We propose, develop and implement the simulation extrapolation (SIMEX) methodology for Cox regression models when the log hazard function is linear in the model parameters but nonlinear in the variables measured with error (LPNE). The class of LPNE functions contains but is not limited to strata indicators, splines, quadratic and interaction terms. The first order bias correction method proposed here has the advantage that it remains computationally feasible even when the number of observations is very large and multiple models need to be explored. Theoretical and simulation results show that the SIMEX method outperforms the naive method even with small amounts of measurement error. Our methodology was motivated by and applied to the study of time to chronic kidney disease (CKD) progression as a function of baseline kidney function and applied to the Atherosclerosis Risk in Communities (ARIC), a large epidemiological cohort study
Crainiceanu, Ciprian M.; Ruppert, David; and Coresh, Josef, "COX MODELS WITH NONLINEAR EFFECT OF COVARIATES MEASURED WITH ERROR: A CASE STUDY OF CHRONIC KIDNEY DISEASE INCIDENCE" (September 2006). Johns Hopkins University, Dept. of Biostatistics Working Papers. Working Paper 116.