Marginalized models for right-truncated and interval-censored time-to-event data

Analysis of clustered data is often performed using random effects regression models. In such conditional models, a cluster-specific random effect is often introduced into the linear predictor function. Parameter interpretation of the covariate effects is then conditioned on the random effects, leading to a subject-specific interpretation of the regression parameters. Recently, Marginalized Multilevel Models (MMM) and the Bridge distribution models have been proposed as a unified approach, which allows one to capture the within-cluster correlations by specifying random effects while still allowing for marginal parameter interpretation. In this paper, we investigate these two approaches, and the conditional Generalized Linear Mixed Model (GLMM), in the context of right-truncated, interval-censored time-to-event data, further characterized by clustering and additional overdispersion. While these models have been applied in literature to model the mean, here we extend their application to modeling the hazard function for the survival endpoints. The models are applied to analyze data from the HET-CAM experiment which was designed to assess the potential of a compound to cause injection site reaction. Results show that the MMM and Bridge distribution approaches are useful when interest is in the marginal interpretation of the covariate effects.