Methods of Estimating Weibull Model Using Breast Cancer Patients Life Time ‘. .

Abstract

The data for this study is derived from cancer registry in Survillance Epidemiolgy and End Results (SEER) for 1582 women diagnosed with breast cancer in the year 1992 at age 50-54 . Mortality among these women to the time since diagnosis and to the stage of the diseases at diagnosis were related . The study period ,extending through 7 years is divided into seven one year periods and for each stage we examine the relationship of stages among breast cancer patients to the seven years survival time and we conclude that breast cancer patients placed in stage four are consistent with the seven years sun/ival time .So fi"om SEER we obtained data for 240 women diagnosed with breast cancer and are placed in stage four at age 50-54 . We relate mortality among these women to the time since diagnosis and to the years of diagnosis 1988, 1989,l990,l991,1992. The Webiull distribution has received much attention in recent years ,specially as a model of lifetimes in survival theory.The relationship of stage four among breast cancer patients is examined using the Weibull distribution it is observed that distribution of survival can be represented by Weibull curve for all five years of diagnosis and the observed data is very similar to the expected data drawn from Weibull distribution. The study is concerned with methods of estimating parameters of the Weibull distribution .The ordinary Least Squares , the method Mo1nent,the Maximum Likelihood and Bayesian methods were were used to estimate the parameters using stage four of the data .It difficult using analytic methods to have an idea of the properties of the four estimators ,as we have one sample size. So the technique of simulation was used to obtain various samples] size.. Total deviation ,mean square error, bias from the real median survival time and bias from the real mean lifetime of each estimator were obtained, for the purpose of comparing methods of estimation. ' The results obtained were some-what expected and estimates easily interpreted .The Least square method and the Bayesian method a