Statistical Modelling 2 (2002), 203–215
Assessing uncertainty about parameter estimates with incomplete
repeated ordinal data
Claudio J. Verzilli,
Medical Statistics Unit, London School of Hygiene & Tropical Medicine,
Keppel Street,
London WC1E 7HT,
U.K.
eMail: claudio.verzilli@lshtm.ac.uk
James R. Carpenter,
Medical Statistics Unit, London School of Hygiene and Tropical Medicine,
London,
U.K.
Abstract:
Data collected in clinical trials involving follow-up patients over a
period of time will almost inevitably be incomplete. Patients will
fail to turn up at some of the intended measurement times or will not
complete the study, giving rise to various patterns of missingness. In
these circumstances, the validity of the conclusions drawn from an
analysis of available cases depends crucially on the mechanism driving
the missing data process; this in turn cannot be known for
certain. For incomplete categorical data, various authors have
recently proposed taking into account in a systematic way the
ignorance caused by incomplete data. In particular, the idea of
intervals of ignorance has been introduced, whereby point estimates
for parameters of interest are replaced by intervals or regions of
ignorance (Vansteelandt and Goetghebeur, 2001; Kenward et al.,
2001; Molenberghs et al., 2001). These are identified by the
set of estimates corresponding to possible outcomes for the missing
data under little or no assumptions about the missing data
mechanism. Here we extend this idea to incomplete repeated ordinal
data. We describe a modified version of standard algorithms used for
fitting marginal models to longitudinal categorical data, which enables
calculation of intervals of ignorance for the parameters of
interest. The ideas are illustrated using dental pain measurements
from a longitudinal clinical trial.
Keywords:
Generalized estimating equations; intervals of ignorance and
uncertainty; longitudinal ordinal data; missing data
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