Probabilistic comparison of survival analysis models using simulation and cancer data

 The object of the present study is to propose the power law process also known as non homogenous poison process which is identical to the weibull process in analyzing and modeling different types of cancer, especially breast cancer.  The key objective is to study the change of the tumor growth as a function of age. The intensity function within the power law process will give us the rate of change of the tumor growth as a function of time.  In addition the key parameter within the intensity function can give us the preliminary indication of the behavior of the tumor subject to a given treatment. POWER LAW PROCESS ANALYSIS  Power law process (PLP) also named nonhomogeneous poisson process (NHPP) as well as weibull process (WP). [4]. PLP has been used in many applications. PLP is a special Poisson process and Poisson process is one of counting process.  A counting process is a stochastic process that possesses the following properties:  1. N(t) >0  2. N(t) is an integer.  3. If s<= t then N(s) <= N(t).  If s< t, then N(t)-N(s) is the number of events occurred during the interval (s,t] .[5] ,... 1 , 0 ! ) ( ] )) ( )) ( [( , ,      k k e k a N b N P k b a b a   POWER LAW PROCESS ANALYSIS NHPP has the intensity function: V(t) has been very successfully used in reliability analysis v(t)=f(beta) . 0 , 0 , 0 , ) ( 1    t for t t                      POWER LAW PROCESS ANALYSIS  We know that if the parameter beta is greater than one, then the tumor size increase means the survival rate decreased. If beta is less than one in survival analysis, then the tumor size decrease which means the survival time increase. If beta equals to one then the tumor size is constant and the NHPP will become homogenous passion process (HPP).  The unbiased estimator of beta is provided by bain and Enelhardt (1991). [8]                n