PLS-Frailty Model for Cancer Survival Analysis Based on Gene Expression Profiles

  • Yi ZhouEmail author
  • Yanan Zhu
  • Siu-wai Leung
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 173)


Partial least squares (PLS) and gene expression profiling are often used in survival analysis for cancer prognosis; but these approaches show only limited improvement over conventional survival analysis. In this context, PLS has mainly been used in dimension reduction to alleviate the overfitting and collinearity issues arising from the large number of genomic variables. To further improve the cancer survival analysis, we developed a new PLS-frailty model that considers frailty as a random effect when modeling the risk of death. We used PLS regression to generate K PLS components from genomic variables and added the frailty of censoring as a random effect variable. The statistically significant PLS components were used in the frailty model for survival analysis. The genomic components representing the frailty followed a Gaussian distribution. Ten-fold cross-validation was used to evaluate the risk discrimination (between high risk and low risk) and survival prediction based on two breast cancer datasets. The PLS-frailty model performed better than the traditional PLS-Cox model in discriminating between the high and low risk clinical groups. The PLS-frailty model also outperformed the conventional Cox model in discriminating between high and low risk breast cancer patients according to their gene expression profiles.


PLS regression Microarray Genomic Cancer PLS frailty 



This study was supported by the research grants (MYRG 2014-00117-ICMS-QRCM and MYRG190-Y3-L3-ICMS11-LSW) received from the University of Macau.


  1. Bastien, P.: PLS-Cox model: application to gene expression. In: Antoch, J. (ed.) Proceedings in Computational Statistics, COMPSTAT 2004, pp. 655–662. Springer, Berlin (2004)Google Scholar
  2. Cox, D.R.: Regression models and life tables. J. R. Stat. Soc. Ser. B (Methodol.) 34, 187–220 (1972)Google Scholar
  3. Goeman, J.J., Oosting, J., Cleton-Jansen, A.-M., Anninga, J.K., Van Houwelingen, H.C.: Testing association of a pathway with survival using gene expression data. Bioinformatics 21, 1950–1957 (2005)Google Scholar
  4. Gui, J., Li, H.: Penalized Cox regression analysis in the high-dimensional and low-sample size settings, with applications to microarray gene expression data. Bioinformatics 21, 3001–3008 (2005)CrossRefGoogle Scholar
  5. Lambert-Lacroix, S., Letué, F., et al.: Partial least squares and Cox model with application to gene expression, working paper (2011)Google Scholar
  6. Lee, D., Lee, Y., Pawitan, Y., Lee, W.: Sparse partial least-squares regression for high-throughput survival data analysis. Stat. Med. 32, 5340–5352 (2013)MathSciNetCrossRefGoogle Scholar
  7. Li, H., Gui, J.: Partial Cox regression analysis for high-dimensional microarray gene expression data. Bioinformatics 20 (Suppl 1), i208–i215 (2004)CrossRefGoogle Scholar
  8. Nguyen, D.V., Rocke, D.M.: Partial least squares proportional hazard regression for application to DNA microarray survival data. Bioinformatics 18, 1625–1632 (2002)CrossRefGoogle Scholar
  9. Park, P.J., Tian, L., Kohane, I.S.: Linking gene expression data with patient survival times using partial least squares. Bioinformatics 18 (suppl 1), S120–S127 (2002)CrossRefGoogle Scholar
  10. Pawitan, Y., Bjöhle, J., Wedren, S., Humphreys, K., Skoog, L., Huang, F., Amler, L., Shaw, P., Hall, P., Bergh, J.: Gene expression profiling for prognosis using Cox regression. Stat. Med. 23, 1767–1780 (2004)CrossRefGoogle Scholar
  11. Ripatti, S., Palmgren, J.: Estimation of multivariate frailty models using penalized partial likelihood. Biometrics 56, 1016–1022 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  12. Rosipal, R., Krämer, N.: Overview and recent advances in partial least squares. In: Saunders, C., Grobelnik, M., Gunn, S., Shawe-Taylor, J. (eds.) Subspace, Latent Structure, and Feature Selection, pp. 34–51. Springer, New York (2006)CrossRefGoogle Scholar
  13. Therneau, T.M., Grambsch, P.M., Pankratz, V.S.: Penalized survival models and frailty. J. Comput. Graph. Stat. 12, 156–175 (2003)MathSciNetCrossRefGoogle Scholar
  14. Van De Vijver, M.J., He, Y.D., van’t Veer, L.J., Dai, H., Hart, A.A., Voskuil, D.W., Schreiber, G.J., Peterse, J.L., Roberts, C., Marton, M.J., et al.: A gene-expression signature as a predictor of survival in breast cancer. New Engl. J. Med. 347, 1999–2009 (2002)Google Scholar
  15. van Houwelingen, H., Putter, H.: Dynamic Prediction in Clinical Survival Analysis. CRC Press, Boca Raton (2011)zbMATHGoogle Scholar
  16. Wold, S., Sjöström, M., Eriksson, L.: PLS-regression: a basic tool of chemometrics. Chemom. Intell. Lab. Syst. 58, 109–130 (2001)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.State Key Laboratory of Quality Research in Chinese Medicine, Institute of Chinese Medical SciencesUniversity of MacauMacaoChina
  2. 2.Department of Clinical Epidemiology and Biostatistics, Graduate School of MedicineOsaka UniversityOsakaJapan
  3. 3.School of InformaticsUniversity of EdinburghEdinburghUK

Personalised recommendations