Survival analysis is one of the types of data analysis that describes the time period until the occurrence of an event of interest such as death or other events of importance in determining what will happen to the phenomenon studied. There may be more than one endpoint for the event, in which case it is called Competing risks. The purpose of this research is to apply the dynamic approach in the analysis of discrete survival time in order to estimate the effect of covariates over time, as well as modeling the nonlinear relationship between the covariates and the discrete hazard function through the use of the multinomial logistic model and the multivariate Cox model. For the purpose of conducting the estimation process for both the discrete hazard function and the time-dependent parameters, two estimation methods have been used that depend on the Bayes method according to dynamic modeling: the Maximum A Posterior method (MAP) This method was done using numerical methods represented by a Iteratively Weighted Kalman Filter Smoothing (IWKFS) and in combination with the Expectation maximization algorithm (EM), the other method is represented by the Hybrid Markov Chains Monte Carlo (HMCMC) method using the Metropolis Hasting algorithm (MH) and Gypsum sampling (GS). It was concluded that survival analysis by descretization the data into a set of intervals is more flexible and fluid, as this allows analyzing risks and diagnosing impacts that vary over time. The study was applied in the survival analysis on dialysis until either death occurred due to kidney failure or the competing event, represented by kidney transplantation. The most important variables affecting the patient’s cessation of dialysis were also identified for both events in this research.
The estimation process is one of the pillars of the statistical inference process as well as the hypothesis test, and the assessment is based on the collection of information and conclusions about the teacher or the community's teachers on the basis of the result