This document compares different dimensionality reduction techniques for survival analysis, including principal component analysis (PCA), partial least squares (PLS), and random matrices (RM). It simulates datasets using R and applies the techniques to analyze survival curves. The results found that PCA outperformed PLS, and that all three variants of RM were comparable and superior to PCA and PLS. The document suggests this unexpected outcome may relate to limitations of R or not incorporating censored data, and recommends further exploring the techniques on real datasets.

1. Survival Analysis Dimension Reduction Techniques:
A Comparison of Select Methods
Iván Rodríguez†
and Claressa L. Ullmayer∗
† The University of Arizona * The University of Alaska, Fairbanks
Researchers often obtain copious and/or
incomplete data that can be superfluous/collinear
in terms of explaining particular outcomes—even
sophisticated analysis software and machinery
struggle under these particular conditions.
Purpose: compare Principal Component Analysis
(PCA), Partial Least Squares (PLS), and
Johnson-Lindenstrauss inspired Random
Matrices (RM) in terms of reducing dataset
dimensionality while retaining generality.
Survival Analysis: overcomes limitations of
standard regression approaches, able to include
positive values, can handle censoring.
PCA: obtains components/eigenvalues from
data’s variance-covariance matrix, maximizes
covariance and correlation of linear combinations
of predictor variable, produces new less
correlated variables by orthogonal
transformations of covariates.
PLS: same as PCA, except maximizes
covariance and correlation of linear combinations
of predictor and response variables, projects
predictor and response variables into new space
to model covariance structure.
RM: matrix with predetermined qualities is
randomly generated and applied to predictor
matrix.
Accelerated Failure Time (AFT) Model: provides
intuitive interpretation of predictor and response
variables via survivor curves, directly models
survival times.
1. simulate datasets using R statistical software
2. generate data and associated true survivor curve
3. implement all dimension reduction techniques on data
4. obtain survivor curve estimates from each procedure
5. calculate bias and mean-squared error on fixed times
6. repeat 1-5 for desired amount of iterations
7. receive final plots to analyze performance
Achlioptas, D. Database-friendly random projections: Johnson-Lindenstrauss with
binary coins. Journal of Computer and System Sciences 66(4): 671-687, 2003.
Dasgupta, S. and A. Gupta. An elementary proof of a theorem of Johnson and
Lindenstrauss. Random Structures and Algorithms 22(1): 60-65, 2003.
Johnson, W.B. and J. Lindenstrauss. Extensions of Lipschitz maps into a Hilbert
space. Contemp Math 26: 189-206, 1984.
Nguyen, Tuan S. and Javier Rojo. Dimension Reduction of Microarray Data in the
Presence of a Censored Survival Response: A Simulation Study. Statistical
Applications in Genetics and Molecular Biology 8(1): 2009.
Nguyen, Tuan S. and Javier Rojo. Dimension Reduction of Microarray Gene
Expression Data: The Accelerated Failure Time Model. Journal of Bioinformatics
and Computational Biology 7(6): 939-954, 2009.
According to the results, PCA outperforms PLS,
all three RM variants are comparable, and all
RMs are superior to PCA and PLS.
1. integrate censored data into investigation
2. apply findings to real datasets such as
microarray gene cancer datasets
3. utilize more powerful software than R and
advanced technology
4. observe effects of altering regression model—
e.g., instead of AFT, implement Cox
Proportional Hazards Model
This project was realized in part thanks to the generous guidance and support from
PI Javier Rojo Jiménez along with Kyle Bradford, Nathan C. Wiseman, Raul Cruz-
Cano, and Rashidul Hasan.
This research was supported by the National Security Agency through Grant
H98230-15-1-0048 to the University of Nevada at Reno, Javier Rojo PI.
Analysis and Discussion
RMs unexpectedly outdo PCA and PLS—could
be connected to the limits of R’s accuracy when
generating datasets and/or not incorporating
censored data.
PLS performs in-depth analysis of predictor and
response variables, yet is bested by PCA—could
also have to do with dataset generation.
Further Inquiry
Acknowledgements
Literature Cited
Results
Assessment Sample CurveIntroduction
Methods