Considerations for analysis of time‐to‐event outcomes measured with error: Bias and correction with SIMEX

Abstract

For time-to-event outcomes, a rich literature exists on the bias introduced by covariate measurement error in regression models, such as the Cox model, and methods of analysis to address this bias. By comparison, less attention has been given to understanding the impact or addressing errors in the failure time outcome. For many diseases, the timing of an event of interest (such as progression-free survival or time to AIDS progression) can be difficult to assess or reliant on self-report and therefore prone to measurement error. For linear models, it is well known that random errors in the outcome variable do not bias regression estimates. With nonlinear models, however, even random error or misclassification can introduce bias into estimated parameters. We compare the performance of 2 common regression models, the Cox and Weibull models, in the setting of measurement error in the failure time outcome. We introduce an extension of the SIMEX method to correct for bias in hazard ratio estimates from the Cox model and discuss other analysis options to address measurement error in the response. A formula to estimate the bias induced into the hazard ratio by classical measurement error in the event time for a log-linear survival model is presented. Detailed numerical studies are presented to examine the performance of the proposed SIMEX method under varying levels and parametric forms of the error in the outcome. We further illustrate the method with observational data on HIV outcomes from the Vanderbilt Comprehensive Care Clinic.

Raking and regression calibration: Methods to address bias from correlated covariate and time‐to‐event error

“…In fact, some forms of error in the outcome will bias the proportional hazards parameter but not the acceleration parameter. 27 The generalized raking estimators are consistent whenever the design-weighted complete case estimating equations (eg, HT estimator) yields consistent estimators; they use influence functions based on the unvalidated data as auxiliary variables to improve efficiency over the complete case estimator and can be used under outcome-dependent sampling. The raking estimators are not sensitive to the measurement error structure, which is in contrast to the RC and RSRC estimators that can perform poorly when the error structure is not correctly specified.…”

Knee and foot contracture occur earliest in children with cerebral palsy: a longitudinal analysis of 2,693 children

“…However, this bias has been shown to be small when differences between groups are moderate in terms of hazard ratios (Oh et al. 2018 ). Furthermore, in some situations in which bias was found to be substantial, bias attenuates observed differences between groups.…”

Improved generalized raking estimators to address dependent covariate and failure‐time outcome error

“…Covariate measurement error, particularly classical measurement error or extensions of it, has been well studied in the literature, and methods to correct the bias resulting from such error have been well developed (Carroll et al., 2006). Although less attention has been given to errors in an outcome of interest, there has been some recent work looking at errors in binary outcomes (Magder & Hughes, 1997; Edwards et al., 2013; Wang et al., 2016), discrete time‐to‐event outcomes (Hunsberger et al., 2010; Magaret, 2008; Meier et al., 2003), and to a lesser extent, continuous time‐to‐event outcomes (Gravel et al., 2018; Oh et al., 2018). There has been even less work to understand the impact of errors in both covariates and a time‐to‐event outcome, but it has recently been shown that ignoring such errors can cause severe bias in estimates of effects of interest (Boe et al., 2020; Giganti et al., 2020; Oh et al., 2019).…”