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Title: Multivariate conditional transformation models in practice: Conditional reference region estimation Authors:  Oscar Lado-Baleato - Universidade de Santiago de Compostela (Spain) [presenting]
Carmen Cadarso Suarez - Universidade de Santiago de Compostela (Spain)
Francisco Gude - Complexo Hospitalario Universitario de Santiago de Compostela (Spain)
Thomas Kneib - University of Goettingen (Germany)
Abstract: When the results of several continuous diagnostic tests are available for the same patient, a multivariate reference region (MVR) is desirable in order to get a clinical interpretation for those results. An MVR, defined as a region that contains 95\% of healthy patients results, allows classifying patients into those apparently healthy, and those with some pathology. In diseases diagnosis, MVRs offer a higher specificity and sensitivity than the application of several univariate reference intervals. Although, MVRs are rarely applied in practice because of interpretability difficulties, and Gaussian assumption restriction. Thus, further statistical research is required in order to provide MVRs with higher applicability, and more straightforward interpretability by physicians. Moreover, as diagnostic tests joint distribution change with patients characteristics, irrespectively of the disease status, covariate-adjusted MVRs are desirable in practice. We present a novel formulation for conditional MVRs based on Multivariate Conditional Transformation Models (MCTMs), a brand new multivariate regression framework. The conditional MVRs places no parametric restriction for the response, and continuous covariates non-linear effects might be estimated from the data. MCTMs reference region proved to be reliable with simulated data, and it solved a real problem in diabetes research.