Functional Inference in Frailty Measurement Error Models for Clustered Survival Data Using the SIMEX Approach

We consider frailty models for clustered survival data in the presence of measurement errors in covariates. We Ž rst show that when the measurement error is accounted for in a full likelihood analysis but the distribution of the unobserved covariate is misspeciŽ ed, the maximum likelihood estimators are asymptotically biased, especially for the variance component, whose bias can be substantial. We then discuss making inference using functional estimation via the SIMEX method where no distribution of the unobserved error-prone covariate is assumed. The SIMEX method is easy to implement by repeatedly Ž tting standard frailty models. We study the asymptotic properties of the SIMEX estimates and show that they are consistent and asymptotically normal. In simulation studies, we compare the SIMEX method and the likelihood method in terms of efŽ ciency and robustness. We also propose a SIMEX score test for the variance component to test for the within-cluster correlation and evaluate its performance through simulation studies. The SIMEX variance component score test does not require specifying distributions for the random effect and the unobserved error-prone covariate, and is easy to implement by repeatedly Ž tting standard Cox models. The proposed methods are illustrated using the Kenya parasitemia data.