Inference in frailty measurement error models.

Abstract

We propose a new class of models, frailty measurement error models (FMEMs), for clustered survival data when covariates are measured with error. We explore FMEMs from three directions: bias analysis, structural modeling and functional modeling. We study the asymptotic bias when measurement error is ignored and when the underlying distribution of the unobserved error-prone covariates is misspecified. We found that ignoring measurement error in covariates will underestimate estimates of regression coefficients and overestimate variance components. As the censoring proportion increases, the attenuation of estimation of regression coefficients becomes more severe. However, it is not necessarily true for the variance component estimation. Structural modeling and functional modeling is developed to make statistical inference in FMEMs. Under structural modeling, we assume a distribution for the unobserved error-prone covariates and calculate nonparametric maximum likelihood estimates (NPMLEs) using an EM algorithm. Under functional modeling, we make no distributional assumption on the unobserved error-prone covariates and use the SIMEX method for parameter estimation. The NPMLEs and SIMEX estimates are compared in terms of efficiency and robustness. NPMLE gives more efficient estimators when correctly specifying the distribution of unobserved covariates X, and could yield biased estimates when such distribution is misspecified. The SIMEX approach is model robust with respect to the misspecification of the distribution of X. However, it yields less efficient estimates than NPMLE and is computationally intensive. We use the SIMEX approach to test the variance components in FMEMs and extended the results to the discrete frailty measurement error models. All the proposed methods are applied to the west Kenya parasitemia data and their performance is evaluated through simulations.