Survival Analysis of Breast Cancer Patients Using Additive Hazards Regression Models

Goutam Barman¹ , Babulal Seal²

1. Department of Statistics, Krishnagar Government College, Nadia, INDIA.
2. Department of Statistics and Informatics, Aliah University, Kolkata, INDIA.

Correspondence should be addressed to: goutambrmn@gmail.com.

Section:Research Paper, Product Type: Isroset-Journal
Vol.3 , Issue.6 , pp.7-10, Jun-2017

Online published on Jun 30, 2017

Copyright © Goutam Barman, Babulal Seal . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

View this paper at   Google Scholar | DPI Digital Library

XML View     PDF Download

How to Cite this Paper

476 Views    266 Downloads    227 Downloads

Abstract :
Breast cancer is the most common malignant disease for females. Cox proportional hazards model are mostly used model to analysis the effects of prognostic factors to the breast cancer patients. In this study Aalen’s additive hazards model and Lin-Ying’s additive hazards model are used for survival analysis of breast cancer patients and compare with the results obtained by Cox proportional hazards model. The proportional hazards assumption was tested by using Schoenfeld residuals and -value less than 0.05 was consider statistically significant. Also overall survival rate were estimated by the Kaplan-Meier product limit method. 686 patients with breast cancer and seven standard prognostic factors, namely age at diagnosis, menopausal state, tumor size, tumor grading, no. of involved nodes, progesterone and estrogen receptor were entered into analysis. Two models, Cox and Lin-Ying’s models, are give the similar results. Four covariates namely tumor size, tumor grade III, nodes and progesterone receptor showed significant impact on the breast cancer patient’s data in both hazard models. Neither Cox model nor Lin-Ying model found age at diagnosis, menopausal state, tumor grade I, II and estrogen receptor as a significant prognostic factor. On the other hand, Aalen’s model shows that tumour grade III is not statistically significant but the other results are similar with Cox and Lin-Ying models. Generally, the Cox and additive hazards models give different pieces of information about the risk factors. So, to get more accurate results about the risk factors, it is desire to use these two models in parallel. However, if the proportional hazards assumption is not satisfied, additive hazards model is an appropriate alternative for the Cox model otherwise both models are appropriate.

Key-Words / Index Term :
Breast cancer, prognostic factor, Cox model, additive hazards models, survival analysis

References :
[1] WCR, “World Cancer Report 2014”, World Health Organization, Switzerland, pp.1-120, 2014
[2] Katalinic A, Pritzkuleit R, Waldmann A, “Recent trends in breast cancer incidence and mortality in Germany”, Breast Care (Basel) Vol.4, Issue.2, pp.75-80, 2009.
[3] Cox DR, “Regression models and life-tables”, Journal of Royal Statistical Society, Vol.34, Issue.2, pp.187-220, 1972.
[4] Mayer BD, “Unemployment insurance and unemployment spells”, Econometrica, Vol.58, Issue.4, pp.775-782, 1990.
[5] Bhat CR, “A hazard-based duration model of shopping activity with nonparametric baseline specification and nonparametric control for unobserved heterogeneity”, Transportation Research Part B: Methodological, Vol.30, Issue.3, pp.189-207, 1996.
[6] Aalen OO, “A model for nonparametric regression analysis of counting process”, Lecture notes in statistics, Vol.2, Issue.2, pp.1-25, 1980.
[7] Aalen OO, “A linear regression model for the analysis of life times”, Stat Med, Vol.8, Issue.8, pp. 907-925, 1989.
[8] Lin DY, Ying Z, “Semi-parametric analysis of the additive risk model”, Biometrika, Vol.81, Issue.1, 61-71, 1994.