Comparing measurement error correction methods for rate-of-change exposure variables in survival analysis

In this article we focus on comparing measurement error correction methods for rate-of-change exposure variables in survival analysis, when longitudinal data are observed prior to the follow-up time. Motivational examples include the analysis of the association between changes in cardiovascular risk factors and subsequent onset of coronary events. We derive a measurement error model for the rate of change, estimated through subject-specific linear regression, assuming an additive measurement error model for the time-specific measurements. The rate of change is then included as a time-invariant variable in a Cox proportional hazards model, adjusting for the first time-specific measurement (baseline) and an error-free covariate. In a simulation study, we compared bias, standard deviation and mean squared error (MSE) for the regression calibration (RC) and the simulation-extrapolation (SIMEX) estimators. Our findings indicate that when the amount of measurement error is substantial, RC should be the preferred method, since it has smaller MSE for estimating the coefficients of the rate of change and of the variable measured without error. However, when the amount of measurement error is small, the choice of the method should take into account the event rate in the population and the effect size to be estimated. An application to an observational study, as well as examples of published studies where our model could have been applied, are also provided.