MODELING MULTIVARIATE LONGITUDINAL MEASUREMENTS AND DISCRETE TIME-TO-EVENT DATA

AN APPROACH FOR JOINTLY MODELING MULTIVARIATE

LONGITUDINAL MEASUREMENTS AND DISCRETE TIME-TO-EVENT DATA

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By Paul S. Albert and Joanna H. Shih

In many medical studies, patients are followed longitudinally and
interest is on assessing the relationship between longitudinal measure-
ments and time to an event. Recently, various authors have proposed
joint modeling approaches for longitudinal and time-to-event data
for a single longitudinal variable. These joint modeling approaches
become intractable with even a few longitudinal variables. In this pa-
per we propose a regression calibration approach for jointly modeling
multiple longitudinal measurements and discrete time-to-event data.
Ideally, a two-stage modeling approach could be applied in which the
multiple longitudinal measurements are modeled in the first stage and
the longitudinal model is related to the time-to-event data in the sec-
ond stage. Biased parameter estimation due to informative dropout
makes this direct two-stage modeling approach problematic. We pro-
pose a regression calibration approach which appropriately accounts
for informative dropout. We approximate the conditional distribu-
tion of the multiple longitudinal measurements given the event time
by modeling all pairwise combinations of the longitudinal measure-
ments using a bivariate linear mixed model which conditions on the
event time. Complete data are then simulated based on estimates
from these pairwise conditional models, and regression calibration is
used to estimate the relationship between longitudinal data and time-
to-event data using the complete data. We show that this approach
performs well in estimating the relationship between multivariate lon-
gitudinal measurements and the time-to-event data and in estimating
the parameters of the multiple longitudinal process subject to infor-
mative dropout.We illustrate this methodology with simulations and
with an analysis of primary biliary cirrhosis (PBC) data.