Goodness-of-fit tests for accelerated life models with right censored data

In statistical analysis; it is very important to check the validity of model assumptions that are imposed on the data to be analyzed before drawing statistical inference based on these model assumptions. This research is motivated by a health insurance data set which captures the relation between insurance status and some covariates, such as gender, household income category, etc. Our interest lies in the effect of the covariates on the duration of the insurance coverage, which is connected to a right censored data problem. Preliminary testing suggests that an Accelerated Life Model fits the effect of gender on the length of insurance coverage. To our best knowledge, there are currently no existing methods to check the model assumption for accelerated life models with right censored data. Therefore, it is the goal of this research to construct a goodness of fit test for accelerated life models with right censored data.; In order to construct such a test, the Empirical Likelihood Method is used as the tool to construct the test statistic, which is based on a Cramer-von Mises type statistic, and the Maximum Likelihood Estimator (MLE) for the parameter-acceleration factor in the model. The Bootstrap Method is applied to find the critical values for the test statistic. The consistency of the MLE of the acceleration factor under the model assumption is established. In order to investigate the effectiveness of the proposed model checking method, computer simulation studies on the power of the proposed goodness of fit test and the confidence intervals for the acceleration factor are also conducted.