Background Clinical investigations have argued for long-term neurological manifestations in both hospitalised and non-hospitalised COVID-19 patients. It is unclear whether long-term neurological symptoms and features depend on COVID-19 severity. Methods From a sample of 208 consecutive non-neurological patients hospitalised for COVID-19 disease, 165 survivors were re-assessed at 6 months according to a structured standardised clinical protocol. Prevalence and predictors of long-term neurological manifestations were evaluated using multivariate logistic regression analyses. Results At 6-month follow-up after hospitalisation due to COVID-19 disease, patients displayed a wide array of symptoms; fatigue (34%), memory/attention (31%) and sleep disorders (30%) were the most frequent. At neurological examination, 40% of patients exhibited neurological abnormalities, such as hyposmia (18.0%), cognitive deficits (17.5%), postural tremor (13.8%) and subtle motor/sensory deficits (7.6%). Older age, premorbid comorbidities and severity of COVID-19 were independent predictors of neurological manifestations in logistic regression analyses. Conclusions Premorbid vulnerability and severity of SARS-CoV-2 infection impact on prevalence and severity of long-term neurological manifestations.

Although Bayesian nonparametric mixture models for continuous data are well developed, there is a limited literature on related approaches for count data. A common strategy is to use a mixture of Poissons, which unfortunately is quite restrictive in not accounting for distributions having variance less than the mean. Other approaches include mixing multinomials, which requires finite support, and using a Dirichlet process prior with a Poisson base measure, which does not allow smooth deviations from the Poisson. As a broad class of alternative models, we propose to use nonparametric mixtures of rounded continuous kernels. An efficient Gibbs sampler is developed for posterior computation, and a simulation study is performed to assess performance. Focusing on the rounded Gaussian case, we generalize the modeling framework to account for multivariate count data, joint modeling with continuous and categorical variables, and other complications. The methods are illustrated through applications to a developmental toxicity study and marketing data. This article has supplementary material online.

Density estimation represents one of the most successful applications of Bayesian nonparametrics. In particular, Dirichlet process mixtures of normals are the gold standard for density estimation and their asymptotic properties have been studied extensively, especially in the univariate case. However a gap between practitioners and the current theoretical literature is present. So far, posterior asymptotic results in the multivariate case are available only for location mixtures of Gaussian kernels with independent prior on the common covariance matrix, while in practice as well as from a conceptual point of view a location-scale mixture is often preferable. In this paper we address posterior consistency for such general mixture models by adapting a convergence rate result which combines the usual low-entropy, high-mass sieve approach with a suitable summability condition. Specifically, we establish consistency for Dirichlet process mixtures of Gaussian kernels with various prior specifications on the covariance matrix. Posterior convergence rates are also discussed.