Cox Regression with Dependent Error in Covariates

• Published in: Biometrics Vol. 74; no. 1; pp. 118 - 126
• Main Authors: Huang, Yijian, Wang, Ching-Yun
• Format: Journal Article
• Language: English
• Published: England Wiley-Blackwell 01.03.2018; Blackwell Publishing Ltd
• Subjects: Acquired Immunodeficiency Syndrome - diagnosis; Acquired Immunodeficiency Syndrome - drug therapy; Acquired Immunodeficiency Syndrome - mortality; BIOMETRIC METHODOLOGY; CD4 Lymphocyte Count - standards; CD4 Lymphocyte Count - statistics & numerical data; Clinical Trials as Topic; Computer Simulation; Contamination; Covariance; Error analysis; Error correction; Functional modeling; Heteroscedastic error; Humans; Instrumental variable; Models, Statistical; Multiplicative error; Nonparametric correction; Nonparametric statistics; Proportional hazards model; Proportional Hazards Models; Regression Analysis; Regression coefficients; Scientific Experimental Error - statistics & numerical data; Statistical analysis; Survival Analysis; Instrumental variable; Multiplicative error; Functional modeling; Heteroscedastic error; Nonparametric correction; Proportional hazards model
• ISSN: 0006-341X; 1541-0420
• DOI: 10.1111/biom.12741

Many survival studies have error-contaminated covariates due to the lack of a gold standard of measurement. Furthermore, the error distribution can depend on the true covariates but the structure may be difficult to characterize; heteroscedasticity is a common manifestation. We suggest a novel dependent measurement error model with minimal assumptions on the dependence structure, and propose a new functional modeling method for Cox regression when an instrumental variable is available. This proposal accommodates much more general error contamination than existing approaches including nonparametric correction methods of Huang and Wang (2000, Journal of the American Statistical Association 95, 1209-1219; 2006, Statistica Sinica 16, 861-881). The estimated regression coefficients are consistent and asymptotically normal, and a consistent variance estimate is provided for inference. Simulations demonstrate that the procedure performs well even under substantial error contamination. Illustration with a clinical study is provided.