Using the accelerated failure time model to analyze current status data with misclassified covariates

Current status data arise commonly in applications when there is only one feasible observation time to check if the failure time has occurred, but the exact failure time remains unknown. To accommodate the covariate effect on failure time, the accelerated failure time (AFT) model has been widely used to analyze current status data with the distribution of the failure time assumed to be specified or unspecified. In this paper, we consider a logistic regression with a misclassfied covariate from the current status observation scheme. A semiparametric AFT model was built to model current status data to eliminate the bias caused by this misclassification. This model is also robust to the misspecification of the failure time compared to the parametric AFT model, as we assume an unknown distribution of the failure time in the proposed model. Furthermore, incorporating the covariate effect on the failure time increases the flexibility of the model. Finally, we adapt the Expectation-Maximization algorithm for estimation, which guarantees the convergence of the estimate. Both theory and empirical studies show the consistency of the estimator.