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》

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》

A general class of association tests for family-based data using weight functions.

Based on the symmetry of transmitted/nontransmitted alleles from heterozygous parents under the null hypothesis of no association, the work proposed here establishes a general statistical framework for constructing association tests with data from nuclear families with multiple affected children. A class of association tests is proposed for both diallelic and multiallelic markers. The proposed test statistics reduce to the transmission disequilibrium test for trios, to T(su) by Martin et al. ([1997] Am. J. Hum. Genet. 61:439-448) for affected sib pairs, and to the pedigree disequilibrium test by Martin et al. ([2000] Am. J. Hum. Genet. 67:146-154); [2001] Am. J. Hum. Genet. 68:1065-1067) when using affected sibships only. The association test used in simulation and for real data (sitosterolemia) is the one which has the best overall power in detecting association. This association test is generally more powerful than the association tests proposed by Martin et al. ([2000] Am. J. Hum. Genet. 67:146-154); [2001] Am. J. Hum. Genet. 68:1065-1067) when using only affected sibships. For the sitosterolemia data set, the association test has its most significant result (P-value=0.0012) for the marker locus on the same bacterial artificial chromosome as the disease locus.

Liu X ，Gordon D 《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》

Method for using complete and incomplete trios to identify genes related to a quantitative trait.

A number of tests for linkage and association with qualitative traits have been developed, with the most well-known being the transmission/disequilibrium test (TDT). For quantitative traits, varying extensions of the TDT have been suggested. The quantitative trait approach we propose is based on extending the log-linear model for case-parent trio data (Weinberg et al. [1998] Am. J. Hum. Genet. 62:969-978). Like the log-linear approach for qualitative traits, our proposed polytomous logistic approach for quantitative traits allows for population admixture by conditioning on parental genotypes. Compared to other methods, simulations demonstrate good power and robustness of the proposed test under various scenarios of the genotype effect, distribution of the quantitative trait, and population stratification. In addition, missing parental genotype data can be accommodated through an expectation-maximization (EM) algorithm approach. The EM approach allows recovery of most of the lost power due to incomplete trios.

Kistner EO ，Weinberg CR 《GENETIC EPIDEMIOLOGY》