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Comparison of Cox, Weibull and Gompertz Regression Models in Survival Analysis Using Breast Cancer Data

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– Comparison of Cox, Weibull and Gompertz Regression Models in Survival Analysis Using Breast Cancer Data –

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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.

Introduction

1.1 Background of the Study

Survival analysis is a class of statistical methods designed to study the occurrence and timing of events. The methods were developed for studying the time from initiating events (such as birth, diagnosis of a disease, start of a treatment e.t.c.) to some terminal events (such as response to a treatment, relapse, death e.t.c.).

These methods are mostly applied in medical sciences. However, the methods were successfully applied to many different kinds of events across disciplines.

Examples include the manufacturing or engineering sectors (how long it takes a machine to fail), social sciences (how long a marriage will last), finance (the time it takes the price of stock in stocks market to drops) and so on.

Sometimes other names are used to refer to this class of methods such as “duration analysis”, “failure time analysis”, “event history analysis”, “transition analysis”, but the basic techniques are the same as in the underlying ideas i.e. understanding the pattern of events in time and what factors cause those events to occur.

Survival analysis measures the probability of how long it takes a given outcome to occur for a group of similar individuals known as failure times (Cox and Oates, 1984). Survival analysis method also measures the probability that the given event in question will last the next point in time (Gokovali et al, 2007).

Survival analysis studies are well known to occur in medical sciences particularly in cancer studies. Depending on the question of the studies, one is interested in the risk groups i.e.

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