Title: Family-based association tests with longitudinal measurements
Description: For many family-based studies, the disease-related phenotypes are often measured longitudinally or repeatedly. This dissertation makes several contributions to utilize the multivariate data more efficiently for testing genetic association, as well as to handle practical problems such as hidden population stratification and missing observation. In the first part, we test for association between SNP rs7566605 and longitudinal Body Mass Index (BMI) from the Childhood Asthma Management Program (CAMP) study. The effect estimates and tests using the within-family data show a striking contrast to those obtained using the between-family data. We explore reasons for the apparent discrepancy and present some simple approaches for combining results over time. We find that the amount of information available for testing within families varies by the choice of model, e.g. additive versus recessive. In other words, a recessive genetic model appears to be less robust to population stratification than an additive model.

In the second part, for a widely used approach FBAT-PC, we propose a modified method FBAT-PCM, which has a closed-form expression and is always more powerful. We also present two alternative approaches, FBAT-LC and FBAT-LCC, based on linear combination of univariate tests. Furthermore, these three approaches are shown to be unified to a general form. We show that all these approaches are powerful, and their relative performance depends upon the underlying model. In the following part, we show that these FBAT approaches are still robust against hidden population stratification, but their power can be heavily affected. We introduce a permutation-based approach FBAT-MinP and an equal combination approach FBAT-EW, both of which are shown be powerful even with the presence of population stratification. In the last part, FBAT-LC and FBAT-LCC are easily extended to accommodate incomplete data and remain to be unbiased tests. We also propose two imputation techniques based on conditional mean model and E-M algorithm, both of which hold the correct false positive rate and generally achieve higher power. We confirm our findings via simulation studies and real analyses for BMI data from the Framingham Heart Study and the CAMP Study.