Interval censoring and marginal analysis in ordinal regression

This article develops a methodology for regression analysis of ordinal response data subject to interval censoring. This work is motivated by the need to analyze data from multiple studies in toxicological risk assessment. Responses are scored on an ordinal severity scale, but not all responses can be scored completely. For instance, in a mortality study, information on nonfatal but adverse outcomes may be missing. In order to address possible within-study correlations, we develop a generalized estimating approach to the problem, with appropriate adjustments to uncertainty statements. We develop expressions relating parameters of the implied marginal model to the parameters of a conditional model with random effects, and, in a special case, we note an interesting equivalence between conditional and marginal modeling of ordinal responses. We illustrate the methodology in an analysis of a toxicological database.