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Hypertensive disorders of pregnancy occur in about 10% of pregnant women around the world. Though there is evidence that hypertension impacts maternal cardiac functions, the relation between hypertension and cardiac dysfunctions is only partially understood. The study of this relationship can be framed as a joint inferential problem on multiple populations, each corresponding to a different hypertensive disorder diagnosis, that combines multivariate information provided by a collection of cardiac function indexes. A Bayesian nonparametric approach seems particularly suited for this setup and we demonstrate it on a dataset consisting of transthoracic echocardiography results of a cohort of Indian pregnant women. We are able to perform model selection, provide density estimates of cardiac function indexes and a latent clustering of patients: these readily interpretable inferential outputs allow to single out modified cardiac functions in hypertensive patients compared to healthy subjects and progressively increased alterations with the severity of the disorder. The analysis is based on a Bayesian nonparametric model that relies on a novel hierarchical structure, called symmetric hierarchical Dirichlet process. This is suitably designed so that the mean parameters are identified and used for model selection across populations, a penalization for multiplicity is enforced, and the presence of unobserved relevant factors is investigated through a latent clustering of subjects. Posterior inference relies on a suitable Markov Chain Monte Carlo algorithm and the model behaviour is also showcased on simulated data.