Posner-Schlossman Syndrome European Study Group: study protocol and baseline patients characteristics of a multicentre study.

BACKGROUND: The aim of the Posner-Schlossman Syndrome European Study Group (PSS-ESG) is to acquire a comprehensive dataset of European patients with PSS. Here, we present the first report on the study protocol and the clinical findings of the patients at baseline. METHODS: The PSS-ESG is a retrospective, multicentre study designed to evaluate patients with PSS. The study, designed and driven by a European Expert Committee includes three datasets: (1) the baseline, (2) the follow-up and (3) the intraocular pressure (IOP)/glaucoma dataset. RESULTS: A total of 11 centres adhered to the PSS-ESG and 107 patients were included (68 males, 39 females) mostly Caucasian (93.4%). At uveitis onset, the patient's age ranged between 11 and 76 years, (mean age: 42±15 years).Best-corrected visual acuity was >0.5 in 80.3% of the eyes, IOP was >40 mm Hg in 44% of the eyes. Keratic precipitates were found in 78.5% of the eyes. No flare or cells in anterior chamber were detected in 56% and 53% of the cases, respectively. PCR analysis on aqueous sample was positive for cytomegalovirus-DNA in 50.6% out of the 81 tested patients. CONCLUSIONS: The PSS-ESG is the first multicentre study aimed to collect a comprehensive dataset of patients with PSS in non-Asian countries. A middlde-aged Caucasian male with a low-grade anterior chamber inflammation, keratic precipitates, preserved visual acuity and marked increased in IOP seemed to be the standard PSS patient across the 11 uveitis and glaucoma centres participating in the PSS-ESG.

A pseudo-analytic generalization of the memoryless property for continuous random variables and its use in pricing contingent claims.

We explore an extension of the memoryless property for continuous random variables by using the concept of pseudo-sum. Subsequently, we demonstrate the practicality of this approach through two financial applications in which pseudo-sums characterize the values of arbitrage-free contingent claims. Moreover, we are able to establish new interesting connections between different probability distributions.

Estimation of reinforced urn processes under left-truncation and right-censoring.

We propose a non-parametric estimator for bivariate left-truncated and right-censored observations that combines the expectation-maximization algorithm and the reinforced urn process. The resulting expectation-reinforcement algorithm allows for the inclusion of experts' knowledge in the form of a prior distribution, thus belonging to the class of Bayesian models. This can be relevant in applications where the data is incomplete, due to biases in the sampling process, as in the case of left-truncation and right-censoring. With this new approach, the distribution of the truncation variables is also recovered, granting further insight into those biases, and playing an important role in applications like prevalent cohort studies. The estimators are tested numerically using artificial and empirical datasets, and compared with other methodologies such as copula models and the Kaplan-Meier estimator.

On single point forecasts for fat-tailed variables.

We discuss common errors and fallacies when using naive "evidence based" empiricism and point forecasts for fat-tailed variables, as well as the insufficiency of using naive first-order scientific methods for tail risk management. We use the COVID-19 pandemic as the background for the discussion and as an example of a phenomenon characterized by a multiplicative nature, and what mitigating policies must result from the statistical properties and associated risks. In doing so, we also respond to the points raised by Ioannidis et al. (2020).

Computing the exact distributions of some functions of the ordered multinomial counts: maximum, minimum, range and sums of order statistics.

Starting from seminal neglected work by Rappeport (Rappeport 1968 Algorithms and computational procedures for the application of order statistics to queuing problems. PhD thesis, New York University), we revisit and expand on the exact algorithms to compute the distribution of the maximum, the minimum, the range and the sum of the J largest order statistics of a multinomial random vector under the hypothesis of equiprobability. Our exact results can be useful in all those situations in which the multinomial distribution plays an important role, from goodness-of-fit tests to the study of Poisson processes, with applications spanning from biostatistics to finance. We describe the algorithms, motivate their use in statistical testing and illustrate two applications. We also provide the codes and ready-to-use tables of critical values.

An Analysis of the Number of Medical Malpractice Claims and Their Amounts.

Starting from an extensive database, pooling 9 years of data from the top three insurance brokers in Italy, and containing 38125 reported claims due to alleged cases of medical malpractice, we use an inhomogeneous Poisson process to model the number of medical malpractice claims in Italy. The intensity of the process is allowed to vary over time, and it depends on a set of covariates, like the size of the hospital, the medical department and the complexity of the medical operations performed. We choose the combination medical department by hospital as the unit of analysis. Together with the number of claims, we also model the associated amounts paid by insurance companies, using a two-stage regression model. In particular, we use logistic regression for the probability that a claim is closed with a zero payment, whereas, conditionally on the fact that an amount is strictly positive, we make use of lognormal regression to model it as a function of several covariates. The model produces estimates and forecasts that are relevant to both insurance companies and hospitals, for quality assurance, service improvement and cost reduction.