Received: 10 October 2016 Revised: 10 August 2017 Accepted: 6 October 2017
Considerations for analysis of time-to-event outcomes
measured with error: Bias and correction with SIMEX
Eric J. Oh
Bryan E. Shepherd
Pamela A. Shaw
Department of Biostatistics,
Epidemiology and Informatics, Perelman
School of Medicine, University of
Pennsylvania, Philadelphia, PA, U.S.A.
Department of Biostatistics, Vanderbilt
University School of Medicine, Vanderbilt
University, Nashville, TN, U.S.A.
Department of Statistics, University of
Auckland, Auckland, New Zealand
Pamela A. Shaw, Department of
Biostatistics, Epidemiology and
Informatics, Perelman School of
Medicine, University of Pennsylvania,
Philadelphia, PA, U.S.A.
National Institutes of Health,
Grant/Award Number: P30 AI110527, R01
AI093234, U01 AI069923 and U01
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.
accelerated failure time, Cox model, measurement error, SIMEX, survival analysis
There are many examples in clinical research where the outcome of interest relies on an imprecisely measured event time.
Researchers studying the epidemiology of chronic conditions may enroll subjects some time after an initial diagnosis, and
so research questions focused on the timing of events post diagnosis may need to rely on patient recall or chart review
of electronic medical records, both of which are subject to error. For example, human biologists and demographers are
interested in the variability in the age at menarche (first menstruation).
Oftentimes, subjects are enrolled several years
after menarche, and so the event time is based on retrospective recall and hence subject to error. As Holt et al
studies comparing age at menarche reported retrospectively to those reported in medical records have shown that dif-
ferences in the two can be attributed to recall error symmetrically distributed around zero. In addition, epidemiological
researchers frequently use observational databases, where data accuracy can also be a concern. In observational studies of
1276 Copyright © 2017 John Wiley & Sons, Ltd. wileyonlinelibrary.com/journal/sim Statistics in Medicine. 2018;37:1276–1289.