ABSTRACT
In biomedical research, along with censored time-to-event data and baseline covariates, repeated measurements of biomarkers are also collected at a number of time points. A
of this is HIV research (Wang and Taylor, 2001; Pawitan and Self, 1993), in which the biomarker CD4 lymphocyte count is measured at regularly scheduled intervals. In these studies patients are followed until an event, such as progression to AIDS or death. In addition to biomarker data, other covariates, such as treatment and demographic information, are recorded at baseline. In order to understand the natural history of the disease and to search for a “surrogate marker” for the time to AIDS or death, investigators are often interested in both modeling the progression of the CD4 count and estimating the relative risk of progressing to AIDS associated with different CD4 count levels. Data such as this are important for other studies including those of prostate cancer in which research interest lies in the association between level or rate of change of prostate specific antigen (PSA) and time to cancer recurrence (Ye et al., 2008b), as well as studies of cognitive aging (Proust et al., 2006) which investigate the relationship between cognitive functioning decline and time to dementia.
