Testing quantitative traits for association and linkage in the presence or absence of parental data

Zhu and Elston developed a transmission disequilibrium test for quantitative traits by defining a linear transformation to condition out founder information. The method tests the null hypothesis of no linkage or association and can be applied to general pedigree structures. However, this method requires both genotype and phenotype parental information, which may be difficult to obtain. In this paper, we describe parametric and non-parametric methods to relax this requirement when only nuclear families are sampled. We show that neither method is affected by population stratification in the absence of linkage. The statistical power and validity of the tests are investigated by simulation. A simple simulation method to calculate the power of the nonparametric method is also discussed. In practice, the data may have some families with parental phenotype and genotype information available and some without. We briefly discuss how all the data may be analyzed jointly.