Source: Ann. Appl. Stat.
Volume 4, Number 3
In many medical studies, patients are followed longitudinally and
interest is on assessing the relationship between longitudinal
measurements 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 paper 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 second stage. Biased parameter estimation due to
informative dropout makes this direct two-stage modeling
approach problematic. We propose a regression calibration
approach which appropriately accounts for informative dropout.
We approximate the conditional distribution of the multiple
longitudinal measurements given the event time by modeling all
pairwise combinations of the longitudinal measurements 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 longitudinal measurements and the time-to-event
data and in estimating the parameters of the multiple
longitudinal process subject to informative dropout. We
illustrate this methodology with simulations and with an
analysis of primary biliary cirrhosis (PBC) data.
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