The occurrence of lifetime data is a problem which is commonly encountered in various researches, including surveys, clini
cal trials and epidemiological studies. Recently there has been extensive methodological research on analyzing lifetime data.
 However, because usually little information from data is available to correctly estimate, the inferences might be sensitive to
 untestable assumptions which this calls for a sensitivity analysis to be performed. In this paper, we describe how to evaluate
 the effect that perturbations to the Log-Beta Weibull Regression Responses. Also, we review and extend the application
 and interpretation of influence analysis methods using censored data analysis. A full likelihood-based approach that allows
 yielding maximum likelihood estimates of the model parameters is used. Some simulation studies are conducted to evalute
 the performance of the proposed indicts in detecting sensitivity of key model parameters. We illustrate the methods expressed
 by analyzing the cancer data.