Dimension reduction of microarray gene expression data: the accelerated failure time model.

Area of Science:

• Statistics
• Machine Learning
• Data Mining

Background:

• Partial Least Squares (PLS) is a statistical method for analyzing data with many predictor variables.
• Traditional PLS methods rely on Pearson correlation, which is sensitive to outliers in data.
• Outliers can significantly distort the results of statistical analyses, leading to inaccurate conclusions.

Purpose of the Study:

• To develop and evaluate rank-based Partial Least Squares (PLS) methods that are robust to outliers.
• To incorporate censoring information into rank-based PLS methods.
• To compare the performance of new rank-based PLS methods against traditional PLS and other dimension reduction techniques.

Main Methods:

• Replaced Pearson correlation with Spearman rank correlation in PLS optimization criteria.
• Developed Rank-based Modified Partial Least Squares (RMPLS), Rank-based Reweighted Partial Least Squares (RRWPLS), and Rank-based Mean-Imputation Partial Least Squares (RMIPLS).
• Incorporated censoring information using methods by Nguyen and Rocke (2004) and Datta et al. (2007).
• Evaluated methods using simulation studies and four real datasets under an Accelerated Failure Time (AFT) model.

Main Results:

• Rank-based PLS methods are insensitive to outliers in predictors and response.
• RMPLS showed improved performance over un-ranked PLS and other methods in the presence of outliers.
• RMPLS minimized cross-validation error of fit and mean squared error of fit in outlier scenarios.
• RMPLS performance was comparable to other PLS variants when no outliers were present.

Conclusions:

• Rank-based PLS methods offer a robust alternative to traditional PLS when dealing with outlier-prone data.
• RMPLS is a highly effective dimension reduction technique, particularly in the presence of response outliers.
• The developed rank-based approaches provide valuable tools for robust statistical modeling and dimension reduction.