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.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS339 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org