We consider the exponentiated Weibull regression model that may have many covariates, some of which may not be significantly related to the survival time. In that we use some auxiliary information on insignificant covariates in the unrestricted model to produce a restricted model. The shrinkage estimators optimally combine the unrestricted and restricted estimators and outperform MLE under the quadratic loss. Asymptotic properties of these estimators including biases and risks will be discussed. A simulation study is conducted to assess the performance of the proposed estimators with respect to the unrestricted MLE and this study will be incorporated with varying sample sizes, different hazard shapes, and different censored levels. Estimators will be compared based on bias, risk, and mean squared prediction error. The relevance of the proposed estimators will be illustrated with a real data set.