Em Approach on Influence Measures in Competing Risks Via Proportional Hazard Regression Model

In a conventional competing risk s model, the time to failure of a particular experimental unit might be censored and the cause of failure can be known or unknown. In this thesis the analysis of this particular model was based on the cause-specific hazard of Cox model. The Expectation Maximization (EM) was considered to obtain the estimate of the parameters. These estimates were then compared to the Newton-Raphson iteration method. A generated data where the failure times were taken as exponentially distributed was used to further compare these two methods of estimation. From the simulation study for this particular case, we can conclude that the EM algorithm proved to be more superior in terms of mean value of parameter estimates, bias and root mean square error. To detect irregularities and peculiarities in the data set, the residuals, Cook distance and the likelihood distance were computed. Unlike the residuals, the perturbation method of Cook's distance and the likelihood distance were effective in the detection of observations that have influenced on the parameter estimates. We considered both the EM approach and the ordinary maximum likelihood estimation (MLE) approach in the computation of the influence measurements. For the ultimate results of influence measurements we utilized the approach of the one step . The EM one-step and the maximum likelihood (ML) one-step gave conclusions that are analogous to the full iteration distance measurements. In comparison, it was found that EM one-step gave better results than the ML one step with respect to the value of Cook's distance and likelihood distance. It was also found that Cook's distance i s better than the likelihood distance with respect to the number of observations detected.

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