Marginally Interpretable Linear Transformation Models for Clustered Observations
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Clustered observations are ubiquitous in controlled and observational studies and arise naturally in multicenter trials or longitudinal surveys. I present two novel models 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. Both models provide analytic formulae for the marginal distributions, one of which features directly interpretable parameters. 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. I present re-analyses of five applications from different domains, including models for non-normal and discrete responses, and explain how specific models for the estimation of marginal distributions can be defined within this novel modelling framework and how the results can be interpreted in a marginal way.
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