Cox Regression with Accurate Covariates Unascertainable: A Nonparametric-Correction Approach
针对Cox回归中协变量测量不准确的问题，提出一种无需额外假设的估计方法，利用重复测量数据校正回归系数，并通过艾滋病临床试验验证效果。
Abstract Many survival studies involve covariates that are not accurately ascertainable; CD4 lymphocyte count in HIV/AIDS research is a typical example for which the gold standard of the measurement is not available. This article proposes a consistent estimation procedure for Cox regression under the additive measurement error model. Distinct from existing methods, the proposed estimation for regression coefficients does not require any additional assumptions. We establish the normalized partial-score function as a functional of empirical processes, which facilitates the construction of an estimating function with the same limit using replicated mismeasured covariates. The resulting regression coefficient estimators are shown to be consistent and asymptotically normal; a consistent sandwich variance estimate is presented. We also suggest estimators for the baseline cumulative hazard function. Numerical studies demonstrate that the procedure performs well under practical sample sizes. Application to an AIDS clinical trial is provided. Finally, we suggest a unified approach to estimating function construction and large-sample study with partial covariate information, in light of the functional representation of the partial-score function.