||5R01CA053787-09 Interpret this number
||University Of Michigan At Ann Arbor
||Repeated Categorical Measurements
The broad, long-term objective of this research project is to develop
models and methodology for the analysis of repeated categorical responses.
The repeated responses may be from a single outcome measured repeatedly
through time, or they may be from several response variables measured one
or more times each. It is often the case with repeated categorical
responses that marginal distributions are of more interest than the
complete joint distribution of the responses. The general theme of this
proposal is likelihood based marginal modeling and its applications. A
marginal model is specified in terms of a set of models for marginal
distribution, and that set of models forms an implicit model for the joint
distribution of responses. The approach to inference is a full likelihood
approach, in the sense that the likelihood based on the joint distribution
of the responses is what is maximized. The specific aims are to: (1)
develop a stable algorithm for fitting marginal models by the method of
maximum likelihood to large, sparse contingency tables; (2) development
statistical methodology for marginal model based analyses in the presence
of missing data; (3) explore marginal models within the context of
exchangeable random variables; (4) develop parsimonious mixtures of
marginal models that facilitate the estimation of scientifically
interpretable parameters in the context of evaluating diagnostic tests;
and (5) develop and evaluate profile likelihood methodology for marginal
Multivariate categorical response data arise in many of the study designs
used in biomedical research. In longitudinal studies a group of subjects
is followed over time and data are typically collected at pre-specified
points during the course of the study. In cross-over experiments subjects
are randomized to one of several treatment sequence groups, wherein they
receive a prescribed set of treatments in sequence. The successive
treatment periods are usually separated by a suitably chosen period of
time to allow the effects of the preceding treatments to washout of the
subject's systems. In clinical trials there are frequently multiple
endpoints of interest, such as response to therapy and side-effects of the
therapy. The same is true for toxicological studies where there may be
interest in, say, both birth status (e.g., normal, malformed, or dead) and
birth weight (e.g., low, normal, high). In studies of diagnostic tests
the observational units (e.g., a tissue sample) are routinely evaluated
using a variety of tests and/or by a variety of evaluators (e.g.,
different laboratories, or pathologists). It is thus clear that
statistical models and methodology for the analysis of repeated
categorical responses are broadly applicable to a wide range of study
designs frequently employed in health sciences research.
Assessing rater agreement using marginal association models.
, Becker M.P.
Statistics in medicine, 2002-06-30; 21(12), p. 1743-60.
A multiple imputation strategy for incomplete longitudinal data.
, Becker M.P.
Statistics in medicine, 2001 Sep 15-30; 20(17-18), p. 2741-60.
EM algorithms without missing data.
, Yang I.
, Lange K.
Statistical methods in medical research, 1997 Mar; 6(1), p. 38-54.
Multivariate contingency tables and the analysis of exchangeability.
Ten Have T.R.
, Becker M.P.
Biometrics, 1995 Sep; 51(3), p. 1001-16.
Marginal modeling of binary cross-over data.
, Balagtas C.C.
Biometrics, 1993 Dec; 49(4), p. 997-1009.
Log-linear modelling of pairwise interobserver agreement on a categorical scale.
, Agresti A.
Statistics in medicine, 1992-01-15; 11(1), p. 101-14.