Stationary Wavelet Packet Transform and Dependent Laplacian Bivariate Shrinkage Estimator for Array-CGH Data Smoothing

Array-based comparative genomic hybridization (aCGH) has merged as a highly efficient technique for the detection of chromosomal imbalances. Characteristics of these DNA copy number aberrations provide the insights into cancer, and they are useful for the diagnostic and therapy strategies. In this article, we propose a statistical bivariate model for aCGH data in the stationary wavelet packet transform (SWPT) and apply this bivariate shrinkage estimator into the aCGH smoothing study. Because our new dependent Laplacian bivariate shrinkage estimator covers the dependency between wavelet coefficients and the shift invariant SWPT results include both low- and high-frequency information, our dependent Laplacian bivariate shrinkage estimator based SWPT method (named as SWPT-LaBi) has fundamental advantages to solve aCGH data smoothing problem compared to other methods. In our experiments, two standard evaluation methods, the Root Mean Squared Error (RMSE) and the Receiver Operating Characteristic (ROC) curve, are calculated to demonstrate the performance of our method. In all experimental results, our SWPT-LaBi method outperforms the previous most commonly used aCGH smoothing algorithms on both synthetic data and real data. Meantime, we also propose a new synthetic data generation method for aCGH smoothing algorithms evaluation. In our new data model, the noise from real aCGH data is extracted and used to improve synthetic data generation.