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.     

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.     

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.     

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.     

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.     

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: history, subdivision, and admixture.

Disease association with a genetic marker is often taken as a preliminary indication of linkage with disease susceptibility. However, population subdivision and admixture may lead to disease association even in the absence of linkage. In a previous paper, we described a test for linkage (and linkage disequilibrium) between a genetic marker and disease susceptibility; linkage is detected by this test only if association is also present. This transmission/disequilibrium test (TDT) is carried out with data on transmission of marker alleles from parents heterozygous for the marker to affected offspring. The TDT is a valid test for linkage and association, even when the association is caused by population subdivision and admixture. In the previous paper, we did not explicitly consider the effect of recent history on population structure. Here we extend the previous results by examining in detail the effects of subdivision and admixture, viewed as processes in population history. We describe two models for these processes. For both models, we analyze the properties of (a) the TDT as a test for linkage (and association) between marker and disease and (b) the conventional contingency statistic used with family data to test for population association. We show that the contingency test statistic does not have a chi 2 distribution if subdivision or admixture is present. In contrast, the TDT remains a valid chi 2 statistic for the linkage hypothesis, regardless of population history.     

Transmission/disequilibrium test based on haplotype sharing for tightly linked markers

Studies using haplotypes of multiple tightly linked markers are more informative than those using a single marker. However, studies based on multimarker haplotypes have some difficulties. First, if we consider each haplotype as an allele and use the conventional single-marker transmission/disequilibrium test (TDT), then the rapid increase in the degrees of freedom with an increasing number of markers means that the statistical power of the conventional tests will be low. Second, the parental haplotypes cannot always be unambiguously reconstructed. In the present article, we propose a haplotype-sharing TDT (HS-TDT) for linkage or association between a disease-susceptibility locus and a chromosome region in which several tightly linked markers have been typed. This method is applicable to both quantitative traits and qualitative traits. It is applicable to any size of nuclear family, with or without ambiguous phase information, and it is applicable to any number of alleles at each of the markers. The degrees of freedom (in a broad sense) of the test increase linearly as the number of markers considered increases but do not increase as the number of alleles at the markers increases. Our simulation results show that the HS-TDT has the correct type I error rate in structured populations and that, in most cases, the power of HS-TDT is higher than the power of the existing single-marker TDTs and haplotype-based TDTs.     

The problems of using the transmission/disequilibrium test to infer tight linkage

Family-based association methods such as the transmission/disequilibrium test (TDT) have become very popular during the past few years, often being preferred to case-control studies because family-based approaches avoid the difficulties of ascertainment of appropriate populations of cases and controls for case-control studies. Significant TDT results indicate both linkage and allelic association. However, significant TDT results are often interpreted as implying tight linkage of marker and disease locus, and we shall argue here that, in general, this interpretation is not justified.     

Genome-wide association filtering using a highly locus-specific transmission/disequilibrium test

Multimarker transmission/disequilibrium tests (TDTs) are powerful association and linkage tests used to perform genome-wide filtering in the search for disease susceptibility loci. In contrast to case/control studies, they have a low rate of false positives for population stratification and admixture. However, the length of a region found in association with a disease is usually very large because of linkage disequilibrium (LD). Here, we define a multimarker proportional TDT (mTDT _P ) designed to improve locus specificity in complex diseases that has good power compared to the most powerful multimarker TDTs. The test is a simple generalization of a multimarker TDT in which haplotype frequencies are used to weight the effect that each haplotype has on the whole measure. Two concepts underlie the features of the metric: the ‘common disease, common variant’ hypothesis and the decrease in LD with chromosomal distance. Because of this decrease, the frequency of haplotypes in strong LD with common disease variants decreases with increasing distance from the disease susceptibility locus. Thus, our haplotype proportional test has higher locus specificity than common multimarker TDTs that assume a uniform distribution of haplotype probabilities. Because of the common variant hypothesis, risk haplotypes at a given locus are relatively frequent and a metric that weights partial results for each haplotype by its frequency will be as powerful as the most powerful multimarker TDTs. Simulations and real data sets demonstrate that the test has good power compared with the best tests but has remarkably higher locus specificity, so that the association rate decreases at a higher rate with distance from a disease susceptibility or disease protective locus.     

Power comparisons of the transmission/disequilibrium test and sib-transmission/disequilibrium-test statistics.

Brachydactyly type B (BDB), an autosomal dominant disorder, is the most severe of the brachydactylies and is characterized by hypoplasia or absence of the terminal portions of the index to little fingers, usually with absence of the nails. The thumbs may be of normal length but are often flattened and occasionally are bifid. The feet are similarly but less severely affected. We have performed a genomewide linkage analysis of three families with BDB, two English and one Portugese. The two English families show linkage to the same region on chromosome 9 (combined multipoint maximum LOD score 8.69 with marker D9S257). The 16-cM disease interval is defined by recombinations with markers D9S1680 and D9S1786. These two families share an identical disease haplotype over 18 markers, inclusive of D9S278-D9S280. This provides strong evidence that the English families have the same ancestral mutation, which reduces the disease interval to <12.7 cM between markers D9S257 and D9S1851 in chromosome band 9q22. In the Portuguese family, we excluded linkage to this region, a result indicating that BDB is genetically heterogeneous. Reflecting this, there were atypical clinical features in this family, with shortening of the thumbs and absence or hypoplasia of the nails of the thumb and hallux. These results enable a refined classification of BDB and identify a novel locus for digit morphogenesis in 9q22.     

A sibship test for linkage in the presence of association: the sib transmission/disequilibrium test.

Linkage analysis with genetic markers has been successful in the localization of genes for many monogenic human diseases. In studies of complex diseases, however, tests that rely on linkage disequilibrium (the simultaneous presence of linkage and association) are often more powerful than those that rely on linkage alone. This advantage is illustrated by the transmission/disequilibrium test (TDT). The TDT requires data (marker genotypes) for affected individuals and their parents; for some diseases, however, data from parents may be difficult or impossible to obtain. In this article, we describe a method, called the "sib TDT" (or "S-TDT"), that overcomes this problem by use of marker data from unaffected sibs instead of from parents, thus allowing application of the principle of the TDT to sibships without parental data. In a single collection of families, there might be some that can be analyzed only by the TDT and others that are suitable for analysis by the S-TDT. We show how all the data may be used jointly in one overall TDT-type procedure that tests for linkage in the presence of association. These extensions of the TDT will be valuable for the study of diseases of late onset, such as non-insulin-dependent diabetes, cardiovascular diseases, and other diseases associated with aging.     

Monte Carlo pedigree disequilibrium test for markers on the X chromosome

Because of the need for fine mapping of disease loci and the availability of dense single-nucleotide-polymorphism markers, many forms of association tests have been developed. Most of them are applicable only to triads, whereas some are amenable to nuclear families (sibships). Although there are a number of methods that can deal with extended families (e.g., the pedigree disequilibrium test [PDT]), most of them cannot accommodate incomplete data. Furthermore, despite a large body of literature on association mapping, only a very limited number of publications are applicable to X-chromosomal markers. In this report, we first extend the PDT to markers on the X chromosome for testing linkage disequilibrium in the presence of linkage. This method is applicable to any pedigree structure and is termed "X-chromosomal pedigree disequilibrium test" (XPDT). We then further extend the XPDT to accommodate pedigrees with missing genotypes in some of the individuals, especially founders. Monte Carlo (MC) samples of the missing genotypes are generated and used to calculate the XMCPDT (X-chromosomal MC PDT) statistic, which is defined as the conditional expectation of the XPDT statistic given the incomplete (observed) data. This MC version of the XPDT remains a valid test for association under linkage with the assumption that the pedigrees and their associated affection patterns are drawn randomly from a population of pedigrees with at least one affected offspring. This set of methods was compared with existing approaches through simulation, and substantial power gains were observed in all settings considered, with type I error rates closely tracking their nominal values.