Longitudinal genetic studies provide a very valuable resource for exploring key genetic and environmental factors that affect complex traits over time. Genetic analysis of longitudinal genetic data that incorporates temporal variations is important for understanding genetic architecture and biological variations of common complex diseases. It may provide a powerful tool to identify genetic determinants of complex diseases, and to understand at which stage of human development that the genetic determinants are important. Moreover, important environmental factors which are associated with the complex diseases, such as diet, familial income, and smoking status, can be identified. Although they are important, there is a paucity of statistical methods to analyze longitudinal human genetic data. For instance, there is no combined linkage and association analysis of the Framingham Heart Study data. The reason is that there are no longitudinal statistical models, methods, and software for a joint linkage and association study of temporal quantitative traits of complex diseases. In the classical theory of statistical genetics, the research is limited to analyzing genetic data in which phenotypes and related measurements are observed only one time. For longitudinal genetic data, however, phenotype traits and related measurements are usually observed and recorded over time. Therefore, multiple measurements are available for a subject, which depend on the subject's age or time. Due to the lack of statistical models and methods in analyzing longitudinal genetic data, some studies collapse the measurements to be a single value and run an analysis based on the classical theory of statistical genetics. For instance, there are multiple measurements of either systolic or diastolic blood pressure, age and body mass index for a participant over time in the Framingham Heart Study data. However, the sample averages of the blood pressure, age and body mass index are usually used in genome scan linkage studies. This is, essentially, not a longitudinal analysis. The phenotype traits are usually varying with age, and so there are temporal variations. After collapsing the multiple measurements to be a single value, no temporal variations can be detected in an analysis. This type of analysis may not always be able to get ideal results and to draw the best information from the data. This proposal extends the character process model of function-valued traits for combined linkage and association mapping of longitudinal genetic data. This proposal will develop models and methods which take major gene effects, LD information, polygenic and environmental effects into account. The temporal trends and familial structure will be simultaneously incorporated into the models. The interaction between genetic effects and age or time can be tested via hypothesis testings.

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