Abstract:
In medical studies, patients are often followed up over time and their disease related biomarkers
are measured repeatedly. Together with these multiple longitudinal biomarkers, the survival
status (time to death) of such patients are observed. When the analysis is focused on evaluating
the effect of multiple longitudinal biomarkers on the time to an event (death), such analysis is
often carried out by using joint models of multiple longitudinal data and time-to-event data. The
multiple longitudinal biomarkers are correlated within a patient since the measurement of one
patient exhibits more similarity than measurement from different patients. This research utilizes
the joint modeling capability of Generalized Linear Mixed Models (GLMMs) with multiple
longitudinal biomarkers along with the date of measurement are considered as the predictors of
the GLMM and the response of the model is taken to be the time to death. The need of joint
modeling of GLMMs arose due to the fact that time-to-event data are concerned with both
actual deaths and censored observations. Therefore, the response variable is expressed
dichotomously giving both the time to the event (death) and the status of the event (censored or
not). The time to death (number of days) was taken to be a Poisson response variable while the
status (censored or not) was taken as a Binary random variable in the joint GLMM. The
proposed methodology was applied to a set of Primary Biliary Cirrhosis (PBC) data. The results
of the joint model expressing time to death of PBC patients revealed that presence of edema,
serum bilirubin level, prothrombin time, age of the patient, and the interaction of Bilirubin and
Albumin levels are significantly associated with the survival of the PBC patients. The goodness
of the fitted joint model was satisfied by the Generalized Pearson Chi-square goodness of fit test
statistics.
