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

Abstract

BACKGROUND: 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. METHODS: 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. FINDINGS: Based on the obtained estimating survival function, we can predict the survival time of the patients and decide about their treatment protocol. CONCLUSION: 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. KEY WORDS: Maximum likelihood estimation, bayesian estimation, bimodal, leukemia, mixture models, survival mean.