Abstract
In some studies, especially clinical studies, failure (death).as a result of other (external) factors, Any additional risks that may occur that compete with the case under study are called competing risks, which affect the hazard function of the Cox model. It is referred to Censoring Data From the Right, which is affected by differences in time and the phenomenon under investigation. The time of occurrence of these risks is known between two examinations, as in the Censoring Data From the Right, depending on the nature of the data for the case under study. The impact of these risks on the hazard function is estimated based on the Cox proportional hazards model, Which was estimated through the parametric part represented by the partial maximum potential method and using numerical algorithms (Newton Raphson - Down Hill) to estimate the parameters. represented by the effect of variables on the Cox hazard function , The other nonparametric part is to estimate the effect of time on the risk function through the Kaplan-Meier formula. These methods were applied to experimental data through large-scale simulations with different sample sizes from Censoring Data From the Right to size (n=30,70,100,140) As well as four initial default values for the parameters and three models of arithmetic parameters And standard deviations . After that, it was applied to real data for people with breast cancer for a random sample size of (100) for the control data from the right in order to obtain the best estimation methods. After analyzing the simulation results and real data, the results obtained showed that the Downhill (DH) algorithm is the best estimation method compared to the Newton-Raphson (NR) algorithm Depending on the statistical criterion for comparison, the average root mean square error of the model (Average Root Mean Square Error) . After estimating the competitive risk for real data based on the cumulative risk function (CIF), which explained the effect of common variables in increasing the competitive risk on the risk function of the Cox model.
Keywords: Hazard function, Censoring Data From the Right, Cox proportional hazards model, partial Maximum likelihood, Newton-Raphson algorithm, Downhill algorithm
