Power calculations for the transmission/disequilibrium and affected sib pair tests using elementary probability methods

The transmission/disequilibrium test (TDT) and the affected sib pair test (ASP) both test for the association of a marker allele with some conditions. Here, we present methods for calculating the probability of detecting the association (power) for a study examining a fixed number of families for suitability for the study and for calculating the number of such families to be examined. Both calculations use a genetic model for the association. The model considered posits a bi-allelic marker locus that is linked to a bi-allelic disease locus with a possibly nonzero recombination fraction between the loci. The penetrance of the disease is an increasing function of the number of disease alleles. The TDT tests whether the transmission by a heterozygous parent of a particular allele at a marker locus to an affected offspring occurs with probability greater than 0.5. The ASP tests whether transmission of the same allele to two affected sibs occurs with probability greater than 0.5. In either case, evidence that the probability is greater than 0.5 is evidence for association between the marker and the disease. Study inclusion criteria (IC) can greatly affect the necessary sample size of a TDT or ASP study. IC considered by us include a randomly selected parent at least one parent or both parents required to be heterozygous. It also allows a specified minimum number of affected offspring to be required (TDT only). We use elementary probability calculations rather than complex mathematical manipulations or asymptotic methods (large sample size approximations) to compute power and requisite sample size for a proposed study. The advantages of these methods are simplicity and generality.     

Linkage detection adaptive to linkage disequilibrium: the disequilibrium maximum-likelihood-binomial test for affected-sibship data

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.     

一种有效的复杂疾病基因定位的检测法

连锁不平衡（LD）应用于某些复杂疾病基因的定位,近年来发展了许多LD定位方法,除TDT外,大多数LD定位方法须先假定无人群混和,人群混合可增大在疾病基因定位时犯Ⅰ类错误的机率,产生无效结果。此方法利用LD来检测标记位点和疾病敏感位点（DSL）的连锁（有连锁不平衡）相关（有连锁）。分析时采用不相关样本,已知其父母基因型和至少父母之一为杂合子,再将随机样本依基因型不同分类,然后对来自不同类的数据应用有力的统计方法进行单独和联合分析。此LD定位法不仅适用于患病和正常个体,而且有效消除据父母基因分类的样本定位时人群混合的影响,分析结果和模拟结果也表明此方法解决了在检测标记位点和疾病敏感位点之间的连锁和相关时人群混和的问题,但与TDT比,此法在检测的位点为DSL时丙能有效和充分地利用矫正数据,检测位点不是DSL时,此法和TDT法可相互补充更有效地检测连锁的DSL。     

Use of susceptibility scoring in conjunction with the genotypic transmission disequilibrium test

We explored the utility of selecting a genetically predisposed subgroup to increase the finding of a genetic signal in the Genetic Analysis Workshop 14 Collaborative Study on the Genetics of Alcoholism dataset. A subgroup of affected probands with low environmental risk exposures was defined using a susceptibility score calculated from an environmental risk model. Thirty-nine probands with highly positive scores were selected, along with their parents, for use in a genotypic transmission disequilibrium test (TDT) test. We compared the results of the genotypic TDT in this subgroup to the TDT results using all probands and their parents. For some markers, the susceptibility scoring approach resulted in smaller p-values, while for other markers, evidence for a genetic signal weakened. Further explorations into genetic and environmental population characteristics that benefit from this approach are warranted.     

The score statistic of the LD-lod analysis: detecting linkage adaptive to linkage disequilibrium

We study the properties of a modified lod score method for testing linkage that incorporates linkage disequilibrium (LD-lod). By examination of its score statistic, we show that the LD-lod score method adaptively combines two sources of information: (a) the IBD sharing score which is informative for linkage regardless of the existence of LD and (b) the contrast between allele-specific IBD sharing scores which is informative for linkage only in the presence of LD. We also consider the connection between the LD-lod score method and the transmission-disequilibrium test (TDT) for triad data and the mean test for affected sib pair (ASP) data. We show that, for triad data, the recessive LD-lod test is asymptotically equivalent to the TDT; and for ASP data, it is an adaptive combination of the TDT and the ASP mean test. We demonstrate that the LD-lod score method has relatively good statistical efficiency in comparison with the ASP mean test and the TDT for a broad range of LD and the genetic models considered in this report. Therefore, the LD-lod score method is an interesting approach for detecting linkage when the extent of LD is unknown, such as in a genome-wide screen with a dense set of genetic markers.     

Interpreting genotype × environment interaction in tropical maize using linked molecular markers and environmental covariables

An understanding of the genetic and environmental basis of genotype×environment interaction (GEI) is of fundamental importance in plant breeding. In mapping quantitative trait loci (QTLs), suitable genetic populations are grown in different environments causing QTLs×environment interaction (QEI). The main objective of the present study is to show how Partial Least Squares (PLS) regression and Factorial Regression (FR) models using genetic markers and environmental covariables can be used for studying QEI related to GEI. Biomass data were analyzed from a multi-environment trial consisting of 161 lines from a F_3:4 maize segregating population originally created with the purpose of mapping QTLs loci and investigating adaptation differences between highland and lowland tropical maize. PLS and FR methods detected 30 genetic markers (out of 86) that explained a sizeable proportion of the interaction of maize lines over four contrasting environments involving two low-altitude sites, one intermediate-altitude site, and one high-altitude site for biomass production. Based on a previous study, most of the 30 markers were associated with QTLs for biomass and exhibited significant QEI. It was found that marker loci in lines with positive GEI for the highland environments contained more highland alleles, whereas marker loci in lines with positive GEI for intermediate and lowland environments contained more lowland alleles. In addition, PLS and FR models identified maximum temperature as the most-important environmental covariable for GEI. Using a stepwise variable selection procedure, a FR model was constructed for GEI and QEI that exclusively included cross products between genetic markers and environmental covariables. Higher maximum temperature in low- and intermediate-altitude sites affected the expression of some QTLs, while minimum temperature affected the expression of other QTLs. Received: 10 January 1999 / Accepted: 12 March 1999     

Staphylococcus aureus mobile genetic elements

Among the bacteria groups, most of them are known to be beneficial to human being whereas only a minority is being recognized as harmful. The pathogenicity of bacteria is due, in part, to their rapid adaptation in the presence of selective pressures exerted by the human host. In addition, through their genomes, bacteria are subject to mutations, various rearrangements or horizontal gene transfer among and/or within bacterial species. Bacteria’s essential metabolic functions are generally encoding by the core genes. Apart of the core genes, there are several number of mobile genetic elements (MGE) acquired by horizontal gene transfer that might be beneficial under certain environmental conditions. These MGE namely bacteriophages, transposons, plasmids, and pathogenicity islands represent about 15 % Staphylococcus aureus genomes. The acquisition of most of the MGE is made by horizontal genomic islands (GEI), recognized as discrete DNA segments between closely related strains, transfer. The GEI contributes to the wide spread of microorganisms with an important effect on their genome plasticity and evolution. The GEI are also involve in the antibiotics resistance and virulence genes dissemination. In this review, we summarize the mobile genetic elements of S. aureus.     

Fine-mapping of the type 1 diabetes locus (IDDM4) on chromosome 11q and evaluation of two candidate genes (FADD and GALN) by affected sibpair and linkage-disequilibrium analyses

Previous studies have identified a susceptibility region for insulin-dependent (type 1) diabetes mellitus on chromosome 11q13 (IDDM4). In this study, 15 polymorphic markers were analyzed for 382 affected sibpair (ASP) families with type 1 diabetes. Our analyses provided additional evidence for linkage for IDDM4 (a peak LOD score of 3.4 at D11S913). The markers with strong linkage evidence are located within an interval of approximately 6 cM between D11S4205 and GALN. We also identified polymorphisms in two candidate genes, Fas-associated death domain protein (FADD) and galanin (GALN). Analyses of the data by transmission/disequilibrium test (TDT) and extended TDT (ETDT) did not provide any evidence for association/linkage with these candidate genes. However, ETDT did reveal significant association/linkage with the marker D11S987 (P=0.0004) within the IDDM4 interval defined by ASP analyses, suggesting that IDDM4 may be in the close proximity of D11S987.     

Transmission test for linkage disequilibrium: the insulin gene region and insulin-dependent diabetes mellitus (IDDM).

A population association has consistently been observed between insulin-dependent diabetes mellitus (IDDM) and the "class 1" alleles of the region of tandem-repeat DNA (5'' flanking polymorphism [5''FP]) adjacent to the insulin gene on chromosome 11p. This finding suggests that the insulin gene region contains a gene or genes contributing to IDDM susceptibility. However, several studies that have sought to show linkage with IDDM by testing for cosegregation in affected sib pairs have failed to find evidence for linkage. As means for identifying genes for complex diseases, both the association and the affected-sib-pairs approaches have limitations. It is well known that population association between a disease and a genetic marker can arise as an artifact of population structure, even in the absence of linkage. On the other hand, linkage studies with modest numbers of affected sib pairs may fail to detect linkage, especially if there is linkage heterogeneity. We consider an alternative method to test for linkage with a genetic marker when population association has been found. Using data from families with at least one affected child, we evaluate the transmission of the associated marker allele from a heterozygous parent to an affected offspring. This approach has been used by several investigators, but the statistical properties of the method as a test for linkage have not been investigated. In the present paper we describe the statistical basis for this "transmission test for linkage disequilibrium" (transmission/disequilibrium test [TDT]). We then show the relationship of this test to tests of cosegregation that are based on the proportion of haplotypes or genes identical by descent in affected sibs. The TDT provides strong evidence for linkage between the 5''FP and susceptibility to IDDM. The conclusions from this analysis apply in general to the study of disease associations, where genetic markers are usually closely linked to candidate genes. When a disease is found to be associated with such a marker, the TDT may detect linkage even when haplotype-sharing tests do not.     

Accounting for Population Structure in Gene-by-Environment Interactions in Genome-Wide Association Studies Using Mixed Models

Although genome-wide association studies (GWASs) have discovered numerous novel genetic variants associated with many complex traits and diseases, those genetic variants typically explain only a small fraction of phenotypic variance. Factors that account for phenotypic variance include environmental factors and gene-by-environment interactions (GEIs). Recently, several studies have conducted genome-wide gene-by-environment association analyses and demonstrated important roles of GEIs in complex traits. One of the main challenges in these association studies is to control effects of population structure that may cause spurious associations. Many studies have analyzed how population structure influences statistics of genetic variants and developed several statistical approaches to correct for population structure. However, the impact of population structure on GEI statistics in GWASs has not been extensively studied and nor have there been methods designed to correct for population structure on GEI statistics. In this paper, we show both analytically and empirically that population structure may cause spurious GEIs and use both simulation and two GWAS datasets to support our finding. We propose a statistical approach based on mixed models to account for population structure on GEI statistics. We find that our approach effectively controls population structure on statistics for GEIs as well as for genetic variants.     

Gene-environment interaction and the mapping of complex traits: some statistical models and their implications

The manifestation of many complex diseases or traits is very likely the result of an inextricable interplay of the biological and the environmental. Yet the role of environmental effect has traditionally been played down, for various reasons. In this paper, some simple statistical models that incorporate gene-environment interaction (GEI) have been proposed and their behavior and implications investigated. These implications concern the conditional independence assumption in likelihood calculation of pedigree data, the fine-tuning of the sib pair method for mapping quantitative traits, apportioning of disease or trait variation due to specific causes. In addition, they concern properties of gene mapping methods that do not take GEI into account, and they bring into question the utility of commonly used measures of genetic effects such as recurrence risk ratio for relative pairs, twin concordance rates, and heritability coefficients. In the presence of GEI, all these measures are functions not only of genetic effects and gene frequency, but also of environmental effects, the distribution of environmental factors in the population, and of GEI. Above all, these measures are all measures of familial aggregation, since they can be significant even in the absence of any genetic component of the disease. Thus their use as indicators of the genetic basis of complex diseases is cast into doubt.     

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.     

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.     

Type 1 diabetes genetic susceptibility encoded by HLA DQB1 genes in Romania

Most cases of type 1 diabetes (T1DM) are due to an immune-mediated destruction of the pancreatic beta cells, a process that is conditioned by multiple genes and environmental factors. The main susceptibility genes are represented by the class II HLA-DRB1 and DQB1 alleles. The aim of our study was to reconfirm the contribution of HLA-DQB1 polymorphisms to T1DM genetic susceptibility for the Romanian population. For this, 219 Romanian T1DM families were genotyped at high resolution for HLA DQB1 using the PCR-SSOP method (Polymerase Chain Reaction - Sequence Specific Oligonucleotide Probes). Allele transmission to diabetics and unaffected siblings was studied using the Transmission Disequilibrium Test (TDT). We found an increased transmission of DQB1*02 (77.94% transmission, p(TDT) = 7.18 x 10(-11)) and DQB1*0302 (80.95% transmission, p(TDT) = 2.25 x 10(-10)) alleles to diabetics, indicating the diabetogenic effect of these alleles. Conversely, DQB1*0301, DQB1*0603, DQB1*0602, DQB1*0601 and DQB1*05 alleles are protective, being significantly less transmitted to diabetics. In conclusion, our results confirmed the strong effect of HLA-DQB1 alleles on diabetes risk in Romania, with some characteristics which can contribute to the low incidence of T1DM in this country.     

Association of single-nucleotide polymorphisms at the Delta locus with genotype by environment interaction for sensory bristle number in drosophila Melanogaster

The nature of forces maintaining variation for quantitative traits can only be assessed at the level of individual genes affecting variation in the traits. Identification of single-nucleotide polymorphisms (SNPs) associated with variation in Drosophila sensory bristle number at the Delta (Dl) locus provides us with the opportunity to test a model for the maintenance of variation in bristle number by genotype by environment interaction (GEI). Under this model, genetic variation is maintained at a locus under stabilizing selection if phenotypic values of heterozygotes are more stable than homozygotes across a range of environments, and the mean allelic effect is much smaller than the standard deviation of allelic effects across environments. Homozygotes and heterozygotes for two SNPs at Dl, one affecting sternopleural and the other abdominal bristle number, were reared in five different environments. There was significant GEI for both bristle traits. Neither condition of the model was satisfied for Dl SNPs exhibiting GEI for sternopleural bristle number. Heterozygotes for the abdominal bristle number SNPs were indeed the most stable genotype for two of the three environment pairs exhibiting GEI, but the mean genotypic effect was greater than the standard deviation of effects across environments. Therefore, this mechanism of GEI seems unlikely to be responsible for maintaining the common bristle number polymorphisms at Dl.     

Multipoint linkage-disequilibrium-mapping approach based on the case-parent trio design

In the present study we propose a multipoint approach, for the mapping of genes, that is based on the case-parent trio design. We first derive an expression for the expected preferential-allele-transmission statistics for transmission, from either parent to an affected child, for an arbitrary location within a chromosomal region demarcated by several genetic markers. No assumption about genetic mechanism is needed in this derivation, beyond the assumption that no more than one disease gene lies in the region framed by the markers. When one builds on this representation, the way in which one may maximize the genetic information from multiple markers becomes obvious. This proposed method differs from the popular transmission/disequilibrium test (TDT) approach for fine mapping, in the following ways: First, in contrast with the TDT approach, all markers contribute information, regardless of whether the parents are heterozygous at any one marker, and incomplete trio data can be utilized in our approach. Second, rather than performing the TDT at each marker separately, we propose a single test statistic that follows a chi(2) distribution with 1 df, under the null hypothesis of no linkage or linkage disequilibrium to the region. Third, in the presence of linkage evidence, we offer a means to estimate the location of the disease locus along with its sampling uncertainty. We illustrate the proposed method with data from a family study of asthma, conducted in Barbados.     

The future is now - will the real disease gene please stand up?

The transmission/disequilibrium test (TDT) [Spielman et al.: Am J Hum Genet 1993;52:506-516] has been postulated as the future of gene mapping for complex diseases, provided one is able to genotype a dense enough map of markers across the genome. Risch and Merikangas [Science 1996;273:1516-1517] suggested a million-marker screen in affected sibpair (ASP) families, demonstrating that the TDT is a more powerful test of linkage than traditional linkage tests based on allele-sharing when there is also association between marker and disease alleles. While the future of genotyping has arrived, successes in family-based association studies have been modest. This is often attributed to excessive false positives in candidate gene studies. This problem is only exacerbated by the increasing numbers of whole genome association (WGA) screens. When applied in ASPs, the TDT statistic, which assumes transmissions to siblings are independent, is not expected to have a constant variance in the presence of variable linkage. This results in generally more extreme statistics, hence will further aggravate the problem of having a large number of positive results to sort through. So an important question is how many positive TDT results will show up on a chromosome containing a disease gene due only to linkage, and will they obfuscate the true disease gene location. To answer this question we combined theory and computer simulations. These studies show that in ASPs the normal version of the TDT statistic has a mean of 0 and a variance of 1 in unlinked regions, but has a variance larger than 1 in linked regions. In contrast, the pedigree disequilibrium test (PDT) statistic adjusts for correlation between siblings due to linkage and maintains a constant variance of 1 at unassociated markers irrespective of linkage. The TDT statistic is generally larger than the PDT statistic across linked regions. This is true for unassociated as well as associated markers. To compare the two tests we ranked both statistics at the disease locus, or an associated marker, among statistics at all other markers. The TDT did better job than PDT placing the score of the associated marker near the top. Though, strictly speaking, the TDT in ASPs should be interpreted as a test of linkage and not a test of association, there is a good chance that if a marker stands out, the marker is associated as well as linked. In conclusion, our results suggest that TDT is an effective screening tool for WGA studies, especially in multiplex families.     

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.