Statistical Modelling 10 (2010), 241–264
Modelling multivariate disease rates with a latent structure mixture model
PJ Hewson
School of Mathematics and Statistics,
University of Plymouth,
Drake Circus,
Plymouth PL4 8AA
UK
eMail: paul.hewson@plymouth.ac.uk
TC Bailey
School of Engineering, Computing and Mathematics,
University of Exeter
UK
Abstract:
There has been considerable recent interest in multivariate modelling of
the geographical distribution of morbidity or mortality rates for potentially
related diseases. The motivations for this include investigation of
similarities or dissimilarities in the risk distribution for the different
diseases, as well as ‘borrowing strength’ across disease rates to shrink the
uncertainty in geographical risk assessment for any particular disease. A
number of approaches to such multivariate modelling have been suggested and
this paper proposes an extension to these which may provide a richer range
of dependency structures than those encompassed so far. We develop a model
which incorporates a discrete mixture of latent structures and argue that
this provides potential to represent an enhanced range of correlation
structures between diseases at the same time as implicitly allowing for
less restrictive spatial correlation structures between geographical units.
We compare and contrast our approach to other commonly used multivariate
disease models and demonstrate comparative results using data taken from
cancer registries on four carcinomas in some 300 geographical units in
England, Scotland and Wales.
Keywords:
factor analysis; latent structure; mixture model; multivariate disease rates
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