Data depth for mixed-type data through MDS. An application to biological age imputation

Abstract

For a mixed-type dataset, we propose a new procedure to assess the quality of an observation as a central tendency. Next, we apply this technique to valuate the functional condition of a human organism in terms of its biological age, which is based on biomarkers, medical conditions, life habits, and sociodemographic variables. These records are of mixed type since they are made up by numerical and categorical variables. In order to evaluate the centrality of an observation in a mixed-type dataset, we obtain a Multidimensional Scaling representation and use some classical notion of multivariate data depth in an appropriate space. The biological age of an individual is finally assessed in terms of the age that would make it as deep as possible with respect to a sample of individuals of a similar age subject to it retaining all other features unchanged.