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Clustered observations are ubiquitous in controlled and observational studiesand arise naturally in multi-centre trials or longitudinal surveys. We presenta novel model for the analysis of clustered observations where the marginaldistributions are described by a linear transformation model and thecorrelations by a joint multivariate normal distribution. The joint modelprovides an analytic formula for the marginal distribution. Owing to therichness of transformation models, the techniques are applicable to any type ofresponse variable, including bounded, skewed, binary, ordinal, or survivalresponses. We demonstrate how the common normal assumption for reaction timescan be relaxed in the sleep deprivation benchmark dataset and report marginalodds ratios for the notoriously difficult toe nail data. We furthermore discussthe analysis of two clinical trials aiming at the estimation of marginaltreatment effects. In the first trial, pain was repeatedly assessed on abounded visual analog scale and marginal proportional-odds models arepresented. The second trial reported disease-free survival in rectal cancerpatients, where the marginal hazard ratio from Weibull and Cox models is ofspecial interest. An empirical evaluation compares the performance of the novelapproach to general estimation equations for binary responses and toconditional mixed-effects models for continuous responses. An implementation isavailable in the "tram" add-on package to the R system and was benchmarkedagainst established models in the literature.

A Transformation Perspective on Marginal and Conditional Models