On the use of Cox regression in the presence of an irregularly observed time-dependent covariate.

Abstract

We consider the joint modelling of longitudinal and event time data. The longitudinal data are irregularly collected and the event times are subject to right censoring. Most methods described in the literature are quite complex and do not belong to the standard statistical tools. We propose a more practical approach using Cox regression with time-dependent covariates. Since the longitudinal data are observed irregularly, we have to account for differences in observation frequency between individual patients. Therefore, the time elapsed since last observation (TEL) is added to the model. TEL and its interaction with the time-dependent covariate show a strong effect on the hazard. The latter indicates that older recordings have less impact than recent recordings. Pros and cons of this methodology are discussed and a simulation study is performed to study the effect of TEL on the hazard. The fitted Cox model serves as a starting point for the prediction of future patient's events. Our method is applied to a study on chronic myeloid leukaemia (CML) with longitudinal white blood cell counts (WBC) as time-dependent covariate and patient's death as event.