COMPARISON OF COX, WEIBULL AND GOMPERTZ REGRESSION MODELS IN SURVIVAL ANALYSIS USING BREAST CANCER DATA
COMPARISON OF COX, WEIBULL AND GOMPERTZ REGRESSION MODELS IN SURVIVAL ANALYSIS USING BREAST CANCER DATA
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Date
2014-11
Authors
MOHAMMED, USMAN
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Abstract
Survival analysis is a class of statistical methods designed to study the occurrence and timing of events. This study aimed to compare the results of semi-parametric Cox proportional hazards model and parametric models (Weibull and Gompertz) to determine the model that best fits breast cancer data. Kaplan-Meier (K-M) method was used to estimate and graph the survival curves using the data obtained from Ahmadu Bello University Teaching Hospital Zaria on 312 breast cancer patients between 1997 and 2012. The mean age of the breast cancer patients was found to be 43.39 years with standard deviation of 11.74 years and overall median survival time of 10 months. The 5-year overall survival rate was about 35.0%. In comparing the semi-parametric Cox model and parametric (Weibull and Compertz) models, Akaike Information Criterion (AIC) was used to evaluate the three models. Weibull regression model had the least AIC value (422.60) which shows best performance in handling breast cancer data, where as Cox regression model has the highest AIC value (530.65) followed by Gompertz model with AIC value (430.28). From the results of the analysis obtained, for Cox, Weibull and Gompertz regression models, age, occupation and stage II of the breast cancer does not have significant effect on the mortality of the patients, (p = 0.0440, 0.0270, 0.1740 respectively) but results of the treatment and stage III of breast cancer have significant effect on the mortality of the patients, (p = 0.0001, 0.00001 respectively). p < 0.01 is considered as statistical significant. The results of this study showed that, according to our breast cancer data, the parametric Weibull regression model could better determine the factors associated with the breast cancer disease than the semi-parametric Cox proportional hazards model. That is, Weibull
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model provided a better fit to the study data than the Cox proportional hazards and Gompertz models.
Description
A THESIS SUBMITTED TO THE POST GRADUATE SCHOOL, AHMADU BELLO UNIVERSITY, ZARIA, DEPARTMENT OF MATHEMATICS, IN PARTIAL FULFILMENT FOR THE AWARD OF DEGREE OF MASTER OF SCIENCE (M.SC.) IN STATISTICS.
NOVEMBER, 2014
Keywords
COMPARISON,, COX,, WEIBULL, GOMPERTZ REGRESSION,, MODELS,, SURVIVAL ANALYSIS,, BREAST,, CANCER DATA.