In this paper we present ROC methodology and analyze the ROC curve. We describe first the historical background and its relation with signal detection theory. Some mathematical properties of this curve are given, and in particular the relation with stochastic orders and statistical hypotheses testing are described. We present also a medical application of the Neymann–Pearson lemma
The Shannon entropy based on the probability density function is a key information measure with applications in different areas. Some alternative information measures have been proposed in the literature. Two relevant ones are the cumulative residual entropy (based on the survival function) and the cumulative past entropy (based on the distribution function). Recently, some extensions of these measures have been proposed. Here, we obtain some properties for the generalized cumulative past entropy. In particular, we prove that it determines the underlying distribution. We also study this measure in coherent systems and a closely related generalized past cumulative Kerridge inaccuracy measure.
Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) may present with a wide variety of symptoms, including neurological manifestations. We investigated clinical, demographic, laboratory, neurophysiological and imaging characteristics of SARS-CoV-2-positive children with seizures and analyzed differences between children admitted during the periods with prevalent circulation of the Alpha/Delta and Omicron variants, respectively. Patients’ characteristics were analyzed according to the presence or absence of seizures and then according to the SARS-CoV-2 variants. Five-hundred and four SARS-CoV-2-positive patients were included: 93 (18.4%) with seizures and 411 (81.6%) without. Patients with seizures were older, had more commonly an underlying epilepsy and had more frequently altered C-reactive protein than those without seizures. Electroencephalography was abnormal in 5/38 cases. According to the SARS-CoV-2 variant, seizures were recorded in 4.7% of the total number of hospitalized patients during the Alpha/Delta period, and in 16.9% of patients admitted during the Omicron period. During the Alpha/Delta variants, seizures were more commonly observed in patients with epilepsy compared to those observed during the Omicron period. Our findings suggest that although SARS-CoV-2 may potentially trigger seizures, they are generally not severe and do not require intensive care admission.
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