A corrected profile likelihood method for survival data with covariate measurement error under the Cox model

Abstract

In survival analysis, covariate measurement error has been studied extensively for the Cox model. In this article, we propose a corrected profile likelihood approach, and show that many existing methods can be unified by our approach. Furthermore, we extend our discussion to general measurement error and Berkson models, as opposed to the classical additive error model that has been widely used in the literature. We investigate the impact of model misspecification of the measurement error process and uncover interesting findings. Empirical studies are carried out to illustrate the usage of the proposed methods and to assess their performance. The Canadian Journal of Statistics 43: 454–480; 2015 © 2015 Statistical Society of Canada

Simulation Extrapolation Method for Cox Regression Model with a Mixture of Berkson and Classical Errors in the Covariates using Calibration Data

“…On the other hand, methods addressing the issue of Berkson error in the covariates in Cox regression model are very scarce and this problem still has to be well-discussed in the literature. Among the very limited number of references, [22] discussed an extension to a Berkson error of a corrected profile likelihood method for Cox model with classical error in the covariates. It is important to note that methods that simply deal with classical error or Berkson error exclusively may not work well when errors of both types are involved in the covariates.…”

Approximate profile likelihood estimation for Cox regression with covariate measurement error

“…Correction methods proposed by Nakamura, 10 Yi and Lawless, 17 Yan and Yi 20 were constructed from likelihood function or score function of a Cox model under a covariate measurement error model provided that distributions of error variables have already been estimated from an internal or an external validation study. Furthermore, they were not computer‐intensive as SIMEX, 7,8 imputation‐based approach 14 and methods proposed by Zucker 19,21 .…”

“…For example, Nakamura 10 proposed a corrected score approach under the normality assumption of mutually independent error variables; Huang and Wang 11 developed a nonparametric correction method to modify the normalized partial score function; Hu and Lin 12 studied a general strategy called semiparametric regression approach when there are replicated measurements in validation study; Song and Huang 13 provided a refinement approach called conditional score approach based on the nonparametric correction method; 11 Li and Ryan 14 proposed an imputation‐based approach by assuming a linear spline model on the baseline hazard function. For likelihood‐based function, Hu et al 15 proposed a semiparametric approach under the normal error assumption; both Augustin 16 and Yi and Lawless 17 applied the methodology of corrected log‐likelihood proposed by Nakamura 18 to the Cox model, but the later employed a weak parametric form for the baseline hazard function; Zucker 19 proposed a pseudo‐partial likelihood method, which can be applied to studies with external or internal validation sample, or studies with replication data; Yan and Yi 20 proposed a corrected profile likelihood approach under three types of additive error models; Zucker et al 21 developed a modified partial likelihood score method to handle both independent and dependent measurement error models.…”

Estimation and hypothesis testing with error‐contaminated survival data under possibly misspecified measurement error models

“…Since the seminal paper by Prentice (1982), there has been extensive interest in discussing the analysis of error‐prone survival data, and several methods have been proposed to accommodate covariate measurement error effects on estimation procedures. Typical methods include the regression calibration method and its variants (e.g., Prentice, 1982; Xie, Wang & Prentice, 2001; Liao et al, 2011), the simulation–extrapolation algorithm (e.g., Yi & He, 2012), the partial likelihood‐based method (e.g., Buzas, 1998; Huang & Wang, 2000), likelihood‐based approaches (e.g., Hu, Tsiatis & Davidian, 1998; Zucker, 2005; Yi & Lawless, 2007; Yan & Yi, 2015; Yan & Yi, 2016), the “corrected” score approach and its variants (e.g., Nakamura, 1992; Huang & Wang, 2000; Hu & Lin, 2004; Song & Huang, 2005), the conditional score method (e.g., Tsiatis & Davidian, 2001), and estimating equation methods (e.g., Wang & Song, 2013).…”