Comparative Analysis of the Cox Semi-parametric and Weibull Parametric Models on Colorectal Cancer Data
International Journal of Data Science and Analysis
Volume 6, Issue 1, February 2020, Pages: 41-47
Received: Jan. 26, 2020;
Accepted: Feb. 13, 2020;
Published: Mar. 17, 2020
Views 432 Downloads 111
Usman Umar, Department of Mathematics, Usmanu Danfodiyo University, Sokoto, Nigeria
Marafa Haliru Muhammad, Department of Mathematics, Usmanu Danfodiyo University, Sokoto, Nigeria; Planning Division, Usmanu Danfodiyo University Teaching Hospital, Sokoto, Nigeria
The survival and hazard functions are key concepts in survival analysis for describing the distribution of event times. The survival function gives, for every time, the probability of surviving (or not experiencing the event). The hazard function gives the potential that the event will occur, per time unit, given that an individual has survived up to the specified time. While these are often of direct interest, many other quantities of interest (e.g., median survival) may subsequently be estimated from knowing either the hazard or survival function. This research was a five-year retrospective study on data from a record of colorectal cancer patients that received treatments from 2013 to 2017 in Radiotherapy Department of Usmanu Danfodiyo University Teaching Hospital, Sokoto, being it one of the cancer registries in Nigeria. 9 covariates were selected to fit colorectal cancer data using Cox and Weibull Regression Models. From the result it is concluded that the predictor variables could significantly predict the survival of colorectal cancer patients using Cox. Also the result of the Weibull Proportional Hazard Model shows that the model is adequate enough to predict the survival of the colorectal patients. The A. I. C result shows that, according to our colorectal cancer data, the semi-parametric Cox regression model performed better than the parametric Weibull proportional hazards model. However, in the present study, the Cox model provided an efficient and a better fit to the study data than Weibull model.
Marafa Haliru Muhammad,
Comparative Analysis of the Cox Semi-parametric and Weibull Parametric Models on Colorectal Cancer Data, International Journal of Data Science and Analysis.
Vol. 6, No. 1,
2020, pp. 41-47.
Brenner, H., Kloor, M., & Pox, C. P. (2014). Colorectal cancer. The Lancet, 1490-1502.
Potter, J. D., & Hunter, D. (2008). Colorectal Cancer. In H.-O. Adami, D. Hunter, & D. Trichopoulos, Textbook of Cancer Epidemiology (pp. 275-297). New York: Oxford University Press, Inc.
Arnold, M., Sierra, M. S., Laversanne, M., & Soerjomataram, I. (2017). Global patterns and trends in colorectal cancer incidence and mortality. Gut, pp. 683-691.
Hosmer D. W., Lemeshow S., and May S. (2008). Applied Survival Analysis: Regression Modeling of Time- to- Event Data. 234-654.
Nigerian National System of Cancer Registries (NSCR) 2018.
Abdulkareem, F., (2009). Epidemiology and Incidence of Common Cancer in Nigeria. Presentation of Cancer Registration and Epidemiology Workshop. April, 2009.
Dickman, P. W. and Hakulinen, T. (2008). Population-Based Cancer Survival Analysis. John Wiley and Sons, UK 23-65.
Kleinbaum D G and Klein M. (2005) Survival Analysis New York: Springer. 16-53.
Dickman, P. W. (2010). An Introduction and Some Recent Development in Statistical Methods for Population-Based Cancer Survival Analysis. Statistical Methods for Population-Based Cancer Survival Analysis. Milan, 33-55.
Adejumo, A. O. and Ahmadu, A. O. (2016) A Study of the Slope of Cox Proportional Hazard and Weibull Models. Science World Journal Vol 11 (No 3) 2016.
Quantin, C., Michal, A., Thierry, M., Gillian, B., Todd, M., Mohammed, A., et al., (1999) Variation over Time of the Effects of Prognostic Factors in a Population based Study of Colon Cancer: Comparison of Statistical Models. American Journal of Epidemiology, Vol. 150, 11-20.
Ahmed E. F., Paul W. V., Don H., (2007) Modeling survival in colon cancer: a methodological review. Molecular Cancer 2007, 6: 15 doi: 10.1186/1476-4598-6-15.
Abdulkabir M., Ahmadu A. O., Udokang A. E., Raji S. T., (2015). Gradient Curve of Cox Proportional Harzard and Weibull Models. Automatic Control of Physiological State and Function, 2:2 http://dx.doi.org/10.4172/2090-5092.1000108
Wang Kesheng, Xuefeng Liu, Yue Pan, Daniel Owusu1, Chun Xu. (2017) Comparison of Cox Regression and Parametric Models. Journal of Data Science 16 (2017), 423-442.
World Health Organisazation. 2013a Cancer Control: A Global Snaptshot in 2015http://www.who.int/cancer/cancer-snapshot-2015/en/ Accesed on 9 November 2016.
Knut A. M., Dejan Ignjatovic, Marianne A. M. (2017) Tailored Treatment of Colorectal Cancer: Surgical, Molecular, and Genetic Considerations. Clinical Medicine Insights: Oncology. DOI: 10.1177/1179554917690766.
Armstrong, B. K. (1992). The Role of Cancer Registry in Cancer Control. Cancer Causes and Control. 3: 569–579.
Zaki A. (2015) Log-linearity for Cox’sregression model. University of Oslo.
Yuan, Xingchen, "Survival Model and Estimation for Lung Cancer Patients." (2005). Electronic Theses and Dissertations. Paper 1002. http://dc.etsu.edu/etd/1002.
Sylla BS, Wild CP (2011). A million Africans a Year Dying from Cancer by 2030: What can cancer research and control offer to the continent? Int J Cancer.
Collett, D.(2003). Modelling Survival Data in Medical Research. Chapman and Hall, London, 37-87.
Cox D: Regression Models and Life Tables (with Discussion). J Roy Stat Soc B 1972, 4: 187-220.
Akaike H (1977). A new look at the statistical model identification. IEEE Trans Automatic Control, 19, 716-23.
Klein J, Moeschberger M. (1997) Survival Analysis: Techniques for Censored and Truncated Data, New York: Springer-Verlag.