Cox regression with accurate covariates unascertainable: A nonparametric-correction approach

Many survival studies involve covariates that are not accurately ascertaina ble; CD4 lymphocyte count in HIV/AIDS research is a typical example for whi ch the gold standard of the measurement is not available. This article prop oses a consistent estimation procedure for Cox regression under the additiv e measurement error model. Distinct from existing methods, the proposed est imation for regression coefficients does not require any additional assumpt ions. We establish the normalized partial-score function as a functional of empirical processes. which facilitates the construction of an estimating f unction with the same limit using replicated mismeasured covariates. The re sulting regression coefficient estimators are shown to be consistent and as ymptotically normal; a consistent sandwich variance estimate is presented. We also suggest estimators for the baseline cumulative hazard function. Num erical 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 functiona l representation of the partial-score function.