Effective Factors on Survival Time of the leukemic Patients and Estimating the Mean of Survival Time by Expectation and Maximization Algorithm and Monte Carlo Markov Chains Simulation Method

Leukemia is a kind of malignancy blood system which leads to death of human beings in a very short period of time. In this paper, the effective factors on survival time of the acute lymphoblastic leukemia (ALL) patients have been considered to achieve a linear regression model show the relation between the life-time after diagnosis and some explanatory factors. In this study, the data of 52 patients died from ALL was used. The designed model contained three variables, hemoglobin, large undifferentiated cell (LUC) and age. According to the data suggesting, a kind of mixture distribution, we considered a mixture model for survival time. Applying the EM-algorithm, we have found the maximum likelihood estimate of mean survival time and the Bayesian estimate of the mean survival time by Monte Carlo Markov Chain method. Based on the obtained estimating survival function, we can predict the survival time of the patients and decide about their treatment protocol. It is suggested that by conducting larger studies and statistical analysis used in this paper, a correlative can be found between clinical & paraclinical findings and the survival time. This model can be used in often kinds of diseases for determining the prognosis.