臨床試驗中，解釋變數調適隨機分派（Covariate-Adaptive Randomization；CAR）是一種優化隨機化試驗設計的方法，其概念是在平衡治療組與控制組受試者人數的同時，能夠有效控制重要解釋變數對實驗結果的影響，降低實驗的偏差和提高統計檢定力。然而，在實務中，解釋變數被錯誤分類是不可避免的，當用於 CAR 的解釋變數被錯誤分類時，不僅無法達到解釋變數的平衡，也會影響後續進行檢定的有效性。由於 CAR 方法常用於存活資料分析，因此在本研究中我們使用 Cox 比例風險模型，推導出當解釋變數被錯誤分類時，對於 CAR 下穩健的檢定統計量的漸近分布的影響。此外，我們通過模擬研究，評估了兩種常見的 CAR 方法以及完全隨機分派的情況下，當解釋變數存在不同程度的錯誤分類時，不同檢定統計量的犯型 I 誤機率和檢定力曲線。並藉由國立成功大學醫學院附設醫院所提供的女性乳癌患者臨床資料進行實例分析，進一步驗證模擬中得到的結果。

In clinical trials, Covariate-Adaptive Randomization (CAR) is a method for optimizing the randomization design. The concept behind CAR is to balance the number of subjects in the treatment and control groups while effectively controlling the influence of important covariates on the experimental outcomes. CAR ensures a more balanced randomization process, reduces experimental bias, and improves the statistical power of the analysis. However, in practice, misclassification of covariates is inevitable. When the covariates used in CAR are misclassified, not only does it prevent the balance of covariates but also affects the effectiveness of subsequent tests. As CAR is often used in survival analysis, in this study, we utilize the Cox proportional hazards model to derive the impact of misclassified covariates on the asymptotic distribution of robust test statistics under CAR.

Additionally, we conducted simulation studies to evaluate the Type I error rates and power curves of different test statistics under two common CAR methods and simple randomization when the covariates are subject to varying degrees of misclassification. Furthermore, we validated the results through a case study using clinical data from female breast cancer patients provided by the National Cheng Kung University Hospital.

Efron, B. (1971). Forcing a sequential experiment to be balanced. Biometrika, 58(3), 403-417.

Fan, L., Yeatts, S. D., Wolf, B. J., McClure, L. A., Selim, M., & Palesch, Y. Y. (2018). The impact of covariate misclassification using generalized linear regression under covariate–adaptive randomization. Statistical methods in medical research, 27(1), 20-34.

International conference on harmonisation of technical requirements for registration of pharmaceuticals for human use. (1998). STATISTICAL PRINCIPLES FOR CLINICAL TRIALS E9. https://database.ich.org/sites/default/files/E9_Guideline.pdf

Kumar, M., Nanavati, R., Modi, T. G., & Dobariya, C. (2016). Oral cancer: Etiology & risk factors: A review. Journal of cancer research and therapeutics, 12(2), 458-463.

Lin, D. Y., & Wei, L. J. (1989). The robust inference for the Cox proportional hazards model. Journal of the American statistical Association, 84(408), 1074-1078.

Ma, W., Hu, F., & Zhang, L. (2015). Testing hypotheses of covariate-adaptive randomized clinical trials. Journal of the American Statistical Association, 110(510), 669-680.

Peto, R., & Peto, J. (1972). Asymptotically efficient rank invariant test procedures. Journal of the Royal Statistical Society: Series A (General), 135(2), 185-198.

Peto, R., Pike, M., Armitage, P., Breslow, N. E., Cox, D. R., Howard, S. V., ... & Smith, P. G. (1976). Design and analysis of randomized clinical trials requiring prolonged observation of each patient. I. Introduction and design. British journal of cancer, 34(6), 585-612.

Shao, J., Yu, X., & Zhong, B. (2010). A theory for testing hypotheses under covariate-adaptive randomization. Biometrika, 97(2), 347-360.

Sun, Y. S., Zhao, Z., Yang, Z. N., Xu, F., Lu, H. J., Zhu, Z. Y., ... & Zhu, H. P. (2017). Risk factors and preventions of breast cancer. International journal of biological sciences, 13(11), 1387-1397.

Wang, T., & Ma, W. (2021). The impact of misclassification on covariate‐adaptive randomized clinical trials. Biometrika, 77(2), 451-464.

Ye, T., & Shao, J. (2020). Robust tests for treatment effect in survival analysis under covariate-adaptive randomization. Journal of the Royal Statistical Society Series B: Statistical Methodology, 82(5), 1301-1323.

Zelen, M. (1974). The randomization and stratification of patients to clinical trials. Journal of Chronic Diseases, 27(7-8), 365–375.