A Corrected Pseudo-score Approach for Additive Hazards Model with Longitudinal Covariates Measured with Error

In medical studies, it is often of interest to characterize the relationship between a time-to-event and covariates, not only time-independent but also time-dependent. Time-dependent covariates are generally measured intermittently and with error. Recent interests focus on the proportional hazards framework, with longitudinal data jointly modeled through a mixed effects model. However, approaches under this framework depend on the normality assumption of the error, and might encounter intractable numerical difficulties in practice. This motivates us to consider an alternative framework, that is, the additive hazards model, about which little research has been done when time-dependent covariates are measured with error. We propose a simple corrected pseudo-score approach for the regression parameters with no assumptions on the distribution of the random effects and the error beyond those for the variance structure of the latter. The estimator has an explicit form and is shown to be consistent and asymptotically normal. We illustrate the method via simulations and by application to data from an HIV clinical trial.