Nonlinear function-on-scalar MINQUE with application to genetic heritability
Open AccessFunctional data analysis (FDA) primarily is designed for the analysis of random trajectories and infinite-dimensional data. Many studies already developed adequate statistical estimation and inference techniques. FDA provides the opportunity to better understand the genetic influence on the temporal development of diseases in longitudinal studies. Quantifying heritability can explain the contribution of genetic variation to the risk architecture of complex human diseases and traits. Some studies already established some methodologies for defining or estimating heritability. FDA draw more and more people’s attentions and is applied in estimating heritability for longitudinally measured phenotypes. There is a study constructed a minimum norm quadratic unbiased estimation (MINQUE) of variance components in functional linear models, presented by Matthew Reimherr and Dan Nicolae. Furthermore, we extend the procedure to a more generalized environment without the linear assumption. We introduce a general methodology for estimating the heritability by minimum norm quadratic estimation (MINQE) in both functional local polynomial model and functional partially linear model. A functional partially linear estimation procedure for model coefficients using a profile weighted least squares approach is proposed. Our methodology is applied in the Childhood Asthma Management Program(CAMP), a 4-year longitudinal study examining the long term effects of daily asthma medications on children. Meanwhile, it is not only limited to chilhood asthma but also compare these results with the adulthood asthma program, Asthma Clinical Research Network (ACRN).
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