IntroductionIn many survival studies, some covariates may be contaminated with error due to the lack of a gold standard of measurement, for example, CD4 count and viral load in HIV/AIDS research and nutritional intakes in cancer epidemiology. Just as with regression analyses in general (Carroll et al., ), accounting for the error is imperative in Cox regression since substantial bias may otherwise arise (Prentice, ; Hughes, ; Li and Ryan, ). Write survival time as S and censoring time as C. As a result of censoring, they are observed only through follow‐up time T=min(S,C) and censoring indicator Δ=I(S≤C), where I(·) is the indicator function. To focus on main ideas, we shall confine our attention to time‐independent covariates X∘≡(X,Z⊤)⊤ with scalar X being error‐prone and the rest Z accurately measured. The proportional hazards model (Cox, ) postulates dΛ(t∣X∘)=exp(β⊤X∘)dΛ0(t),S ╨ C∣X∘, where Λ(·∣X∘) is the cumulative hazard function of S given X∘, Λ0(·) is an unspecified baseline cumulative hazard function, β is an unknown regression coefficient, and ╨ denotes statistical independence. While X is not directly observable, its error‐contaminated version W instead is observed, as well as so‐called replication data or instrumental data (cf. Carroll et al., , Section 2.3) but not validation
Biometrics – Wiley
Published: Jan 1, 2018
Keywords: ; ; ; ; ;
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