在醫學研究中，當主要結果難以即時觀察或需長時間追蹤時，常以替代終點作為替代。如何選取適當的替代終點並評估其效度，是替代終點分析中的關鍵課題。文獻中建議可透過中介分析，藉由估計「中介比例（proportion mediated, PM）」來量化替代終點的效能。然而，若替代終點與最終結果之間存在未觀測的混淆因子，可能導致替代悖論，使治療效果的解釋產生偏誤。目前尚缺乏能有效避免替代悖論的統計模型。為解決此問題，本研究提出一套基於工具變數方法的中介比例評估架構，以處理未觀測混淆所造成的偏誤，進而提升替代終點效度評估的準確性。本方法適用於三種類型的結果變數，包括連續型、二元型與存活時間。對於連續型結果，本研究提出 PM 的不偏估計量，能準確識別有效的替代終點；對於二元與存活型結果，則著重於替代終點效度的推論，並提供理論上方向判斷的依據。透過大量模擬研究，評估所提方法在各種情境下的統計性能與應用潛力。

In medical research, when primary outcomes are difficult to observe promptly or require long-term follow-up, surrogate endpoints are often employed as substitutes. Selecting appropriate surrogate endpoints and evaluating their validity are critical challenges in surrogate endpoint analysis. The literature suggests that mediation analysis can be used to quantify the effectiveness of a surrogate by estimating the proportion mediated (PM). However, the presence of Unmeasured confounders between the surrogate and the final outcome may lead to the surrogate paradox, resulting in biased interpretations of treatment effects. Currently, there is a lack of statistical models capable of effectively avoiding the surrogate paradox.
To address this issue, this study proposes a mediation analysis framework based on instrumental variable (IV) methods to correct for bias caused by Unmeasured confounding, thereby improving the accuracy of surrogate endpoint evaluation. The proposed approach is applicable to three types of outcome variables:
continuous, binary, and time-to-event. For continuous outcomes, the study derives an unbiased estimator of PM that can reliably identify valid surrogates. For binary and survival outcomes, the focus is placed on directional inference of surrogate validity, offering theoretical justification for determining the appropriateness of a surrogate. Extensive simulation studies are conducted to assess the statistical performance and practical utility of the proposed methods under various scenarios.

[1] Michael Baiocchi, Jing Cheng, and Dylan S Small. Instrumental variable methods for causal inference. Statistics in medicine, 33(13):2297–2340, 2014.
[2] Yen-Tsung Huang, Jih-Chang Yu, and Jui-Hsiang Lin. Surrogate marker assessment using mediation and instrumental variable analyses in a case-cohort design. The Annals of Applied Statistics, 17(2):1239–1259, 2023.
[3] Yi Li, Kazuki Yoshida, Jay S Kaufman, and Maya B Mathur. A brief primer on conducting regression-based causal mediation analysis. Psychological Trauma: Theory, Research, Practice, and Policy, 15(6):930, 2023.
[4] Layla Parast. Surrogate marker evaluation: A tutorial using r. Statistics in Medicine, 44(10-12):e70048, 2025.
[5] Linda Valeri and Tyler J VanderWeele. Mediation analysis allowing for exposure– mediator interactions and causal interpretation: theoretical assumptions and implementation with sas and spss macros. Psychological methods, 18(2):137, 2013.
[6] Tyler J VanderWeele. Surrogate measures and consistent surrogates. Biometrics, 69(3):561–565, 2013