Cox Regression with Accurate Covariates Unascertainable: A Nonparametric-Correction Approach

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.

Key Words:

• Censored data
• Estimating equation
• Functional delta method
• Measurement error
• Partial likelihood
• Proportional hazards model
• Replication data
• Semiparametric inference