Loglinear spatial factor analysis: an application to diabetes mellitus complications

Abstract

SUMMARYThe investigation of spatial variation in disease rates is a standard epidemiological practice used to describe the geographic clustering of diseases which is helpful for making hypotheses about the possible 'factors' responsible for differences in risk. Up to the most recent statistical and computational developments, studies have almost entirely focused on the spatial modeling of univariate distributions of cases, that is, on the spatial modeling of single diseases. However, many diseases show similar patterns of geographical variation which may suggest the existence of common underlying risk factors, whether these are related to the environment, to particular local food habits, or to the clustering of a particular population (genetic origin). In this work, for multivariate categorical data pointwise geo-referenced in a 'geostatistical' fashion, we propose a model for the study of the joint spatial variation of more diseases. Our approach is based on a hierarchical (generalized linear mixed) multivariate model where the underlying latent structure is given by a Gaussian geostatistical spatial factor model. The methodology proposed can be seen as an extension of the geostatistical linear model of coregionalization, and of the related 'factorial kriging analysis', to the case of geo-referenced, in general multi-way, contingency tables. An application of the proposed methodology is shown on an epidemiological data set coming from an extensive survey on diabetes mellitus patients which involved the majority of the family practitioners of the region of Umbria in central Italy in 1990. Attention is centered on the study of nephropathy and retinopathy, two of the chronic diabetic complications affecting life quality and expectancy.

Modelling multivariate disease rates with a latent structure mixture model

“…Our approach effectively generalises the 'mixture of factor analysers' model (Ghahramani and Hinton, 1996) to one that can deal with non-Gaussian responses. In that sense the models we have developed can be considered as extensions to the latent structure models that are seeing increasing use in biometric applications, such as those presented by Dunson (2003); Wang and Wall (2003); Minozzo and Fruttini (2004); Dunson and Herring (2005).…”

“…Latent structure models are not restricted to area applications. Christensen and Amemiya (2002) have suggested an approach applicable to point data which has been illustrated by Minozzo and Fruttini (2004) who examined bivariate point measures of types of diabetes morbidity. Similar models are also seeing use outside cancer epidemiology.…”

Hierarchical Factor Models for Large Spatially Misaligned Data: A Low‐Rank Predictive Process Approach

“…Hogan and Tchernis (2004) fitted a one-factor spatial model and compared the results using different forms of spatial dependence through the single factor. Minozzo and Fruttini (2004) applied log-linear spatial FA to geo-referenced frequency counts adopting the classical proportional covariance model to the latent factors.…”

Cancer incidence in men: a cluster analysis of spatial patterns

“…Although recent methods for joint disease mapping were first developed to investigate co-occurrence of two events [ 5 - 7 ], and then extended to more than two events [ 8 ], these models are still not well-suited for analyzing many cancers simultaneously. Cluster analysis includes several exploratory techniques that were developed to identify data grouping and to generate hypotheses.…”