Flexible semiparametric analysis of longitudinal genetic studies by reduced rank smoothing

In longitudinal genetic studies, investigators collect repeated measurements on a trait that changes with time along with genetic markers. For family-based longitudinal studies, since repeated measurements are nested within subjects and subjects are nested within families, both the subject level and the measurement level correlations must be taken into account in the statistical analysis to achieve more accurate estimation. In such studies, the primary interests include testing for a quantitative trait locus effect, and estimating the age-specific quantitative trait locus effect and residual polygenic heritability function. We propose flexible semiparametric models and their statistical estimation and hypothesis testing procedures for longitudinal genetic data. We employ penalized splines to estimate non-parametric functions in the model. We find that misspecifying the baseline function or the genetic effect function in a parametric analysis may lead to a substantially inflated or highly conservative type I error rate on testing and large mean-squared error on estimation. We apply the proposed approaches to examine age-specific effects of genetic variants reported in a recent genomewide association study of blood pressure collected in the Framingham Heart Study.