Statistical Modelling 11 (2011), 279–310
Generalized shared-parameter models and missingness at random
An Creemers
I-BioStat, Universiteit Hasselt
Belgium
Niel Hens
I-BioStat, Universiteit Hasselt
and
Centre for Health Economics Research and Modeling Infectious Diseases
(CHERMID),
Centre for the Evaluation of Vaccination (WHO Collaborating Centre),
Vaccine & Infectious Disease Institute,
University of Antwerp
Belgium
Marc Aerts
I-BioStat, Universiteit Hasselt
Belgium
Geert Molenberghs
I-BioStat, Universiteit Hasselt
Agoralaan 1
B–3590 Diepenbeek
and
I-BioStat, Katholieke Universiteit Leuven
Belgium
eMail: geert.molenberghs@uhasselt.be
Geert Verbeke
I-BioStat, Universiteit Hasselt
and
I-BioStat, Katholieke Universiteit Leuven
Belgium
Michael G Kenward
Medical Statistics Unit,
London School of Hygiene and Tropical Medicine
UK
Abstract:
When data are incomplete, models are often catalogued according to one
of the three modelling frameworks to which they belong: selection models
(SeM), pattern-mixture models (PMM) and shared-parameter models (SPM).
The missing data mechanism is conventionally classified as missing
completely at random (MCAR), missing at random (MAR) and missing not at
random (MNAR). Under MCAR, measurement and missingness mechanism are
independent, but that is not the case for MAR. The definition of MAR is
in SeM terms. Molenberghs et al. (1998) provided a characterization for
PMM. Here, MAR is characterized in the SPM framework, using an extended
SPM class. A subfamily, satisfying the MAR condition, is studied in detail.
Particular implications for non-monotone missingness as well as for
longitudinal data subject to dropout are studied. It is indicated how
SPM can be constrained such that dropout at a given point in time can
depend on current and past, but not on future measurements. Although, a
natural requirement, it is less easily imposed in the PMM and SPM frameworks
than in the SeM case. Some of the models proposed are illustrated using a
clinical trial in toenail dermatophyte onychomycosis.
Keywords:
available-case missing value restrictions;
ignorability;
missing at random counterpart;
missing completely at random;
missing non-future-dependent restrictions;
non-future dependence;
pattern-mixture model;
selection model
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