Longitudinal genetic studies provide a valuable resource for exploring key genetic and environmental factors that affect complex traits over time. Genetic analysis of longitudinal data that incorporates temporal variations is important for understanding genetic architecture and biological variations of common complex diseases. Although they are important, there is a paucity of statistical methods to analyze longitudinal human genetic data. In this project, longitudinal methods are developed for temporal association mapping to analyze population longitudinal data. Both parametric and non-parametric models are proposed. The models can be applied to multiple di-allelic genetic markers such as single nucleotide polymorphisms and multi-allelic markers such as micro-satellites. By analytical formulae, we show that the models take both the linkage disequilibrium and temporal trends into account simultaneously. Variance-covariance structure is constructed to model the single measurement variation and multiple measurement correlations of an individual based on the theory of stochastic processes. Novel penalized spline models are used to estimate the time-dependent mean functions and regression coefficients. The methods were applied to analyze Framingham Heart Study data of Genetic Analysis Workshop (GAW) 13 and GAW 16. The temporal trends and genetic effects of the systolic blood pressure are successfully detected by the proposed approaches. Simulation studies were performed to find out that the non-parametric penalized linear model is the best choice in fitting real data. The research sheds light on the important area of longitudinal genetic analysis, and it provides a basis for future methodological investigations and practical applications.

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Fan, Ruzong; Wang, Yifan; Yan, Qi et al. (2016) Gene-Based Association Analysis for Censored Traits Via Fixed Effect Functional Regressions. Genet Epidemiol 40:133-43
Fan, Ruzong; Wang, Yifan; Chiu, Chi-Yang et al. (2016) Meta-analysis of Complex Diseases at Gene Level with Generalized Functional Linear Models. Genetics 202:457-70
Boghossian, Nansi S; Sicko, Robert J; Kay, Denise M et al. (2016) Rare copy number variants implicated in posterior urethral valves. Am J Med Genet A 170:622-33
Fan, Ruzong; Chiu, Chi-Yang; Jung, Jeesun et al. (2016) A Comparison Study of Fixed and Mixed Effect Models for Gene Level Association Studies of Complex Traits. Genet Epidemiol :
Fan, Ruzong; Wang, Yifan; Boehnke, Michael et al. (2015) Gene Level Meta-Analysis of Quantitative Traits by Functional Linear Models. Genetics 200:1089-104
Wang, Yifan; Liu, Aiyi; Mills, James L et al. (2015) Pleiotropy analysis of quantitative traits at gene level by multivariate functional linear models. Genet Epidemiol 39:259-75
Fan, Ruzong; Chen, Victoria; Xie, Yunlong et al. (2015) A Functional Data Analysis Approach for Circadian Patterns of Activity of Teenage Girls. J Circadian Rhythms 13:3
Fan, Ruzong; Zhu, Bin; Wang, Yuedong (2014) Stochastic dynamic models and Chebyshev splines. Can J Stat 42:610-634
Fan, Ruzong; Wang, Yifan; Mills, James L et al. (2014) Generalized functional linear models for gene-based case-control association studies. Genet Epidemiol 38:622-37
Lobach, Iryna; Fan, Ruzong; Manga, Prashiela (2014) Genotype-based association models of complex diseases to detect gene-gene and gene-environment interactions. Stat Interface 7:51-60

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