Doubly truncated data are common data structures of case-cohort studies in clinical practices. The researchers collect cases with a specific event of interest within a given time period. For example, we may collect cases information from medical records, cancer registry records and National Health Insurance Research Database. Such study designs accompanied with some sampling criterions result in biases when inferring population. Chou (2009) proposed a U-statistic-based estimating equation for parameter estimation in AFT model. In this study, we modify the estimating equation and further conduct more simulation scenarios. The simulation results show that the proposed methods are not superior to Chou (2009) and sensitive to population distributions.