Transmission/disequilibrium tests for quantitative traits.

Spielman et al. [1993] proposed a transmission-disequilibrium test (TDT), based on marker data collected on affected offspring and their parents, to test for linkage between a genetic marker and a binary trait provided there is allelic association. It has been shown that this TDT is powerful and is not affected by allelic association due to population stratification in the absence of linkage. For quantitative traits, George and Elston [1987] proposed a likelihood method to detect the effect of a candidate gene in pedigree data when familial correlations are present. This test will detect allelic association but will do so in the absence of linkage. In this paper, we investigate two new likelihood-ratio test statistics for multi-generational quantitative traits to test either for linkage in the presence of allelic association or for allelic association in the presence of linkage, such as may be due to linkage disequilibrium. We compare these two tests analytically and by simulation with respect to 1) the sample size required for the asymptotic null distributions to be valid and 2) their power to detect association in those cases in which they are not sensitive to population stratification unless linkage is present. In general, 80 nuclear families with two children each and at least one heterozygous parent, or the equivalent number of children in large pedigrees, are enough for the asymptotic null distribution of the proposed conditional and TDT methods to be valid. The theoretical power is close to the simulated power except for the case of a recessive allele with low frequency. A sampling strategy is proposed that dramatically improves power.

Zhu X ，Elston RC 《GENETIC EPIDEMIOLOGY》

Power comparison of regression methods to test quantitative traits for association and linkage.

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

Zhu X ，Elston RC 《GENETIC EPIDEMIOLOGY》

Linkage and association studies of QTL for nuclear families by mixed models.

The transmission disequilibrium test (TDT) has been utilized to test the linkage and association between a genetic trait locus and a marker. Spielman et al. (1993) introduced TDT to test linkage between a qualitative trait and a marker in the presence of association. In the presence of linkage, TDT can be applied to test for association for fine mapping (Martin et al., 1997; Spielman and Ewens, 1996). In recent years, extensive research has been carried out on the TDT between a quantitative trait and a marker locus (Allison, 1997; Fan et al., 2002; George et al., 1999; Rabinowitz, 1997; Xiong et al., 1998; Zhu and Elston, 2000, 2001). The original TDT for both qualitative and quantitative traits requires unrelated offspring of heterozygous parents for analysis, and much research has been carried out to extend it to fit for different settings. For nuclear families with multiple offspring, one approach is to treat each child independently for analysis. Obviously, this may not be a valid method since offspring of one family are related to each other. Another approach is to select one offspring randomly from each family for analysis. However, with this method much information may be lost. Martin et al. (1997, 2000) constructed useful statistical tests to analyse the data for qualitative traits. In this paper, we propose to use mixed models to analyse sample data of nuclear families with multiple offspring for quantitative traits according to the models in Amos (1994). The method uses data of all offspring by taking into account their trait mean and variance-covariance structures, which contain all the effects of major gene locus, polygenic loci and environment. A test statistic based on mixed models is shown to be more powerful than the test statistic proposed by George et al. (1999) under moderate disequilibrium for nuclear families. Moreover, it has higher power than the TDT statistic which is constructed by randomly choosing a single offspring from each nuclear family.

Fan R ，Xiong M 《BIOSTATISTICS》

Informative-transmission disequilibrium test (i-TDT): combined linkage and association mapping that includes unaffected offspring as well as affected offspring.

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

Guo CY ，Lunetta KL ，DeStefano AL ，Ordovas JM ，Cupples LA ... -  《GENETIC EPIDEMIOLOGY》

A Bayesian approach to the transmission/disequilibrium test for binary traits.

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

George V ，Laud PW 《GENETIC EPIDEMIOLOGY》