. Hum. Genet. 68:937–950) suggested strong evidence of linkage and LD on chromosome 11, but only marginal evidence on chromosome 8. While conditioning on marker D11S937 on chromosome 11, a separate trait locus on chromosome 8 was estimated at , with a 95% confidence interval of (8.75, 14.59), and the test statistic shows significant evidence of linkage and LD (P-value=0.0198) in this region of chromosome 8. Genet Epidemiol 25:1–13, 2003. © 2003 Wiley-Liss, Inc.

The transmission disequilibrium test (TDT) has become a family-based method of reference to search for linkage disequilibrium (LD). Although it was first developed for dichotomous traits, numerous approaches have extended the TDT to quantitative phenotypes that either rely on regression or variance component techniques. Both of these approaches are based on some phenotypic distribution assumptions, the violation of which can lead to inflation of type I error rates, and derive information from phenotypic variability, so that their power is very low under some selection schemes (e.g., one-tailed selection). We propose a new family-based test of association for quantitative traits, denoted maximum-likelihood-binomial (MLB)-QTDT, which addresses the two previous issues by incorporating a latent binary variable that captures the LD information between the marker allele and the quantitative phenotype. The method can be understood as a classical TDT for binary traits that would include pure affected and pure unaffected children, and the probability for a child to be affected or unaffected depends on his/her quantitative phenotypic value. Simulation studies under the null hypothesis show that the MLB-QTDT provides very consistent type I errors even in small and/or selected samples. Under the alternative hypothesis, the MLB-QTDT has good power to analyze one-tailed selected samples, and performs as well as a classical approach in other designs. The MLB-QTDT is a flexible distribution-free method to test for LD with quantitative phenotypes in nuclear families, and can easily incorporate previous extensions developed in the context of family-based association studies with binary traits.

Many diseases or traits exhibit a varying age at onset. Recent data examples of prostate cancer and childhood diabetes show that compared to simply treating the disease outcome as affected vs. unaffected, incorporation of age-at-onset information into the transmission/disequilibrium type of test (TDT) does not appear to change the results much. In this paper, we evaluate the power of TDT as a function of age at onset, and show that age-at-onset information is most useful when the disease is common, or the relative risk associated with the high-risk genotype varies with age. Moreover, an extremely old unaffected subject can contribute substantially to the power of the TDT, sometimes as much as old-onset subjects. We propose a modified test statistic for testing no association between the marker at the candidate locus and age at onset. The simulation study was conducted to evaluate the finite sample properties of proposed and the TDT test statistics under various sampling schemes for trios of parents and offspring, as well as for sibling clusters where unaffected siblings were used as controls.

Haplotype sharing analysis was used to investigate the association of affection status with single nucleotide polymorphism (SNP) haplotypes within candidate gene 1 in one sample each from the isolated and the general population of Genetic Analysis Workshop (GAW) 12 simulated data. Gene 1 has direct influence on affection and harbors more than 70 SNPs. Haplotype sharing analysis depends heavily on previous haplotype estimation. Using GENEHUNTER haplotypes, strong evidence was found for most SNPs in the isolated population sample, thus providing evidence for an involvement of this gene, but the maximum -log(10)(p) values for the haplotype sharing statistics (HSS) test statistic did not correspond to the location of the true variant in either population. In comparison, transmission disequilibrium test (TDT) analysis showed the strongest results at the disease-causing variant in both populations, and these were outstanding in the general population. In this example, TDT analysis appears to perform better than HSS in identifying the disease-causing variant, using SNPs within a candidate gene in an outbred population. Simulations showed that the performance of HSS is hampered by closely spaced SNPs in strong linkage disequilibrium with the functional variant and by ambiguous haplotypes.

Association mapping in linked regions is a current major approach for the identification of genes for complex diseases. Loci contributing to linkage, even with small values of sibling recurrence risk (lambda(s)), may be equivalent to substantial underlying genetic effects for association studies. For disease alleles with a frequency as low as 1%, highly reliable association studies (80% power for significance level alpha=10(-6)) require only 277, 781, and 1289 families or cases and controls for loci detected with lambda(s) of 1.5, 1.1, and 1.05, respectively, under a multiplicative genetic model. Under alternative models, provided epistatic effects are minor, larger achievable sample sizes will provide sufficient power to map almost any disease gene that may have initially contributed to linkage.

Interleukin 13 (IL-13) has been demonstrated to have a crucial role in animal models of allergy and asthma. In human case-control genetic-association studies, the Arg130Gln polymorphism has been associated with elevated total serum IgE and an asthma diagnosis in atopic and nonatopic individuals (Graves et al. [2000] J. Allergy Clin. Immunol. 105:506-513; Heinzmann et al. [2000] Hum. Mol. Genet. 9:549-559). To apply family-based association methods, we obtained DNA samples from 685 asthmatic children from 640 sibships and their parents in the Childhood Asthma Management Program (CAMP). Six hundred and sixty-six asthmatic children had complete phenotypic information and were used for this analysis. We performed quantitative association analysis using the transmission disequilibrium test (TDT) on 22 individual phenotypes and 5 grouped phenotypes relating to allergy, airway responsiveness, pulmonary function, bronchodilator responsiveness, and asthma severity, using genotypes at the Arg130Gln polymorphism of the IL-13 gene. A positive association was obtained between Arg130Gln and a grouped phenotype of allergy (consisting of the individual phenotypes of eosinophils, IgE, and positive skin tests), using FBAT-GEE, a multivariate extension of the family-based association test (Lange et al. [2002] Biostatistics 1:1-15). The three phenotypes were then evaluated individually and revealed a significant association between total eosinophil count and the Arg130Gln locus; there was a trend for association between total IgE and the Arg130Gln polymorphism. The Arg130Gln polymorphism is associated with an elevated eosinophil count as well as with a grouped allergy phenotype, in children with mild to moderate asthma. No evidence for association was found between Arg130Gln and airway responsiveness, asthma diagnosis, or asthma severity.

The BCL3 gene has been considered a susceptibility locus for nonsyndromic cleft lip with or without cleft palate (NSCL/P), based on association and linkage studies in some populations. We evaluated an intragenic marker at the BCL3 gene and the microsatellite D19S178 (1.1 cM distant from the BCL3 gene) among 98 infants born with NSCL/P and their parents, using the transmission disequilibrium test (TDT) and a method for haplotype analysis. Our analysis, based on BCL3 alleles, revealed the existence of a marginal association of allele 135pb of the BCL3 gene with NSCL/P (χ2=3.60; P=0.058; 1 df), with a major effect in female (χ2=5.77; P=0.016; 1 df) and in familial cases (χ2=3.79; P=0.051; 1 df). However, the haplotype analysis detected no significant segregation distortion, even if the alleles of the D19S178 were grouped into two classes. These findings support previous findings that BCL3 plays a role in the etiology of NSCL/P as an allele of low penetrance or as a modifier locus. We hypothesize that there might be more than one mutation in this gene associated with NSCL/P, or alternatively, that more than one mutation has arisen associated with the 135-bp allele. Genet. Epidemiol. 23:364–374, 2002 © 2002 Wiley-Liss, Inc.

We use likelihood-based score statistics to test for association between a disease and a diallelic polymorphism, based on data from arbitrary types of nuclear families. The Nonfounder statistic extends the transmission disequilibrium test (TDT) to accommodate affected and unaffected offspring, missing parental genotypes, phenotypes more general than qualitative traits, such as censored survival data and quantitative traits, and residual correlation of phenotypes within families. The Founder statistic compares observed or inferred parental genotypes to those expected in the general population. Here the genotypes of affected parents and those with many affected offspring are weighted more heavily than unaffected parents and those with few affected of fspring. We illustrate the tests by applying them to data on a polymorphism of the SRD5A2 gene in nuclear families with multiple cases of prostate cancer. We also use simulations to compare the power of these family-based statistics to that of the score statistic based on Cox’s partial likelihood for censored survival data, and find that the family-based statistics have considerably more power when there are many untyped parents. The software program FGAP for computing test statistics is available at http://www.stanford.edu/dept/HRP/epidemiology/FGAP. Genet. Epidemiol. 22:128‐145, 2002. © 2002 Wiley-Liss, Inc.

Compound heterozygous mutations are mutations that occur on different copies of genes and may completely “knock-out” gene function. Compound heterozygous mutations have been implicated in a large number of diseases, but there are few statistical methods for analyzing their role in disease, especially when such mutations are rare. A major barrier is that phase information is required to determine whether both gene copies are affected and phasing rare variants is difficult. Here, we propose a method to test compound heterozygous and recessive disease models in case–parent trios. We propose a simple algorithm for phasing and show via simulations that tests based on phased trios have almost the same power as tests using true phase information. A further complication in the study of compound heterozygous mutations is that only families where both parents carry mutations are informative. Thus, the informative sample size will be quite small even when the overall sample size is not, making asymptotic approximations of the null distribution of the test statistic inappropriate. To address this, we develop an exact test that will give appropriate P-values regardless of sample size. Using simulation, we show that our method is robust to population stratification and significantly outperforms other methods when the causal model is recessive.

The transmission/disequilibrium test (TDT) for binary traits is a powerful method for detecting linkage between a marker locus and a trait locus in the presence of allelic association. The TDT uses information on the parent-to-offspring transmission status of the associated allele at the marker locus to assess linkage or association in the presence of the other, using one affected offspring from each set of parents. For testing for linkage in the presence of association, more than one offspring per family can be used. However, without incorporating the correlation structure among offspring, it is not possible to correctly assess the association in the presence of linkage. In this presentation, we propose a Bayesian TDT method as a complementary alternative to the classical approach. In the hypothesis testing setup, given two competing hypotheses, the Bayes factor can be used to weigh the evidence in favor of one of them, thus allowing us to decide between the two hypotheses using established criteria. We compare the proposed Bayesian TDT with a competing frequentist-testing method with respect to power and type I error validity. If we know the mode of inheritance of the disease, then the joint and marginal posterior distributions for the recombination fraction (θ) and disequilibrium coefficient (δ) can be obtained via standard MCMC methods, which lead naturally to Bayesian credible intervals for both parameters. Genet. Epidemiol. 22:41–51, 2002. © 2002 Wiley-Liss, Inc.

We compare the statistical power of the transmission disequilibrium test (TDT) with that of two likelihood-based linkage tests, the classical LOD score and a modified LOD score in which a linkage disequilibrium (LD) parameter is incorporated into the likelihood (LD-LOD). We hypothesize that, when LD is present, the LD-LOD will have the greatest power of the three tests because the TDT breaks a multiplex pedigree into triads, and the LOD score has previously been shown to have lower power when LD is present but not accounted for. We test this hypothesis using a simulation study in which we generate affected sib-pair (ASP) pedigrees under a range of genetic models, varying the genotypic relative risk (GRR) from 6 to 16. Because the likelihood-based tests require that a genetic model be specified, we compare the tests under two scenarios. First, we assume the true genetic model in the analysis, and second, we compare the tests when the LD-LOD (LOD) is maximized over two wrong genetic models. For the generating models we considered, we find that the LD-LOD has greater power than the TDT even when the genetic models is mis-specified and the results corrected for multiple tests. Extreme differences occur under the multiplicative and dominant models, for which the difference in power is as high as 40% at complete LD. The LOD score provides the lowest power in the presence of LD for the range of GRR considered here.

Transmission disequilibrium test (TDT) is a nuclear family-based analysis that can test linkage in the presence of association. It has gained extensive attention in theoretical investigation and in practical application; in both cases, the accuracy and generality of the power computation of the TDT are crucial. Despite extensive investigations, previous approaches for computing the statistical power of the TDT are neither accurate nor general. In this paper, we develop a general and highly accurate approach to analytically compute the power of the TDT. We compare the results from our approach with those from several other recent papers, all against the results obtained from computer simulations. We show that the results computed from our approach are more accurate than or at least the same as those from other approaches. More importantly, our approach can handle various situations, which include (1) families that consist of one or more children and that have any configuration of affected and nonaffected sibs; (2) families ascertained through the affection status of parent(s); (3) any mixed sample with different types of families in (1) and (2); (4) the marker locus is not a disease susceptibility locus; and (5) existence of allelic heterogeneity. We implement this approach in a user-friendly computer program: TDT Power Calculator. Its applications are demonstrated. The approach and the program developed here should be significant for theoreticians to accurately investigate the statistical power of the TDT in various situations, and for empirical geneticists to plan efficient studies using the TDT.

We randomly chose replicates 28 and 29 of the simulated data sets of Genetic Analysis Workshop 12 to model the dependence of affection status on covariates, quantitative traits, and genes using all living pedigree members. First we explored the relationship of affection status to demographic and environmental factors using logistic regression and the Cox proportional hazards models. In the second stage of our analyses the generalized transmission disequilibrium test (GTDT) was applied to nuclear families with at least two affected siblings to select single markers and high-risk alleles, which were tested in the population association analyses including all pedigree members. Multiple logistic regression models were fitted to investigate the joint contributions of genetic and nongenetic factors and a block-recursive modeling approach was adopted to study inherent hierarchical dependence structure in the data. We found that allele 2 on marker 35 of chromosome 6 is associated with higher risk compared with the other 3 alleles of this marker. In addition to this significant genetic effect, age at exam and four of the five quantitative traits (QT1, QT2, QT4, and QT5) had a significant association with the disease. Our results were obtained without knowledge of the true disease generating models.

Comorbidity, the association of two disorders, occurs commonly with complex diseases. In this paper, we investigate the effects of both true (within-family) comorbidity and spurious comorbidity due to ascertainment bias on the validity of both the parental and sibling control transmission/disequilibrium test. Specifically, we consider settings in which a candidate gene is unlinked to the target phenotype but is in linkage disequilibrium with a comorbid phenotype. We derive conditions under which the presence of true and/or spurious comorbidity will result in an artificial correlation between the target phenotype and the candidate gene.

The Hutterite and Collaborative Study on the Genetics of Asthma data sets provided by Genetic Analysis Workshop 12 were analyzed using a regression-based transmission/disequilibrium test that assesses linkage between a marker locus and quantitative trait locus when allelic association is present, as proposed by George et al. [Am J Hum Genet 65:236-45, 1999]. Because the same marker set and analytical technique was used, the results from these data sets are amenable for comparison. Statistically significant results common to both data sets were found on chromosomes 1 and 3. A noteworthy result, significant at p < 10(-4), was detected on chromosome 18 in the Hutterites.

George et al. [1999 Am J Hum Genet 65:236-245] proposed a regression-based TDT method for quantitative traits consisting of regressing the trait on the parental transmission of a marker allele. Zhu and Elston [2000] also developed a TDT method for quantitative traits by defining a linear transformation to condition out founder information. Both methods test the null hypothesis of no linkage or association and can be applied to general pedigree structures. In this paper, we compare the power of these two methods through simulation, sampling those nuclear families with at least one heterozygous parent. Overall, we find that a variant of Zhu and Elston's method with 2 d.f. is more powerful. However, if the mode of inheritance is known, then a most powerful test with 1 d.f. can be found. All these regression TDT tests require linkage to detect association, but a test that does not require linkage will be more powerful.

Due in part to an influential paper by Risch and Merikangas [(1996) Science 273:1516-1517], which suggested that disequilibrium tests would have greater power to detect genes of small effect than would linkage tests, interest in the use of the Transmission Disequilibrium Test (TDT) as an analysis tool for genomewide studies is steadily growing. However, the paper by Risch and Merikangas made several simplifying assumptions. One such assumption was that the underlying gene showed allelic homogeneity, and another was that the allele being measured was the actual susceptibility allele. Here we investigate the effect of allelic heterogeneity on the power of the TDT using multiplicative, additive, dominant, and recessive modes of inheritances in the context of a genomewide study. We further distinguish two cases: first, that the marker alleles are the actual susceptibility alleles, and second, that alleles are measured at a marker linked to the disease gene with zero recombination. We consider two family structures, either a single affected offspring (SAO) and two parents, or an affected sib-pair (ASP) and two parents. We find that, as expected, the power of the TDT declines as the number of susceptibility alleles at the locus being tested increases and the effect on power can be substantial. When a linked marker is measured rather than a susceptibility allele itself, sample sizes reach unattainable levels when as few as two susceptibility alleles are present. Across all the models we consider, the required number of families for a TDT with ASP sampling varies from 19 to over a million families. Thus, the TDT may not be an optimal test in the context of genomic screens under more biologically realistic assumptions.

Case-control studies provide a powerful approach for detecting disease susceptibility loci that have only a weak to moderate impact on the risk of disease, or markers that are in linkage disequilibrium with such loci. However, since any association detected in a case-control study may result from uncontrolled confounding, evidence for disease-marker associations obtained from such studies must be confirmed by alternative methods. Since studies that use the transmission/disequilibrium test or TDT are frequently employed to confirm disease-marker associations detected in case-control studies, data are increasingly available from both case-control studies and "TDT studies" of the same disease-marker association. It would, therefore, be useful to have a single measure of the magnitude of the disease-marker association that would allow for comparison of results from these two study designs. Such a measure could also be used to estimate minimum sample size requirements for TDT studies of previously reported disease-marker associations. An obvious measure of the disease-marker association in TDT studies is the frequency (T) with which heterozygous parents transmit the putative, high-risk marker allele to affected offspring. In this paper, it is shown that T can also be estimated from case-control data with a minimum of assumptions, and that T is the critical parameter for determining power and estimating sample sizes for the TDT.

The transmission disequilibrium test (TDT), an alternative to case-control analysis that is not influenced by population stratification, focuses on affected child trios (ACTs) comprising affected cases and their parents. Unaffected child trios (UCTs) have also been proposed but mainly to rule out segregation distortion. To explore situations when UCTs are preferable to detect transmission distortion, we compared the number of UCTs and ACTs needed to achieve 80% power for a wide variety of scenarios. For a given genetic model, UCT sample size declined rapidly with increasing disease prevalence, whereas ACT sample size remained constant. Furthermore, at some prevalence value (40-60% depending on model parameters), detection of transmission distortion could be accomplished with fewer UCTs than ACTs. Such high prevalence may be found in special populations (diabetes among Pima Indians), secondary conditions (renal/retinal complications in diabetes), and pharmacogenetics (responders to treatment). Also, because exposure to an additional risk factor can increase the disease prevalence in an exposed sub-group, we explored how sample size requirements vary by exposure status. Whereas power differences between exposed and unexposed ACTs could be explained solely by genetic risk ratios, sub-group-specific disease prevalence also played an important role in UCTs. Finally, we considered the impact of including 5, 10, 20, or 30% misclassified ACTs in the UCT sample and found that a 24, 58, 180, or 550% larger sample would be required. In conclusion, UCTs can detect transmission distortion more effectively than ACTs when disease prevalence reaches 40-60%, although some efficiency may be lost owing to misclassification. Moreover, focusing on particular sub-groups defined by exposure status can potentially increase power, but such gains depend heavily on the nature of the gene-exposure interaction.

The probability model of parental transmission (of a multiallelic marker) to affected offspring has been reparameterized in such a way as to distinguish the recombination fraction parameter from the association parameters. The advantage of this reparameterization is that statistical tests can be developed which disentangle linkage and association. It is shown that these tests perform well compared with a standard approach that is commonly used. Further, the simulated data (Problem 2) enable a comparison to be made of the performance of these tests under different family sampling schemes.

A new approach to scanning the genome is presented to detect linkage disequilibrium caused specifically by population admixture. In contrast to current linkage genome scanning methods to find causal genes for complex diseases, this new method should be powerful to find genes for multilocus traits, particularly those genes that lead to the highest population attributable risk. Such a scan using the African-American population is generally feasible for mapping common diseases. A conservative threshold is also provided for such association mapping. Genet. Epidemiol. 17:79–101, 1999. © 1999 Wiley-Liss, Inc.

We analyzed some simulated data to assess the success of statistical methodologies to establish the role of the environmental factors (EF) and to identify associated and linked markers. We considered five replicates for each of the four studies, and, with the knowledge of the generating model, concentrated our analyses on chromosomes (CH) 1, 3, and 5. To determine the influence of EF and associated markers on the affection status (AS), we utilized chi-square tests for independence and recursive partitioning (via the CART software). To identify linked markers, we scanned the relevant chromosomes with nonparametric multipoint linkage (NPL) and transmission/disequilibrium tests. These analyses were performed on the whole data set as well as on subsets of individuals and families defined by exposure to EF. CART correctly selected the associated marker (D1G024) and EF1 for Study (ST) 1 and did not generate trees for the other studies. NPL identified the relevant regions on CH3 and CH5 but failed to do so for CH1, except in ST4. Stratifying families by exposure to EF1 did not consistently increase sensitivity of NPL to the relevant CH3 markers, but did help characterize the genetic heterogeneity and identify linked families.

The extended transmission disequilibrium test (ETDT) of Sham and Curtis [1995] is a powerful test of the null hypothesis of no linkage between a multi-allelic marker locus and a disease susceptibility locus of unknown location in the presence of association between alleles at the two loci. We propose a generalization of the ETDT to test simultaneously for linkage of markers to two unlinked disease loci. Analysis of the simulated data for Problem 2 would suggest improvements in power to detect linkage to pairs of disease loci over single locus tests. This is as a result of the two locus model taking account of epistasis between the disease loci.

The transmission/disequilibrium test (TDT), sib-TDT and two combined tests have been implemented in an attempt to identify loci across the genome that may be involved in alcohol dependence. Since these tests are based on the existence of association between marker and disease loci, the low-density map used (13 cM) will have missed any disease loci situated between markers. Nevertheless, genome-wide suggestive linkage results were found at three markers - D6S474, D8S1715, and D12S372 - two of which also gave nominally significant evidence by two-point linkage analysis. These are regions that deserve further investigation with respect to their involvement in alcohol dependence, and in order to evaluate the relative efficacy of the different methods used.

The role of a gene in a disease may be hidden by the presence of another risk factor such as an environmental factor. In that case, stratifying the data according to this factor strengthens power to detect linkage or association. We followed this strategy on the simulated data provided by GAW11. The transmission/disequilibrium test (TDT) and the maximum likelihood score (MLS) were performed on the first replicate of 100 sib pairs from the population in which the disease risk was significantly influenced by an environmental factor (E1). However, only the TDT was powerful enough to detect one of the four loci involved in the genetic determination of the disease. The MLS showed no evidence for linkage after taking into account the fact that multiple tests were performed. Even when stratifying the sample according to the presence of E1, no additional loci could be detected. Given the simulated models, 100 sib pairs are too low a sample size for a systematic screening of the genome, which in this case was an analysis of 300 markers.

We analyzed 105 multiplex families from the Collaborative Study on the Genetics of Alcoholism (COGA) for markers on chromosome 1 (n = 20) and chromosome 7 (n = 19) with the GENEHUNTER program. On chromosome 1, three markers (D1S532, D1S1588, and D1S534) in single-point analysis and five markers in multipoint analysis (D1S532, D1S1588, D1S1675, D1S534, and D1S1595) showed a nonparametric linkage (NPL) p-value < 0.05. They mapped in two different but nearby regions, spanning, respectively, 18 cM (D1S532, D1S1588) and 19 cM (D1S1675, D1S534, and D1S1595) and separated by a 20-cM interval. The highest NPL score was obtained for D1S534 (NPL = 2.26, p = 0.013 for single-point analysis and NPL = 2.81, p = 0.0029, for multipoint analysis). The maximum NPL score on chromosome 7 was observed for D7S1793 (NPL = 1.72, p = 0.044 for single-point analysis and NPL = 2.02, p = 0.023 for multipoint analysis). The markers which showed NPL p-values < 0.05 on chromosome 1 (D1S532, D1S1588, D1S1675, D1S534, and D1S1595) and on chromosome 7 (D7S1793) were analyzed for association using the transmission/disequilibrium test. None of the alleles at these six loci showed a distorted transmission pattern. These data indicate that the two loci "suggestively" linked to alcohol dependence are either in linkage equilibrium with a susceptibility locus or are too far from the susceptibility locus to show disequilibrium, if present.

We applied the transmission/disequilibrium test (TDT) for sibs (S-TDT) and for families with one parent (1-TDT), to the Collaborative Study on the Genetics of Alcoholism data set. The combined test is used to screen the whole genome to locate genes responsible for alcohol dependence. This analysis supports the previous finding that the region close to GABRB1 on chromosome 4 might be associated with alcohol dependence. The regions close to D6S474 and D11S1998 are also of particular interest. We found segregation distortion at the GR1K1 locus. The segregation distortion might be due to the binning method used in genotyping at this locus.

We applied several novel tests for association and linkage in the presence of association to the Genetic Analysis Workshop 11 Problem 1 data set. Our analyses included a Hardy-Weinberg test for association between a marker and a disease susceptibility locus, a Bayesian transmission/disequilibrium test, and a Bayesian case-control test. Positive results for each of these methods require the presence of population association between the marker and a disease susceptibility locus.

The association of a quantitative trait with transmission disequilibrium of parental marker alleles can be a powerful method to discover the genetic basis of the trait. However, current methods require marker genotypes on all parents. We present a new method that allows the assessment of the association of a quantitative trait with transmission disequilibrium of marker alleles when parental marker genotypes are missing, but marker genotypes for sibships are available. Because our approach is based on regression methods, additional covariates, including multiple marker loci, can be included in our proposed method of analysis. Application of this methodology to the COGA data to assess the association of quantitative traits (ERPs) with marker loci on chromosome 7 failed to identify statistically significant transmission disequilibrium.

There may be a different genetic basis for the two forms of the disease simulated in Problem 2 and the complex disease may be affected by environmental factors. Hence, we investigate the effects of two environmental factors. We selected 400 nuclear families from the data generated for Problem 2. Affection status was investigated in several ways. Individuals with severe and mild forms of the disease were both considered affected, individuals with only the severe form were considered affected while those with the mild form were considered unknown, and individuals with only the mild form were considered affected while those with the severe form were considered unknown. We found evidence of linkage between putative disease loci and markers in the D3G042-D3G049 and D5G031-D5G042 regions when we considered severely and mildly affected individuals as affected and also in the region D1G004-D1G013 when mildly affected individuals were considered unknown. We observed interactions between the first environmental factor and D1G043 among healthy sib pairs.

The transmission disequilibrium test (TDT) recently has become a popular method of testing for linkage in the presence of association due to its simplicity and advantages over other within-family analytic methods. In this paper, we describe a logistic regression extension to the TDT that can be used to test for differences in linkage disequilibrium as a function of one or more continuous and/or categorical explanatory variables. We highlight important features of this method and demonstrate some of its possible uses. We applied these analyses to test for linkage disequilibrium between the dopamine receptor D2 (DRD2) and alcohol dehydrogenase 3 (ADH3) genes and both diagnostic and quantitative indices of alcoholism. Using data from the Collaborative Study on the Genetics of Alcoholism data set, we found evidence suggesting linkage disequilibrium between DRD2 and ADH3 and quantitative indices of alcoholism and correlated phenotypes corresponding to smoking and personality. None of the evidence for linkage disequilibrium varied by sex or age.

Many researchers are considering the use of transmission/disequilibrium tests (TDT) for trios of genotypes (father, mother, child) as a method for localizing genes associated with complex diseases. We evaluate the effect of random errors (allele changes) in trios on the power to detect linkage. For a marker in the simulated data set, one allele is associated with the fictitious disease in a certain subpopulation. For the data as given (no errors), our power to detect linkage using the multiallelic TDT (TDTmhet) is 68% (critical p-value set at 0.0001). We introduce errors into trios at various rates (1%, 5%, or 10%), remove only trios displaying mendelian inconsistencies, and recalculate power to detect linkage. Our principal finding is that there is power loss to detect linkage with the TDTmhet when errors are introduced. We observe power losses of 8%, 16%, and 48% for error rates of 1%, 5%, and 10%, respectively. To determine the source of the power loss, we perform Monte Carlo simulations. At the 1% and 5% rates, we conclude that power loss is due primarily to loss in sample size. At the 10% rate, we observe substantial power loss due to error introduction in addition to sample size reduction. We also determine, given a particular error rate, the probability that we detect errors if we use only mendelian consistency as a check. We find that the mean detection rates for the data sets with 1%, 5%, or 10% error rates are 58%, 60%, and 62%, respectively. As a result, the apparent error rate appears to be almost half the true error rate. Based on these results, we recommend that researchers maintain error rates below 5% when using the TDTmhet for linkage, use additional methods beyond mendelian consistency checks when searching for errors in their data, and modify sample size calculations when accounting for errors in their genotype data.

Recently, George et al. proposed a regression-based transmission/disequilibrium test for linkage using information on the parent-to-offspring transmission status of an allele at a marker locus. We extended this test by simultaneously testing for any population association by incorporating the presence/absence status of the associated allele as a covariate in the model. We used this method to analyze markers on chromosomes 1 through 21 of the Collaborative Study on the Genetics of Alcoholism data on alcoholism for possible association and linkage. We found nominal significance (at the 0.02 level) at eight different regions for linkage, though statistical significance may not be concluded due to multiple testing. The strongest evidence of linkage was observed for markers D4S2639 and D12S397 with p-values less than 0.005. We also found strong association between the trait and alleles 149 of D7S691 and 131 of D21S1437.

We report the results of the analysis of three measures of alcoholism and six associated symptoms using transmission disequilibrium (TDT) analysis on data from the Collaborative Study on the Genetics of Alcoholism data set. Implementation of identity-by-state (IBS) routines for error checking revealed 10 reported full siblings that were rejected as a full sibling to all of their purported full siblings with p < 0.05. TDT analysis revealed two loci with significant transmission disequilibrium (p < 0.001) on chromosomes 1 and 7. Analysis by parental origin found alleles at three loci displaying significant disequilibrium in the transmission of the paternal alleles for at least three of the nine tested traits. These loci are on chromosomes 6, 9, and 13. Analyses of Caucasian families alone and the use of a single affected individual from each family also yielded significant results for the loci on chromosomes 6, 9, and 13.

We approached the simulation as though it were an international study with similar but not identical information being collected from different populations. In keeping with this we analyzed one replicate from each population. Initially we examined the risk of disease in relatives of cases to determine whether the disease appeared to be “more genetic” in one population than in the others and we examined the evidence for environmental risk factors in each population. Non-parametric linkage analysis and transmission/disequilibrium testing (TDT) were used to search for loci linked to the disease in each population. Using these methods we identified several candidate regions for a susceptibility gene which on examination of the answers are explicable in terms of the underlying model.

Methods of both linkage analysis and association analysis may be model-based or model-free. The former are useful for initial exploratory analysis, the latter for more detailed multivariate genometric analysis. Linkage leads to an association, but that association may be solely intrafamilial. Allelic association may be due to pleiotropy, linkage disequilibrium, meiotic drive, selection, or population stratification. Using non-transmitted parental alleles as controls for alleles transmitted to cases, in conjunction with a McNemar-type test, does not detect association in the absence of linkage. Model-based analyses should use models that approximate the complexity of the disease being studied in order to be both robust and powerful.

Since its introduction into the statistical genetics literature, the transmission disequilibrium test (TDT) has seen widespread use in analyses of linkage and association due not only to its simplicity but also to its desirable properties relative to other within-family analytic methods. In this paper, we describe an extension to the TDT useful for examining genetic heterogeneity. This extension uses contingency table analyses such as log-linear analysis to test for differences in linkage disequilibrium across levels of one or more moderator variables. We applied these analyses to test for linkage disequilibrium between the dopamine transporter gene (DAT1) and bipolar disorder, as well as for genetic heterogeneity due to sex, diagnostic breadth, and study site. Using data from two studies (the UCSD/UBC and Cardiff data sets), we found evidence suggesting linkage disequilibrium between DAT1 and bipolar disorder, as well as heterogeneity due to diagnostic breadth and study site.

From a single extended pedigree simulation replicate, high density, affected only subpedigrees were isolated, based on the T > 40 affected status for the disease trait, Q1. On this sample of 14 pedigrees, with a range of two to six affected members (48 total), we conducted a haplotype based, multilocus, nonparametric genome-wide search of the provided data (367 markers) using the computer program GENEHUNTER. As with most genome screens in complex diseases, the objective of this strategy was to identify regions (hot-spots) which breached our predetermined threshold (p < 0.05), requiring confirmation by other groups or consortia. Of the six regions with threshold breaching scores (p < 0.05), the most promising, on chromosome 8 and chromosome 4, corresponded to the locations of MG2 and MG3. Both of these regions have multiple, consecutive markers above threshold and contained the only scores that exceeded p < 0.01. In addition, a fourth hot-spot consisting of a single marker above threshold, was less than 15 cM from MG1 on chromosome 5. The positions of the remaining three hot-spots did not correspond to the any of the major genes and are therefore false positives. An additional analysis of a single nuclear pedigree simulation replicate, using the extended transmission disequilibrium test (ETDT), was applied to markers in each of the above hot-spot regions to look for evidence of disequilibrium with the disease trait. This analysis provided weak additional support for the chromosome 8 finding, even though the sample was very small (36 pedigrees containing 44 affected offspring).

We describe an extension to the TDT (transmission/disequilibrium test) which allows for more than two marker alleles and for covariates measured on the parent or offspring. We also describe a systematic genomic search where the mod score (maximized lod score) is computed for each marker under constraints on the population prevalence or penetrances of a single locus.

The transmission/disequilibrium test (TDT) is extended in two ways for a multiallelic marker: (1) to compare transmitted and nontransmitted alleles from a single heterozygous parent and (2) to compare genotypes formed by the two transmitted alleles and genotypes formed by the two nontransmitted alleles using the information on both parents, heterozygous or not, simultaneously. © 1995 Wiley-Liss, Inc.