Modeling Multivariate Binary Responses with Multiple Levels of Nesting Based on Alternating Logistic Regressions: an Application to Caries Aggregation

Clustered binary responses are commonly encountered in dental research. Data analysis may include modeling both the marginal response probabilities (i.e., risk) and the dependence structure between pairs of responses (i.e., aggregation). While second-order generalized estimating equations (GEE2) is a well-known approach for such data, alternating logistic regressions (ALR) is a computationally efficient alternative method, especially for large clusters. We illustrate ALR with an application to caries aggregation using a dataset with 3 levels of nesting: tooth surfaces within an interproximal (IP) region, IP regions within a jaw, and jaws within a subject. Caries lesions appear to aggregate strongly within subjects with a spatially distributed risk. The minimum within-IP-region odds ratio (OR) was 2.25 (95% confidence interval 1.15, 4.41), and the within-IP-region ORs were always greater than the between-IP-region ORs. ALR is a convenient and useful regression technique for explicit modeling of the dependence structure, and may be applicable to other dental research problems involving clustered or nested responses.