Mapping Multivariate Phenotypes in the Presence of Missing Observations for Family-Based Data

Clinical end-point traits are often characterized by quantitative or qualitative precursors and it has been argued that it may be statistically a more powerful strategy to analyze these precursor traits to decipher the genetic architecture of the underlying complex end-point trait. While association methods for both quantitative and qualitative traits have been extensively developed to analyze population level data, development of such methods are of current research interest for family-level data that pose additional challenges of incorporation of correlation of trait values within a family. Haldar and Ghosh (2015) developed a test which is Statistical equivalent of the classical TDT for quantitative traits and multivariate phenotypes. The model does not require a priori assumptions on the probability distributions of the phenotypes. However, it may often arise in practice that data on the phenotype of interest may not be available for all offspring in a nuclear family. In this study, we explore methodologies to estimate missing phenotypes conditioned on the available ones and carry out the transmission-based test for association on the 'complete' data. We consider three types of phenotypes: continuous, count and categorical. For a missing continuous phenotype, the trait value is estimated using a conditional normal model. For a missing count phenotypes, the trait value is estimated using a conditional Poisson model. For a missing categorical phenotype, the risk of the phenotype status is estimated using a conditional logistic model. We shall carry out simulations under a wide spectrum of genetic models and assess the effect of the proposed imputation strategy on the power of the association test vis-\`a-vis the the ideal situation with no missing data.