The transmission/disequilibrium test and parental-genotype reconstruction: the reconstruction-combined transmission/ disequilibrium test

Spielman and Ewens recently proposed a method for testing a marker for linkage with a disease, which combines data from families with and without information on parental genotypes. For some families without parental-genotype information, it may be possible to reconstruct missing parental genotypes from the genotypes of their offspring. The treatment of such a reconstructed family as if parental genotypes have been typed, however, can introduce bias. In the present study, a new method is presented that employs parental-genotype reconstruction and corrects for the biases resulting from reconstruction. The results of an application of this method to a real data set and of a simulation study suggest that this approach may increase the power to detect linkage.     

利用传递不平衡分析在多群体中鉴别猪脐疝易感基因

在本实验室前期利用白色杜洛克×二花脸F₂资源家系开展脐疝易感位点全基因组扫描定位的基础上,文章在7号染色体上的SWR1928和10号染色体上的SW830易感标记区域,结合脐疝发病机制在多群体中进行脐疝位置功能候选基因的筛选和易感位点的精细定位。在两个显著关联的微卫星位点区域搜寻到12个位置功能候选基因,采用比较测序法,选取12个候选基因内共计40个SNP位点在白色杜洛克×二花脸资源家系F₂/F₃脐疝群体中进行基因分型,利用Plink v1.07软件对基因型数据进行质量控制和传递不平衡(Transmission disequilibrium test,TDT)分析。结果表明,IL16(Interleukin 16)基因中的g.708C>T位点和CDC73(Cell division cycle 73)基因中的g.10664G>A位点与脐疝的关联性达到显著水平(P<0.05)。对这两个位点在西方商业猪种脐疝患病家系中进行基因分型和TDT验证分析,发现CDC73基因中的g.10664G>A位点仍与猪脐疝呈显著关联(P<0.05)。同时对CDC73基因中与资源家系脐疝呈弱相关的两个SNP位点g.10546A>G和g.10811A>G在西方商业猪种中进行TDT验证分析,发现这两个SNP位点与商业猪种脐疝发生的关联性达到极显著水平(P<0.01)。根据文章的分析结果,结合脐疝发生的生理机制及CDC73基因的生物学功能,推测CDC73基因可能为猪脐疝发生的易感基因。     

Respiratory distress syndrome: evaluation of genetic susceptibility and protection by transmission disequilibrium test

Based on epidemiological data and genetic association studies, neonatal respiratory distress syndrome (RDS) is a complex disease with a multigenic background. The genes coding for surfactant proteins (SP) A and B have been assigned as the most likely genes in the etiology of RDS. The major factor predisposing to RDS is prematurity, and thus the phenotype of a very premature newborn infant that does not develop the disease can be regarded as hypernormal. Altogether 107 father-mother-offspring trios were divided into two sets according to the proband's phenotype, to evaluate familial segregation of candidate gene polymorphisms by the transmission disequilibrium test. A set of 76 trios were analyzed for transmission disequilibrium from parents to affected offspring. Another set of 31 trios were studied for allele transmission from parents to hypernormal offspring born very prematurely before the gestational age of 32 weeks. SP-A1-A2 haplotype 6A(2)-1A(0) showed significant excess transmission to affected infants and SP-A1 allele 6A(2) decreased transmission to the hypernormals. The present family study provides strong support for a direct or indirect role of the SP-A alleles as genetic predisposers to RDS in premature infants. The inclusion of parent-hypernormal offspring trios in transmission disequilibrium test is a useful approach to test for genetic protection against a disease.     

Analytic power and sample size calculation for the genotypic transmission/disequilibrium test in case‐parent trio studies

Case‐parent trio studies considering genotype data from children affected by a disease and their parents are frequently used to detect single nucleotide polymorphisms (SNPs) associated with disease. The most popular statistical tests for this study design are transmission/disequilibrium tests (TDTs). Several types of these tests have been developed, for example, procedures based on alleles or genotypes. Therefore, it is of great interest to examine which of these tests have the highest statistical power to detect SNPs associated with disease. Comparisons of the allelic and the genotypic TDT for individual SNPs have so far been conducted based on simulation studies, since the test statistic of the genotypic TDT was determined numerically. Recently, however, it has been shown that this test statistic can be presented in closed form. In this article, we employ this analytic solution to derive equations for calculating the statistical power and the required sample size for different types of the genotypic TDT. The power of this test is then compared with the one of the corresponding score test assuming the same mode of inheritance as well as the allelic TDT based on a multiplicative mode of inheritance, which is equivalent to the score test assuming an additive mode of inheritance. This is, thus, the first time the power of these tests are compared based on equations, yielding instant results and omitting the need for time‐consuming simulation studies. This comparison reveals that these tests have almost the same power, with the score test being slightly more powerful.     

Comments on the entropy-based transmission/disequilibrium test

It has recently been claimed in this journal (Zhao et al. in Hum Genet 121:357–367, 2007) that a so-called “entropy-based” TDT test has improved power over the standard TDT test of Spielman et al. (Am J Hum Genet 52:506–516, 1993). We show that this claim is contradicted by standard statistical theory as well as by our simulation results. We show that the incorrect claim arises because of inappropriate assumptions, and also show that the entropy-based statistic has various undesirable properties.     

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.     

An entropy-based genome-wide transmission/disequilibrium test

Availability of a large collection of single nucleotide polymorphisms (SNPs) and efficient genotyping methods enable the extension of linkage and association studies for complex diseases from small genomic regions to the whole genome. Establishing global significance for linkage or association requires small P-values of the test. The original TDT statistic compares the difference in linear functions of the number of transmitted and nontransmitted alleles or haplotypes. In this report, we introduce a novel TDT statistic, which uses Shannon entropy as a nonlinear transformation of the frequencies of the transmitted or nontransmitted alleles (or haplotypes), to amplify the difference in the number of transmitted and nontransmitted alleles or haplotypes in order to increase statistical power with large number of marker loci. The null distribution of the entropy-based TDT statistic and the type I error rates in both homogeneous and admixture populations are validated using a series of simulation studies. By analytical methods, we show that the power of the entropy-based TDT statistic is higher than the original TDT, and this difference increases with the number of marker loci. Finally, the new entropy-based TDT statistic is applied to two real data sets to test the association of the RET gene with Hirschsprung disease and the Fcγ receptor genes with systemic lupus erythematosus. Results show that the entropy-based TDT statistic can reach p-values that are small enough to establish genome-wide linkage or association analyses.     

Unbiased application of the transmission/disequilibrium test to multilocus haplotypes

When the transmission/disequilibrium test (TDT) is applied to multilocus haplotypes, a bias may be introduced in some families for which both parents have the same heterozygous genotype at some locus. The bias occurs because haplotypes can only be deduced from certain offspring, with the result that the transmissions of the two parental haplotypes are not independent. We obtain an unbiased TDT for individual haplotypes by calculating the correct variance for the transmission count within a family, using information from multiple siblings if they are available. An existing correction for dependence between siblings in the presence of linkage is retained. To obtain an unbiased multihaplotype TDT, we must either count transmissions from one randomly chosen parent or count all transmissions and estimate the significance level empirically. Alternatively, we may use missing-data techniques to estimate uncertain haplotypes, but these methods are not robust to population stratification. An illustration using data from the insulin-gene region in type 1 diabetes shows that the validity and power of the TDT may vary by an order of magnitude, depending on the method of analysis.     

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.     

A note on power approximations for the transmission/disequilibrium test

The transmission/disequilibrium test (TDT) is a popular method for detection of the genetic basis of a disease. Investigators planning such studies require computation of sample size and power, allowing for a general genetic model. Here, a rigorous method is presented for obtaining the power approximations of the TDT for samples consisting of families with either a single affected child or affected sib pairs. Power calculations based on simulation show that these approximations are quite precise. By this method, it is also shown that a previously published power approximation of the TDT is erroneous.     

The transmission/disequilibrium test for linkage on the X chromosome

The transmission/disequilibrium test (TDT), which detects linkage between a marker and disease loci in the presence of linkage disequilibrium, was introduced by Spielman et al. The original TDT requires families in which the genotypes are known for both parents and for at least one affected offspring, and this limits its applicability to diseases with late onset. The sib-TDT, or S-TDT, which utilizes families with affected and unaffected siblings, was introduced as an alternative method, by Spielman and Ewens, and the TDT and S-TDT can be combined in an overall test (i.e., a combined-TDT, or C-TDT). The TDT statistics described so far are for autosomal chromosomes. We have extended these TDT methods to test for linkage between X-linked markers and diseases that affect either males only or both sexes. For diseases of late onset, when parental genotypes are often unavailable, the X-linkage C-TDT may allow for more power than is provided by the X-linkage TDT alone.     

The quantitative trait linkage disequilibrium test: a more powerful alternative to the quantitative transmission disequilibrium test for use in the absence of population stratification

Linkage analysis based on identity-by-descent allele-sharing can be used to identify a chromosomal region harboring a quantitative trait locus (QTL), but lacks the resolution required for gene identification. Consequently, linkage disequilibrium (association) analysis is often employed for fine-mapping. Variance-components based combined linkage and association analysis for quantitative traits in sib pairs, in which association is modeled as a mean effect and linkage is modeled in the covariance structure has been extended to general pedigrees (quantitative transmission disequilibrium test, QTDT). The QTDT approach accommodates data not only from parents and siblings, but also from all available relatives. QTDT is also robust to population stratification. However, when population stratification is absent, it is possible to utilize even more information, namely the additional information contained in the founder genotypes. In this paper, we introduce a simple modification of the allelic transmission scoring method used in the QTDT that results in a more powerful test of linkage disequilibrium, but is only applicable in the absence of population stratification. This test, the quantitative trait linkage disequilibrium (QTLD) test, has been incorporated into a new procedure in the statistical genetics computer package SOLAR. We apply this procedure in a linkage/association analysis of an electrophysiological measurement previously shown to be related to alcoholism. We also demonstrate by simulation the increase in power obtained with the QTLD test, relative to the QTDT, when a true association exists between a marker and a QTL.