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Linkage Analysis by a Transmission/Disequilibrium Test of Russian Sibling Pairs with Coronary Artery DiseaseWe studied the association between coronary artery disease (CAD) and polymorphisms of theABCA1, ACE, AGT, eNOSandEFNB3genes in 85 Russian patients with angiography-proven CAD and 100 of their siblings. No gene analyzed had a z-score value of more than 2.47 for CAD or for its main clinical presentations due to sibling transmission/disequilibrium test (S-TDT). However, the DD genotype ofACEis significantly more prevalent in siblings with CAD [p= 0.025, relative risk(RR)2.8], angina (p= 0.028,RR= 3.3) and myocardial infarction (MI) (p= 0.018,RR= 5.5). An increased risk of CAD, and its main manifestations, was associated with the R1587 allele of theABCA1gene: theRRfor developing CAD was 4.88, for MI 6.18, and for angina 3.69 for siblings who were carriers of the R1587R and R1587K genotypes. Index of stenosis was significantly higher in probands with the K219K and R219K genotypes (p= 0.001). The combination of genotype K219K with R219K was more frequent among siblings with CAD (p= 0.044,RR= 2.38), arterial hypertension (p= 0.023,RR= 2.87) and angina (p= 0.027,RR= 3.3). Thus, none of the genes studied can be considered as the main gene associated with CAD. However, the insertion/deletion (I/D) polymorphism of theACEgene and the R219K and R1587K variants ofABCA1are associated with a higher likelihood of developing CAD, MI and angina among Russians who have siblings affected by CAD.

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.

The transmission/disequilibrium test (TDT) is a popular, simple, and powerful test of linkage, which can be used to analyze data consisting of transmissions to the affected members of families with any kind pedigree structure, including affected sib pairs (ASPs). Although it is based on the preferential transmission of a particular marker allele across families, it is not a valid test of association for ASPs. Martin et al. devised a similar statistic for ASPs, Tsp, which is also based on preferential transmission of a marker allele but which is a valid test of both linkage and association for ASPs. It is, however, less powerful than the TDT as a test of linkage for ASPs. What I show is that the differences between the TDT and Tsp are due to the fact that, although both statistics are based on preferential transmission of a marker allele, the TDT also exploits excess sharing in identity-by-descent transmissions to ASPs. Furthermore, I show that both of these statistics are members of a family of “TDT-like” statistics for ASPs. The statistics in this family are based on preferential transmission but also, to varying extents, exploit excess sharing. From this family of statistics, we see that, although the TDT exploits excess sharing to some extent, it is possible to do so to a greater extent—and thus produce a more powerful test of linkage, for ASPs, than is provided by the TDT. Power simulations conducted under a number of disease models are used to verify that the most powerful member of this family of TDT-like statistics is more powerful than the TDT for ASPs.

Family-based association methods have recently been introduced that allow testing for linkage in the presence of linkage disequilibrium between a marker and a disease even if there is only incomplete parental-marker information. No such tests are currently available for X-linked markers. This report fills this methodological gap by presenting the X-linked sibling transmission/disequilibrium test (XS-TDT) and the X-linked reconstruction-combination transmission/disequilibrium test (XRC-TDT). As do their autosomal counterparts (S-TDT and RC-TDT), these tests make no assumption about the mode of inheritance of the disease and the ascertainment of the sample. They protect against spurious association due to population stratification. The two tests were compared by simulations, which show that (1) the X-linked RC-TDT is, in general, considerably more powerful than the X-linked S-TDT and (2) the lack of parental-genotype information can be offset by the typing of a sufficient number of sibling controls. A freely available SAS implementation of these tests allows the calculation of exact P values.

SummaryA new transmission/disequilibrium-test statistic is proposed for situations in which transmission is uncertain. Such situations arise when transmission of a multilocus marker haplotype is considered, since haplotype phase is often unknown in a substantial number of instances. Even for single-locus markers, transmission is uncertain if one or both parents are missing. In both these situations, uncertainty may be reduced by the typing of further siblings, whose disease status may be unaffected or unknown. The proposed test is a score test based on a partial score function that omits the terms most influenced by hidden population stratification.

SummaryA generalization of the transmission/disequilibrium test to detect association between polymorphic markers and discrete or quantitative traits is discussed, with particular emphasis on marker haplotypes formed by several adjacent loci. Furthermore, strategies for testing haplotype association, using methods from spatial statistics, are developed. This approach compares the “similarity” of transmitted and untransmitted haplotypes, with the aim of determining the regions where there is greater similarity within the transmitted set. This arises from the fact that, although the original haplotypes carrying the mutation will be broken down by recombination, there may be a subset of markers near the mutation that are common to many of the recombinant haplotypes. Thus, by examination of each marker in turn and by measurement of the average size of the region shared identically by state in the transmitted and untransmitted haplotypes, it may be possible to detect regions of linkage disequilibrium that encompass the susceptibility gene.

SummaryThe transmission/disequilibrium (TD) test (TDT), proposed, by Spielman et al., for binary traits is a powerful method for detection of linkage between a marker locus and a disease locus, in the presence of allelic association. As a test for linkage disequilibrium, the TDT makes the assumption that any allelic association present is due to linkage. Allison proposed a series of TD-type tests for quantitative traits and calculated their power, assuming that the marker locus is the disease locus. All these tests assume that the observations are independent, and therefore they are applicable, as a test for linkage, only for nuclear-family data. In this report, we propose a regression-based TD-type test for linkage between a marker locus and a quantitative trait locus, using information on the parent-to-offspring transmission status of the associated allele at the marker locus. This method does not require independence of observations, thus allowing for analysis of pedigree data as well, and allows adjustment for covariates. We investigate the statistical power and validity of the test by simulating markers at various recombination fractions from the disease locus.

SummaryThe transmission/disequilibrium test (TDT) developed by Spielman et al. can be a powerful family-based test of linkage and, in some cases, a test of association as well as linkage. It has recently been extended in several ways; these include allowance for implementation with quantitative traits, allowance for multiple alleles, and, in the case of dichotomous traits, allowance for testing in the absence of parental data. In this article, these three extensions are combined, and two procedures are developed that offer valid joint tests of linkage and (in the case of certain sibling configurations) association with quantitative traits, with use of data from siblings only, and that can accommodate biallelic or multiallelic loci. The first procedure uses a mixed-effects (i.e., random and fixed effects) analysis of variance in which sibship is the random factor, marker genotype is the fixed factor, and the continuous phenotype is the dependent variable. Covariates can easily be accommodated, and the procedure can be implemented in commonly available statistical software. The second procedure is a permutation-based procedure. Selected power studies are conducted to illustrate the relative power of each test under a variety of circumstances.

Summary Linkage disequilibrium has been used to help in the identification of genes predisposing to certain qualitative diseases. Although several linkage-disequilibrium tests have been developed for localization of genes influencing quantitative traits, these tests have not been thoroughly compared with one another. In this report we compare, under a variety of conditions, several different linkage-disequilibrium tests for identification of loci affecting quantitative traits. These tests use either single individuals or parent-child trios. When we compared tests with equal samples, we found that the truncated measured allele (TMA) test was the most powerful. The trait allele frequencies, the stringency of sample ascertainment, the number of marker alleles, and the linked genetic variance affected the power, but the presence of polygenes did not. When there were more than two trait alleles at a locus in the population, power to detect disequilibrium was greatly diminished. The presence of unlinked disequilibrium ( D ′ * ) increased the false-positive error rates of disequilibrium tests involving single individuals but did not affect the error rates of tests using family trios. The increase in error rates was affected by the stringency of selection, the trait allele frequency, and the linked genetic variance but not by polygenic factors. In an equilibrium population, the TMA test is most powerful, but, when adjusted for the presence of admixture, Allison test 3 becomes the most powerful whenever D ′* >.15.

SummaryThe human leukocyte antigen (HLA) complex, encompassing 3.5 Mb of DNA from the centromeric HLA-DPB2 locus to the telomeric HLA-F locus on chromosome 6p21, encodes a major part of the genetic predisposition to develop type 1 diabetes, designated “IDDM1.” A primary role for allelic variation of the class II HLA-DRB1, HLA-DQA1, and HLA-DQB1 loci has been established. However, studies of animals and humans have indicated that other, unmapped, major histocompatibility complex (MHC)–linked genes are participating in IDDM1. The strong linkage disequilibrium between genes in this complex makes mapping a difficult task. In the present paper, we report on the approach we have devised to circumvent the confounding effects of disequilibrium between class II alleles and alleles at other MHC loci. We have scanned 12 Mb of the MHC and flanking chromosome regions with microsatellite polymorphisms and analyzed the transmission of these marker alleles to diabetic probands from parents who were homozygous for the alleles of the HLA-DRB1, HLA-DQA1, and HLA-DQB1 genes. Our analysis, using three independent family sets, suggests the presence of an additional type I diabetes gene (or genes). This approach is useful for the analysis of other loci linked to common diseases, to verify if a candidate polymorphism can explain all of the association of a region or if the association is due to two or more loci in linkage disequilibrium with each other.

SummaryThe sibship disequilibrium test (SDT) is designed to detect both linkage in the presence of association and association in the presence of linkage (linkage disequilibrium). The test does not require parental data but requires discordant sibships with at least one affected and one unaffected sibling. The SDT has many desirable properties: it uses all the siblings in the sibship; it remains valid if there are misclassifications of the affectation status; it does not detect spurious associations due to population stratification; asymptotically it has a χ2 distribution under the null hypothesis; and exact P values can be easily computed for a biallelic marker. We show how to extend the SDT to markers with multiple alleles and how to combine families with parents and data from discordant sibships. We discuss the power of the test by presenting sample-size calculations involving a complex disease model, and we present formulas for the asymptotic relative efficiency (which is approximately the ratio of sample sizes) between SDT and the transmission/disequilibrium test (TDT) for special family structures. For sib pairs, we compare the SDT to a test proposed both by Curtis and, independently, by Spielman and Ewens. We show that, for discordant sib pairs, the SDT has good power for testing linkage disequilibrium relative both to Curtis's tests and to the TDT using trios comprising an affected sib and its parents. With additional sibs, we show that the SDT can be more powerful than the TDT for testing linkage disequilibrium, especially for disease prevalence >.3.

SummaryPopulation-based tests of association have used data from either case-control studies or studies based on trios (affected child and parents). Case-control studies are more prone to false-positive results caused by inappropriate controls, which can occur if, for example, there is population admixture or stratification. An advantage of family-based tests is that cases and controls are well matched, but parental data may not always be available, especially for late-onset diseases. Three recent family-based tests of association and linkage utilize unaffected siblings as surrogates for untyped parents. In this paper, we propose an extension of one of these tests. We describe and compare the four tests in the context of a complex disease for both biallelic and multiallelic markers, as well as for sibships of different sizes. We also examine the consequences of having some parental data in the sample.

Summary 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.

This work was supported in part by the Special Trustees of Guy's Hospital. We would like to thank Robert Curnow and David Balding for their helpful comments on an earlier draft of this article.

Times Cited: 66; International audience; Although genotyping errors affect most data and can markedly influence the biological conclusions of a study, they are too often neglected. Errors have various causes, but their occurrence and effect can be limited by considering these causes in the production and analysis of the data. Procedures that have been developed for dealing with errors in linkage studies, forensic analyses and non-invasive genotyping should be applied more broadly to any genetic study. We propose a protocol for estimating error rates and recommend that these measures be systemically reported to attest the reliability of published genotyping studies.

We have previously described linkage/association between reelin gene polymorphisms and autistic disorder. APOE also participates in the Reelin signaling pathway, by competitively antagonizing Reelin binding to APOE receptor 2 and to very-low-density lipoprotein receptors. The APOE2 protein variant displays the lowest receptor binding affinity compared with APOE3 and APOE4. In this study, we assess linkage/association between primary autism and APOE alleles in 223 complete trios, from 119 simplex Italian families and 44 simplex and 29 multiplex Caucasian-American families. Statistically significant disequilibrium favors the transmission of epsilon2 alleles to autistic offspring, over epsilon3 and epsilon4 (allele-wise transmission/disequilibrium test [TDT], chi2 = 6.16, 2 degrees of freedom [d.f.], P

We applied a new haplotype sharing method to the simulated Genetic Analysis Workshop 12 data for both isolated and general populations without knowledge of the disease model, using affection status as phenotype and three different sample sizes. The highest peak for the mean sharing of the haplotypes was found in the isolated population for the markers D06G034 and D06G035, which flank the candidate genes located on chromosome 6, with -log(10)(p) values of 2.9 and 7.0 in the moderate and large study samples, respectively. The whole genome screen detected three further loci with -log(10)(p) values of 3.0, which turned out to be false positives. None of the true gene loci were detected in the general population even in the largest sample. The test of linkage disequilibrium based on excess haplotype sharing over the linkage equilibrium expectation revealed z-values one order of magnitude higher in the isolated than in the general population. This approach appears to be promising for mapping genes of complex diseases depending on population characteristics. (C) 2001 Wiley-Liss, Inc.

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.

SummaryMost noninfectious disease is caused by low-penetrance alleles interacting with other genes and environmental factors. Consider the simple setting where a diallelic autosomal candidate gene and a binary exposure together affect disease susceptibility. Suppose that one has genotyped affected probands and their parents and has determined each proband's exposure status. One proposed method for assessment of etiologic interaction of genotype and exposure, an extension of the transmission/disequilibrium test, tests for differences in transmission of the variant allele from heterozygous parents to exposed versus unexposed probands. We show that this test is not generally valid. An alternative approach compares the conditional genotype distribution of unexposed cases, given parental genotypes, versus that of exposed cases. This approach provides maximum-likelihood estimators for genetic relative-risk parameters and genotype-exposure–interaction parameters, as well as a likelihood-ratio test (LRT) of the no-interaction null hypothesis. We show how to apply this approach, using log-linear models. When a genotype-exposure association arises solely through incomplete mixing of subpopulations that differ in both exposure prevalence and allele frequency, the LRT remains valid. The LRT becomes invalid, however, if offspring genotypes do not follow Mendelian proportions in each parental mating type—for example, because of genotypic differences in survival—or if a genotype-exposure association reflects an influence of genotype on propensity for exposure—for example, through behavioral mechanisms. Because the needed assumptions likely hold in many situations, the likelihood-based approach should be broadly applicable for diseases in which probands commonly have living parents.

It has been demonstrated in the literature that the transmission/disequilibrium test (TDT) has higher power than the affected-sib-pair (ASP) mean test when linkage disequilibrium (LD) is strong but that the mean test has higher power when LD is weak. Thus, for ASP data, it seems clear that the TDT should be used when LD is strong but that the mean test or other linkage tests should be used when LD is weak or absent. However, in practice, it may be difficult to follow such a guideline, because the extent of LD is often unknown. Even with a highly dense genetic-marker map, in which some markers should be located near the disease-predisposing mutation, strong LD is not inevitable. Besides the genetic distance, LD is also affected by many factors, such as the allelic heterogeneity at the disease locus, the initial LD, the allelic frequencies at both disease locus and marker locus, and the age of the mutation. Therefore, it is of interest to develop methods that are adaptive to the extent of LD. In this report, we propose a disequilibrium maximum-binomial-likelihood (DMLB) test that incorporates LD in the maximum-binomial-likelihood (MLB) test. Examination of the corresponding score statistics shows that this method adaptively combines two sources of information: (a) the identity-by-descent (IBD) sharing score, which is informative for linkage regardless of the existence of LD, and (b) the contrast between allele-specific IBD sharing score, which is informative for linkage only in the presence of LD. For ASP data, the proposed test has higher power than either the TDT or the mean test when the extent of LD ranges from moderate to strong. Only when LD is very weak or absent is the DMLB slightly less powerful than the mean test; in such cases, the TDT has essentially no power to detect linkage. Therefore, the DMLB test is an interesting approach to linkage detection when the extent of LD is unknown.

SummaryThe 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.

SummarySpielman 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.

SummaryRecent admixture between genetically differentiated populations can result in high levels of association between alleles at loci that are ≤10 cM apart. The transmission/disequilibrium test (TDT) proposed by Spielman et al. (1993) can be a powerful test of linkage between disease and marker loci in the presence of association and therefore could be a useful test of linkage in admixed populations. The degree of association between alleles at two loci depends on the differences in allele frequencies, at the two loci, in the founding populations; therefore, the choice of marker is important. For a multiallelic marker, one strategy that may improve the power of the TDT is to group marker alleles within a locus, on the basis of information about the founding populations and the admixed population, thereby collapsing the marker into one with fewer alleles. We have examined the consequences of collapsing a microsatellite into a two-allele marker, when two founding populations are assumed for the admixed population, and have found that if there is random mating in the admixed population, then typically there is a collapsing for which the power of the TDT is greater than that for the original microsatellite marker. A method is presented for finding the optimal collapsing that has minimal dependence on the disease and that uses estimates either of marker allele frequencies in the two founding populations or of marker allele frequencies in the current, admixed population and in one of the founding populations. Furthermore, this optimal collapsing is not always the collapsing with the largest difference in allele frequencies in the founding populations. To demonstrate this strategy, we considered a recent data set, published previously, that provides frequency estimates for 30 microsatellites in 13 populations.

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.

SummaryWe describe a log-linear method for analysis of case-parent–triad data, based on maximum likelihood with stratification on parental mating type. The method leads to estimates of association parameters, such as relative risks, for a single allele, and also to likelihood ratio χ2 tests (LRTs) of linkage disequilibrium. Hardy-Weinberg equilibrium need not be assumed. Our simulations suggest that the LRT has power similar to that of the χ2 “score” test proposed by Schaid and Sommer and that both can outperform the transmission/disequilibrium test (TDT), although the TDT can perform better under an additive model of inheritance. Because a restricted version of the LRT is asymptotically equivalent to the TDT, the proposed test can be regarded as a generalization of the TDT. The method that we describe generalizes easily to accommodate maternal effects on risk and, in fact, produces powerful and orthogonal tests of the contribution of fetal versus maternal genetic factors. We further generalize the model to allow for effects of parental imprinting. Imprinting effects can be fitted by a simple, iterative procedure that relies on the expectation-maximization algorithm and that uses standard statistical software for the maximization steps. Simulations reveal that LRT tests for detection of imprinting have very good operating characteristics. When a single allele is under study, the proposed method can yield powerful tests for detection of linkage disequilibrium and is applicable to a broader array of causal scenarios than is the TDT.

I thank two referees for their thoughtful and constructive comments. This work was supported in part by National Institutes of Health grants GM59507, GM57672, and DA09055.

To the Editors:Laird et al. (1998xThe sib transmission/disequilibrium test is a Mantel-Haenszel test. Laird, N, Blacker, D, and Wilcox, M. Am J Hum Genet. 1998; 63: 915Abstract | Full Text | Full Text PDFSee all References1998 [in this issue]) point out that the sib transmission/disequilibrium test (S-TDT) is identical in principle to the Mantel extension test for trend in multiple strata. We were not aware of this test and independently developed the S-TDT. Despite identity in theory, however, our test differs in practice from the Mantel extension test in two respects.First, unlike the Mantel extension test described by Rosner (1995xRosner, B. See all References1995) and its implementation in SAS programs as described by Laird et al. (1998xThe sib transmission/disequilibrium test is a Mantel-Haenszel test. Laird, N, Blacker, D, and Wilcox, M. Am J Hum Genet. 1998; 63: 915Abstract | Full Text | Full Text PDFSee all References1998), our approach makes a continuity correction in the z score calculation and thus provides a somewhat more accurate approximation of P values. The difference is substantial when the data consist of only a small number of families. For instance, in our numerical example of three families (Spielman and Ewens 1998xA sibship test for linkage in the presence of association: the sib transmission/disequilibrium test. Spielman, RS and Ewens, WJ. Am J Hum Genet. 1998; 62: 450–458Abstract | Full Text | Full Text PDF | PubMed | Scopus (511)See all References1998), the use of a continuity correction led us to a z score of 1.9839, which results in a two-sided P value of .0473. The SAS program computes a two-sided P value of .016, which is also the value computed by use of the formula of Rosner (1995xRosner, B. See all References1995). In this example, the exact P value can be found by exhaustive enumeration of all permutations of the data from the three families: it is 3/70=.0429, which is close to our value and is more than twice the value computed by the SAS program.Laird et al. (1998xThe sib transmission/disequilibrium test is a Mantel-Haenszel test. Laird, N, Blacker, D, and Wilcox, M. Am J Hum Genet. 1998; 63: 915Abstract | Full Text | Full Text PDFSee all References1998) comment that the SAS calculation does not include a continuity correction but imply that the StatXact computer program can compute exact P values for the S-TDT. In practice, no procedure can do this when the sample consists of data from a large number of families, since in such cases an exact calculation would involve an astronomically large number of permutations. For such cases, StatXact resorts to Monte Carlo methods by using samples taken at random from the large number of permutations possible. We ourselves used this procedure for the S-TDT (Spielman and Ewens 1998xA sibship test for linkage in the presence of association: the sib transmission/disequilibrium test. Spielman, RS and Ewens, WJ. Am J Hum Genet. 1998; 62: 450–458Abstract | Full Text | Full Text PDF | PubMed | Scopus (511)See all References1998).Second, instead of the square of the z statistic, which the Mantel extension test applies, we prefer to use the unsquared z statistic, because one of our aims is to provide a combined test for data from some families that are suitable for the S-TDT test and from some that are suitable for the TDT (Spielman and Ewens 1998xA sibship test for linkage in the presence of association: the sib transmission/disequilibrium test. Spielman, RS and Ewens, WJ. Am J Hum Genet. 1998; 62: 450–458Abstract | Full Text | Full Text PDF | PubMed | Scopus (511)See all References1998). The combined test is easily performed by use of the unsquared statistic but not by use of the squared statistic. A computer program that incorporates the continuity correction and that allows for the combination of the S-TDT and TDT procedures is now available at http://spielman07.med.upenn.edu/TDT.htm.

To the Editor:Spielman and Ewens's (1998xA sibship test for linkage in the presence of association: the sib transmission/disequilibrium test. Spielman, RS and Ewens, WJ. Am J Hum Genet. 1998; 62: 450–458Abstract | Full Text | Full Text PDF | PubMed | Scopus (508)See all References1998) proposed extension of the transmission/disequilibrium test (TDT), using discordant sibships, provides a simple and elegant way to apply the TDT in instances in which parents are not available. It is easy to see that the adapted test, called the “sib TDT” (S-TDT), is numerically equivalent to a Mantel-Haenszel test of trend, also known as the “Mantel extension test” (Rosner 1995xRosner, B. See all References1995).The original Mantel-Haenszel test is used routinely in matched case-control studies, to test for association between disease and exposure. When exposure is expressed as a quantitative risk factor with C levels, the Mantel extension test allows the investigator to obtain a 1-df test against the alternative of a monotone trend. For each matched set, a 2×C table classifying subjects according to disease and exposure status is formed. The statistic is determined by assigning the columns quantitative values corresponding to exposure level. The statistic also may be derived as a score test for no association within each matched set, by use of a model for the log odds of disease, which is linear in exposure level.To obtain the S-TDT by use of the Mantel extension test, sibship is used as the stratifying variable, and for each sibship a 2×3 table cross-classifying sibs on the basis of disease status and genotype is formed. The quantitative value of exposure that yields the S-TDT assigns to each genotype the number of putative disease-associated alleles that a sib has (i.e., 2, 1, or 0) for genotypes AA, AB, or BB.The advantages of viewing the S-TDT as a Mantel extension test are threefold. First, the test is already widely available on commercial software. For example, SAS currently implements the Mantel extension test as part of its Cochran-Mantel-Haenszel procedure. This version of the test allows user-specified scores for the levels of the quantitative variable but does not provide a continuity correction. Another program, StatXact, provides an exact P value for the Mantel extension test, as well as the asymptotic P value.Second, it immediately is obvious how to use the test with other genetic models. For example, for an arbitrary genetic model, an investigator may want to use the 2-df Mantel-Haenszel test, which makes no assumption about how risk varies with number of A alleles. To test a dominant model, a value of 1 would be assigned to genotype AA or AB and a value of 0 to genotype BB; to test a recessive model, exposure values of 1 for AA and of 0 for all other genotypes would be used.Third, if the marker is actually a candidate gene, the investigator may wish to estimate risk ratios. Collapsing over sibships and estimating risk ratios by use of the 2×3 margin results in biased estimates, which may be confounded because sibships may come from different populations with different disease risks and allele distributions. Instead, to estimate risk ratios, a Mantel-Haenszel estimate of odds ratio—or, in the general case, conditional logistic regression (Breslow and Day 1980xBreslow, NE and Day, NE. See all References1980)—should be used.