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The proportional hazard Cox regression models play a key role in analyzing censored survival data. We use penalized methods in high dimensional scenarios to achieve more efficient models. This article reviews the penalized Cox regression for some frequently used penalty functions. Analysis of medical data namely ”mgus2” confirms the penalized Cox regression performs better than the cox regression model. Among all penalty functions, LASSO provides the best fit.

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Many populations encountered in survival analysis are often not homogeneous. Individuals are flexible in their susceptibility to causes of death, response to treatment, and influence of various risk factors. Ignoring this heterogeneity can result in misleading conclusions. To deal with these problems, the proportional hazard frailty model was introduced. In this paper, the frailty model is explained as the product of the frailty random variable and baseline hazard rate. We examine the fit of the frailty model to the right-censored data from in the presence of explanatory variables (observable variables) and use it as a practical example to fit the frailty model to the data by considering the Weibull basis distribution and exponential in the likelihood functions. It is used to estimate the model parameters and compare the fit of the models with different criteria.

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Marshall-Olkin introduced a family of distributions which obtained by adding a parameter into other distributions. Santoz-Neto etal study an extended Weibull distribution. In this paper two Raiyle and Pareto extended weibull are studied under some momemts and Bayesian methods with some loss functions such as squared error, entropy, linex, squared error in logarithm and modified linex. Also the MCMC method are study for these two distributions.