Principal Variance Components Analysis for Quantifying Variability in Genomics Data
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1 Principal Variance Components Analysis for Quantifying Variability in Genomics Data Tzu-Ming Chu SAS Institute Inc.
2 Outlines Motivation PVCA (PCA + VCA) Example Mouse Lung Tumorigenicity Data Grouped Batch Profile Normalization (GBP) Discussion
3 Motivation - ANOVA Estimating variations of variance components among SAMPLEs ANOVA Some ANOVA approaches applied in microarrays - Kerr et al (Full-genes Model) - Wolfinger et al (Gene-by-Gene Mixed Model) - Chu et al (Probe-Level Mixed Model) - Feng et al (Empirical Bayesian Mixed Model)
4 Motivation - ANOVA ANOVA issues Lack of gene by gene correlations Quantification of variations among genes Y = Crspding_Ctrl_Grp + Treatment + Status + Residual
5 Principal Variance Components Analysis PCA the foundation of PVCA Variance-Covariance Matrix Mutually orthogonal among principal components VCA Mixed Model on individual principal component Weighted proportion of variations Eigen values Refer to Li et al. 2009, html
6 PVCA - PCA Projection onto eigenvectors ΣP = Σ[P 1,P 2,, P n ] = [ΣP 1, ΣP 2,,ΣP n ] = [λ 1 P 1, λ 2 P 2,,λ n P n ] Σ Eigenvalue λ i represents the variance associated with the i th principal component P 1 λ 1 P 2 λ 2
7 PVCA Analysis Flow Chart PCA analysis on the covariance/correlation matrix Retain the eigenvalues Select the first few Principal Components Estimate variance component by a mixed model to each principal component Compute the eigenvalue-weighted average of VC estimates obtained from each model Standardize all the averaged VC estimates including model residuals, and present them as the proportions of total variance
8 Mouse Lung Tumorigenicity Data Develop microarray-based biomarkers to predict the results from a rodent cancer bioassay following a short term chemical exposure (NTP 1996) Data from (GSE17933) 26 chemicals from 4 studies over 3 years (2005-7) 158 Affymetrix Mouse Genome GeneChips One of the six MAQCII data
9 Batch Mouse Lung Tumorigenicity Data Animal Study ID Animal Batch Vehicle Group a Controls CA NCA Compounds FCON CCON FCO CCO CCO WCO CCO FCO ACO CCO ACO CCO ACO ACO a The first three letters in the abbreviation define the vehicle and route used for administration (FCO = food; CCO = corn oil by gavage; WCO = water by gavage; ACO = air by inhalation). The last number or letter refers to the specific batch the vehicle was used. CA=Carcinogenicity.
10 PVCA Results Y = Crspding_Ctrl_Grp + Study_ID+ Treatment + Status + Residual Average across 12 principal components 80.95% of total variation
11 Grouped Batch Profile (GBP) Normalization Batch profile estimation Based on control arrays Batch profile grouping Clustering on similar profiles Batch profile correction Batch profile scoring
12 GBP Batch Profile Estimation Estimation based on control arrays Assuming additive model Y = α(s) + β(b) + e Model for Control Arrays Y c = α(c) + β(b) + e For simplicity Y ci = µ c + β i + e Estimated Batch Profile
13 GBP Profile Clusters Clustering on standardized profiles
14 GBP Batch Profile Correction Extract mean profile from each cluster to be the representative profile, Correct the corresponding representative profile from data Scoring new batches
15 PVCA GBP Results Before After Average across 19 principal components 80.96% of total variation
16 Prediction of Carcinogenicity 84 prediction models from 8 types of models (Discriminant Analysis, Distance Scoring, General Linear Model, K Nearest Neighbors, Logistic Regression, Partial Least Squares, Partition Trees, and Radial Basis Machine) Randomly hold out 3 batches from 14 batches as validation data Repeat 50 times and assess on Accuracy, AUC, and RMSE Apply on 3 normalized data (MMA,RMA,GBP) Refer to Chu et al for details
17 Cross Validation Results
18 Discussion PVCA provides estimations of variance component among arrays without excluding covariance between genes PVCA can be a useful tool for exploring data PVCA can be a good assessment tool for normalization to quantify how much of variation changed across variance components R and SAS code is available at pvca
19 Acknowlegements Jianying Li (UNC/Chapel Hill) Pierre Bushel (NIEHS) SAS Colleagues Russ Wolfinger Wenjun Bao Li Li Shannon Conners
20
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