In this work, we fit pattern-mixture models to data
sets with
responses that are potentially
missing not at random (MNAR,
Little and
Rubin, 1987). In estimating the regression
parameters
that are identifiable, we use
the pseudo maximum likelihood
method
based on exponential families. This procedure
provides
consistent estimators when the
mean structure is correctly specified
for
each pattern, with further information on the
variance structure
giving an efficient
estimator. The proposed method can be used
to handle a variety of continuous and discrete
outcomes. A test
built on this approach
is also developed for model simplification
in order to improve efficiency. Simulations
are carried out
to compare the proposed
estimation procedure with other methods.
In combination with sensitivity analysis, our
approach can be
used to fit parsimonious
semi-parametric pattern-mixture models
to
outcomes that are potentially MNAR. We apply the
proposed
method to an epidemiologic
cohort study to examine cognition
decline
among elderly.