Exploring the influence of genetic or environmental factors in longitudinal data has been challenging genetic studies. While some
researchers have modeled sequenced data with a few data points as repeated measurements in which covariance is incorporated
with certain time series structures, to date, not much research has been done to address the issue of how genetic factors or environmental
factors affect the underlying behavior of the data with multiple measurements. In this study, we aim to build a statistical framework to
model the anticipated association between the development of a disease and hypothesized genetic or environmental factors.
The longitudinal phenotype data we modeled consists of three parts � the incubation period, the onset, and the disease appearing
period. Assuming the disease onset is missing, we propose a mixture model to model the longitudinal phenotype such as blood pressure
with association to the genotype or environmental factors. An EM based approach is used to estimate the distribution of the onset,
which might be related to either genotype or environmental factors. To estimate the onset distribution, a solution for a weighed logistic
regression under which weights on the outcome variables are proposed. A log likelihood ratio test is used to judge the significance of the
association between the distribution of the onset and the genotype or environmental factors. We conducted extensive simulation studies
to evaluate the model performance and gave desirable Type I error rates and the power of the proposed test.
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