Wavelet-based Parametric Functional Mapping of
Developmental Trajectories with High-dimensional Data
Wei Zhao 1, Hongying Li 2, Wei Hou 2 and Rongling Wu 2*
1 University of California at Los Angeles
2 University of Florida
* To whom correspondence should be addressed. E-mail: rwu{at}stat.ufl.edu.
Submitted on January 13, 2007
Revised on March 5, 2007
Accepted on 10 April 2007
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Abstract |
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The biological and statistical advantages of functional mapping result from joint modelling of the mean-covariance structures for developmental trajectories of a complex trait measured at a series of time points. While an increased number of time points can better describe the dynamic pattern of trait development, a significant difficulty in performing functional mapping arises from prohibitive computational times required as well as modelling the structure of high-dimensional covariance matrix. In this article, we develop a statistical model for functional mapping of quantitative trait loci (QTL) that govern the developmental process of a complex trait based on wavelet dimension reduction. By breaking an original signal down into a spectrum by taking its averages (smooth coefficients) and differences (detail coefficients), we used the discrete Haar wavelet shrinkage technique to transform an inherently high-dimensional biological problem into its tractable low-dimensional representation within the framework of functional mapping constructed by a Gaussian mixture model. Unlike conventional nonparametric modelling of wavelet shrinkage, we incorporate mathematical aspects of developmental trajectories into the smooth coefficients used for QTL mapping, thus preserving the biological relevance of
functional mapping in formulating a number of hypothesis tests at the interplay between gene actions/interactions and developmental patterns for complex traits. This wavelet-based parametric functional mapping has been statistically examined and compared with full-dimensional functional mapping through simulation studies. It holds a great promise as a powerful statistical tool to unravel the genetic machinery of developmental trajectories with large-scale high-dimensional data.
Key Words:
Dimensionality reduction, Functional mapping, Mixture model, Quantitative trait loci, Wavelet transform
