International E-publication: Publish Projects, Dissertation, Theses, Books, Souvenir, Conference Proceeding with ISBN.  International E-Bulletin: Information/News regarding: Academics and Research

Cox-proportional hazard model with flexible penalized spline: application to colon cancer

    ,

Author Affiliations

  • 1Department of Mathematical Sciences, Crescent University, Abeokuta, Nigeria
  • 2Department of Statistics, University of Ibadan, Ibadan, Nigeria

Res. J. Mathematical & Statistical Sci., Volume 11, Issue (1), Pages 4-8, May,12 (2023)

Abstract

This study examines the inherent trends in non-proportional hazard model and how non-linear covariates effect and interaction with time could be estimated by penalized likelihood with B-spline basis function. Bootstrap simulation was used to assess the assumptions and the results shown that the continuous variable “age” exhibited a non-linear trend, so, assessment of Cox PH model is essential to avoid wrong statistical inference.

References

  1. Fisher, L. D., & Lin, D. Y. (1999)., Time-dependent covariates in the Cox proportional-hazards regression model., Annual review of public health, 20(1), 145-157.
  2. Auton, T. (2001)., Modelling Survival Data: Extending the Cox Model., JSTOR, 50(4), 558-559.
  3. Abrahamowicz, M., & MacKenzie, T. A. (2007)., Joint estimation of time‐dependent and non‐linear effects of continuous covariates on survival., Statistics in medicine, 26(2), 392-408.
  4. Cox, D. R. (1972)., Regression models and life‐tables., Journal of the Royal Statistical Society: Series B (Methodological), 34(2), 187-202.
  5. Ata, N., & Sözer, M. T. (2007)., Cox regression models with nonproportional hazards applied to lung cancer survival data., Hacettepe Journal of Mathematics and Statistics, 36(2), 157-167.
  6. Gray, R. J. (1992)., Flexible methods for analyzing survival data using splines, with applications to breast cancer prognosis., Journal of the American Statistical Association, 87(420), 942-951.
  7. Friedman J.H. and Silverman B.W. (1989)., Flexible Parsimonious Smoothing and Additive modelling., American Statistical Association and the American Society for Quality control, 31(1), 3-21.
  8. Amzat K.T and Adeosun S.A (2014)., On a Sequential Probit Model of Infant Mortality in Nigeria. International Journal of Mathematics and Statistics Invention, 2(3), 89-94., undefined
  9. Heinzl, H., & Kaider, A. (1997)., Gaining more flexibility in Cox proportional hazards regression models with cubic spline functions., Computer methods and programs in biomedicine, 54(3), 201-208.
  10. Hess, K. R. (1995)., Graphical methods for assessing violations of the proportional hazards assumption in Cox regression., Statistics in medicine, 14(15), 1707-1723.
  11. Eisen, E. A., Agalliu, I., Thurston, S. W., Coull, B. A., & Checkoway, H. (2004)., Smoothing in occupational cohort studies: an illustration based on penalised splines., Occupational and environmental medicine, 61(10), 854-860.
  12. Eilers, P. H., & Marx, B. D. (1996)., Flexible smoothing with B-splines and penalties., Statistical science, 11(2), 89-121.
  13. Strasak, A. M., Lang, S., Kneib, T., Brant, L. J., Klenk, J., Hilbe, W., ... & VHM & PP Study Group (2009)., Use of penalized splines in extended Cox-type additive hazard regression to flexibly estimate the effect of time-varying serum uric acid on risk of cancer incidence: a prospective, population-based study in 78,850 men., Annals of epidemiology, 19(1), 15-24.
  14. Wand, M. P. & Ormerod, J. (2008)., On semiparametric regression with O, Australian & New Zealand Journal of Statistics, 50(2), 179-198.
  15. Malloy, E. J., Spiegelman, D., & Eisen, E. A. (2009)., Comparing measures of model selection for penalized splines in Cox models., Computational statistics & data analysis, 53(7), 2605-2616.