A commonly used approach to study the association between a time-varying biomarker, such as forced vital capacity (FVC), and a time-to-event outcome, such as new onset of chronic obstructive pulmonary disease (COPD), is to incorporate the biomarker as a time-dependent covariate in a Cox model. This approach, which is known as the time-dependent Cox model (TDCM), requires knowledge of the value of the time-varying biomarker at all time points at which the event of interest occurs [1]. However, in clinical studies, longitudinal biomarker measurements are taken intermittently during scheduled (and sometimes unscheduled) visits, meaning that imputation of missing values is required for those event times at which the biomarker is not observed. In practical application of the TDCM, this is achieved by carrying forward the most recent biomarker measurement. While the use of last observation carried forward (LOCF) is easy to understand and implement, the resulting step function (see fig. 1, panel C for an example) is unlikely to provide a good approximation of the true biomarker trajectory.
