Title: A transformation perspective on marginal and conditional models
Authors: Luisa Barbanti - University of Zurich (Switzerland)
Torsten Hothorn - University of Zurich (Switzerland) [presenting]
Abstract: Clustered observations are ubiquitous in controlled and observational studies and arise naturally in multicenter trials or longitudinal surveys. We present a novel model for the analysis of clustered observations where the marginal distributions are described by a linear transformation model and the correlations by a joint multivariate normal distribution. The joint model provides an analytic formula for the marginal distribution. Owing to the richness of transformation models, the techniques are applicable to any type of response variable, including bounded, skewed, binary, ordinal, or survival responses. We discuss the analysis of two clinical trials aiming at the estimation of marginal treatment effects. In the first trial, the pain was repeatedly assessed on a bounded visual analog scale and marginal proportional-odds models are presented. The second trial reported disease-free survival in rectal cancer patients, where the marginal hazard ratio from Weibull and Cox models is of special interest. An implementation is available in the ``tram'' add-on package to the R system and was benchmarked against established models in the literature.