Estimation in the Cox survival regression model with covariate measurement error and a changepoint

Abstract

The Cox regression model is a popular model for analyzing the relationship between a covariate and a survival endpoint. The standard Cox model assumes a constant covariate effect across the entire covariate domain. However, in many epidemiological and other applications, the covariate of main interest is subject to a threshold effect: a change in the slope at a certain point within the covariate domain. Often, the covariate of interest is subject to some degree of measurement error. In this paper, we study measurement error correction in the case where the threshold is known. Several bias correction methods are examined: two versions of regression calibration (RC1 and RC2, the latter of which is new), two methods based on the induced relative risk under a rare event assumption (RR1 and RR2, the latter of which is new), a maximum pseudo-partial likelihood estimator (MPPLE), and simulationextrapolation (SIMEX). We develop the theory, present simulations comparing the methods, and illustrate their use on data concerning the relationship between chronic air pollution exposure to particulate matter PM10 and fatal myocardial infarction (Nurses Health Study (NHS)), and on data concerning the effect of a subject's long-term underlying systolic blood pressure level on the risk of cardiovascular disease death (Framingham Heart Study (FHS)). The simulations indicate that the best methods are RR2 and MPPLE.

Correcting for Measurement Error in Segmented Cox Model

“…and denote by θ * the solution of u(t * , θ) = 0. As was showed in Agami et al (2020), n 1/2 ( θ − θ * ) converges in distribution to a mean-zero multivariate normal distribution whose covariance matrix can be consistently estimated by…”

“…Generally, the bias correction methods for Cox regression analysis with covariate error, as were studied in Agami et al (2020), involve replacing r(x, z, θ) with some substitute, are as follows: A. Regression Calibration (RC) Methods A1. Simple RC Method (RC1):…”

“…This section presents a simulation study comparing the four validation data for the bias correction methods RC and RR, under several scenarios. The setting of the simulation is the same as in Agami et al (2020), and detailed below. The results are summarized in Table 1 -Table 2 below and are presented in details in Appendix B.…”

“…The proof of convergence of U (t, θ * , φ * , g) to a mean-zero multivariate normal distribution is the same as in the case with no nuisance parameters, see at Agami et al (2020).…”

“…Specifically, the aim is to examine the influence of the validation type on the precision of the model parameters estimation. Agami et al (2020) studied several bias correction methods, and examined their performance under repeated measures from an external reliability design. In this paper, some of these bias correction methods are considered, and the theoretical properties under each source validation is developed for the considered bias correction methods.…”