Clustered binary data are a frequently recurring phenomenon in epidemiological research. In the ophthalmologic field, one always has data on two eyes for an individual and it is problematic as to how to treat such data, particularly if one wishes to look at the effects of several covariates in the same analysis, which may be either person- or eye-specific. Several approaches to this problem have been suggested in the literature, including: (a) conditional models based on the Beta-binomial distribution; (b) more general conditional models; (c) two stage models, whereby logistic regression is performed conditional on a cluster effect parameter and the cluster effect parameter is assumed to be normally distributed across a population of clusters; (d) general estimating equation (GEE) models. These models have not received wide use in the epidemiologic literature, mainly due to lack of knowledge of their comparative benefits. An important task for this grant proposal is to compare these models on a collection of six common data bases as regards ease-of-implementation, goodness-of-ft and ease-of-interpretation. There are also several important unresolved issues in the clustered data field including: (i) the treatment of data with more than one level of nesting or with a more general correlation structure; (ii) the treatment of ordinal clustered data; and (iii) the treatment of clustered survival data. We propose to study these questions based on an extension of methodology which we have previously developed for correlated binary data with an intraclass correlation structure. Finally, computing issues are important in this field since some of the methods proposed are very computer intensive and are difficult to implement. We propose to make available software to implement our methods in PC-compatible FORTRAN and if possible as part of the supplemental library of SAS modules so as to widen the base of users who can assess these methods. The work presented here will have broad public health importance since clustered data always occur in some medical specialties such as ophthalmology and frequency occur in other specialties (such as cardiology).
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