In confirmatory randomized controlled trials of patients with metastatic cancer, progression-free survival (PFS) and overall survival (OS) are often used as multiple primary endpoints. The overall hierarchical strategy is a typical multiplicity adjustment method that analyzes PFS once and performs an interim OS analysis at the time of PFS analysis using an alpha-spending function-only if the statistical significance of PFS is demonstrated. A subsequent final OS analysis is conducted if the interim OS analysis does not result in early stopping for efficacy. In this study, we focused on the adjustment of conditional bias (CB) in hazard ratio estimates for OS in both interim and final analyses when a trial applied the overall hierarchical strategy. As CB-adjusting estimators for a single primary endpoint may have limited performance, we extended the conditional mean-adjusted estimator to the case of an overall hierarchical strategy. Motivated by an actual oncology trial, we evaluated the performance of the proposed estimators through a simulation study. In the case of early stopping for efficacy, the CB of the proposed estimator was smaller than that of the existing methods with comparable root mean squared error.