<p>This study investigates the assessment of causal treatment effects on interval-censored failure time outcomes. Available techniques for this problem primarily rely on full-likelihood-based approaches, which can be computationally burdensome and prone to model misspecification for the compliance group. Motivated by a breast cancer screening study, we propose a weighted likelihood estimator for causal treatment effects under the proportional hazards model. The proposed approach employs the inverse weighting scheme, offering simplicity and enhancing computational efficiency compared to the existing methods. Also it can be implemented by using standard software. We establish the consistency and asymptotic normality of the resulting estimator for the regression parameter. Extensive simulation studies are conducted to evaluate the finite-sample performance of the proposed approach, which suggests that it performs well. Finally, we apply the proposed method to the breast cancer screening study mentioned above and obtain some new insights about the effect of periodic screening on reducing the risk of breast cancer-related mortality.</p>