Choosing Best Robust Estimation Parameters among Some Exponential Family Distributions

Abstract

Survival analysis is statistical route deliberated to explore the time until an event appears. Most research on the reliability of the survival function has some shortcomings in the process of accurate statistical analysis that aims to obtain highly efficient estimates. The necessity for these efficient estimation methods is called robust methods which becomes important when the data for the phenomenon being studied is contaminated, i.e., there are outliers in the observations, which results in estimates that lead to an increase or decrease in the mean square error (MSE), which leads to inaccurate statistical inference. A breast cancer is commences from the abnormal growth of the cells in the mammary gland, ductal carcinoma or lobular carcinoma of the breast the data that has been used has 4024 observations and the independent variables are (Age, Tumor Size, Tumor Stage, and Node Stage). The study focusses on comparing different methods such as (AFT), Regression model, Robust AFT with Tukey’s Biweight function, Robust AFT with Median function and Robust Regression model with Tukey’s Biweight function for each of (Exponential, Weibull and Lognormal) distributions and non-parametric bootstrap is used to derive the standard error, z-values and p-values for each of the classical and robust methods, ensuring robust inference free from asymptotic assumptions.The Aim of this study is to choose the best method from each of (AFT), Regression model, Robust AFT with Tukey’s Biweight function, Robust AFT with Median function and Robust Regression model with Tukey’s Biweight function for each of (Exponential, Weibull and Lognormal) distributions and to choose those parameters that affect the survival time. A comparison was conducted among AFT, Regression model, Robust AFT with Tukey’s Biweight function, Robust AFT with Median function and Robust Regression model with Tukey’s Biweight function. We conclude that that the Robust AFT Lognormal Distribution in Survival Analysis by using Maximum likelihood-Type Estimator with Tukey's Biweight function is the best method, the Robust AFT Weibull Distribution in Survival Analysis by using Maximum likelihood-Type Estimator with Tukey's Biweight function is also the best model. As well as the Robust AFT for (Exponential, Weibull and Lognormal) by using Maximum likelihood-Type Estimator with Median weight function shows the best result.