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Health-related quality of life (HRQoL) in the context of COVID-19 is not fully understood. We assessed HRQoL using Patient-Reported Outcomes Measurement Information System® measures among 559 former COVID-19 patients and 298 non-infected individuals. HRQoL was captured once up to 2 years after the initial test. Additionally, we described associations of characteristics with impaired HRQoL. Overall, HRQoL scores were inferior among former patients. A meaningful group difference of at least three T-score points was discernible until 12 months after testing for fatigue (3.1), sleep disturbance (3.5), and dyspnoea (3.7). Cognitive function demonstrated such difference even at >18 months post-infection (3.3). Following dichotomization, pronounced differences in impaired HRQoL were observed in physical (19.2% of former patients, 7.3% of non-infected) and cognitive function (37.6% of former patients, 16.5% of non-infected). Domains most commonly affected among former patients were depression (34.9%), fatigue (37.4%), and cognitive function. Factors that associated with HRQoL impairments among former patients included age (OR ≤2.1), lower education (OR ≤5.3), and COVID-19-related hospitalization (OR ≤4.7), among others. These data underline the need for continued attention of the scientific community to further investigate potential long-term health limitations after COVID-19 to ultimately establish adequate screening and management options for those affected.
where $b\,:\, \mathbb{R}^d \rightarrow \mathbb{R}^d$ is a Lipschitz-continuous function, $A \in \mathbb{R}^{d \times d}$ is a positive-definite matrix, $(Z_t)_{t\geqslant 0}$ is a d-dimensional rotationally symmetric $\alpha$-stable Lévy process with $\alpha \in (1,2)$ and $x\in\mathbb{R}^{d}$. We use two Euler–Maruyama schemes with decreasing step sizes $\Gamma = (\gamma_n)_{n\in \mathbb{N}}$ to approximate the invariant measure of $(X_t)_{t \geqslant 0}$: one uses independent and identically distributed $\alpha$-stable random variables as innovations, and the other employs independent and identically distributed Pareto random variables. We study the convergence rates of these two approximation schemes in the Wasserstein-1 distance. For the first scheme, under the assumption that the function b is Lipschitz and satisfies a certain dissipation condition, we demonstrate a convergence rate of $\gamma^{\frac{1}{\alpha}}_n$. This convergence rate can be improved to $\gamma^{1+\frac {1}{\alpha}-\frac{1}{\kappa}}_n$ for any $\kappa \in [1,\alpha)$, provided b has the additional regularity of bounded second-order directional derivatives. For the second scheme, where the function b is assumed to be twice continuously differentiable, we establish a convergence rate of $\gamma^{\frac{2-\alpha}{\alpha}}_n$; moreover, we show that this rate is optimal for the one-dimensional stable Ornstein–Uhlenbeck process. Our theorems indicate that the recent significant result of [34] concerning the unadjusted Langevin algorithm with additive innovations can be extended to stochastic differential equations driven by an $\alpha$-stable Lévy process and that the corresponding convergence rate exhibits similar behaviour. Compared with the result in [6], our assumptions have relaxed the second-order differentiability condition, requiring only a Lipschitz condition for the first scheme, which broadens the applicability of our approach.
In this article, we study an optimization problem for a couple including two breadwinners with uncertain life times. Both breadwinners need to choose the optimal strategies for consumption, investment, housing, and life insurance purchasing to maximize the utility. In this article, the prices of housing assets and investment risky assets are assumed to be correlated. These two breadwinners are considered to have dependent mortality rates to include the breaking heart effect. The method of copula functions is used to construct the joint survival functions of two breadwinners. The analytical solutions of optimal strategies can be achieved, and numerical results are demonstrated.
The localized nature of severe weather events leads to a concentration of correlated risks that can substantially amplify aggregate event-level losses. We propose a copula-based regression model for replicated spatial data to characterize the dependence between property damage claims arising from a common storm when analyzing its financial impact. The factor copula captures the location-based spatial dependence between properties, as well as the aspatial dependence induced by the common shock of experiencing the same storm. The framework allows insurers to flexibly incorporate the observed heterogeneity in marginal models of skewed, heavy-tailed, and zero-inflated insurance losses, while retaining the model interpretation in decomposing latent sources of dependence. We present a likelihood-based estimation to address the computational challenges from the discreteness and high dimensionality in the outcome of interest. Using hail damage insurance claims data from a US insurer, we demonstrate the effect of dependence on claims management decisions.
We establish a sample path moderate deviation principle for the integrated shot noise process with Poisson arrivals and non-stationary noises. As in Pang and Taqqu (2019), we assume that the noise is conditionally independent given the arrival times, and the distribution of each noise depends on its arrival time. As applications, we derive moderate deviation principles for the workload process and the running maximum process for a stochastic fluid queue with the integrated shot noise process as the input; we also show that a steady-state distribution exists and derive the exact tail asymptotics.
In a recent paper, the authors studied the distribution properties of a class of exchangeable processes, called measure-valued Pólya sequences (MVPSs), which arise as the observation process in a generalized urn sampling scheme. Here we present several results in the form of ‘sufficientness’ postulates that characterize their predictive distributions. In particular, we show that exchangeable MVPSs are the unique exchangeable models whose predictive distributions are a mixture of the marginal distribution and the average of a probability kernel evaluated at past observations. When the latter coincides with the empirical measure, we recover a well-known result for the exchangeable model with a Dirichlet process prior. In addition, we provide a ‘pure’ sufficientness postulate for exchangeable MVPSs that does not assume a particular analytic form for the predictive distributions. Two other sufficientness postulates consider the case when the state space is finite.
In this chapter we present two spatial dependent models: one based on defining a latent variable for each area, and the other by defining one latent variable for each pair of latent areas. We call the latter the latent edges model. We compare both models with a real data set. Extensions to spatio-temporal constructions are also considered.
In this chapter we define what a conjugate family is in a Bayesian analysis context and develop detailed examples of some cases; in particular, we review the beta and binomial case, the Pareto and inverse Pareto case, the gamma and gamma case and the gamma and Poisson case. We conclude by providing a list of conjugate models.
In this chapter we show how to define temporal dependent sequences using a moving average type of construction. We compare the performance of this construction with a Markov-process type. We finally extend the models to include seasonal and periodic dependencies.
In this chapter we start with some attempts to construct dependence sequences with order larger than one and present a general result to achieve an invariant distribution via a three-level hierarchical model. We finally present some results involving exponential families.
In today’s insurance market, numerous cyber insurance products provide bundled coverage for losses resulting from different cyber events, including data breaches and ransomware attacks. Every category of incident has its own specific coverage limit and deductible. Although this gives prospective cyber insurance buyers more flexibility in customizing the coverage and better manages the risk exposures of sellers, it complicates the decision-making process in determining the optimal amount of risks to retain and transfer for both parties. This article aims to build an economic foundation for these incident-specific cyber insurance products with a focus on how incident-specific indemnities should be designed for achieving Pareto optimality for both the insurance seller and the buyer. Real data on cyber incidents are used to illustrate the feasibility of this approach. Several implementation improvement methods for practicality are also discussed.
In this chapter we describe a general procedure to construct Markov sequences with invariant distributions. The procedure can be used with conjugate and non-conjugate models and with parametric and nonparametric distributions. We derive several examples in detail and finish with some applications in survival analysis.
In this chapter we introduce the concept of exchangeability and show how to construct exchangeable sequences; we present our first result of how to construct exchangeable sequences and maintain a desirable marginal distribution and provide detailed examples. We finish with an application of exchangeable constructions in a meta analysis. Bugs and R code are provided.
In 2022, an increase in invasive group A streptococcal (iGAS) infections was observed in the Netherlands. A particular increase was seen among children; therefore, we aimed to assess risk factors for iGAS infection in children aged 6 months to 5 years. A prospective case–control study was conducted between February and May 2023. We approached parents of notified iGAS cases to complete a questionnaire on exposures during 4 weeks prior to disease onset. Controls were recruited via social media and matched to cases on sex and birthyear. Conditional logistic regression was performed to estimate odds ratios (OR) of exposures. For the analysis, we included 18 cases and 103 controls. Varicella prior to onset of iGAS disease was reported in two (11%) cases and one (1%) control (OR: 12.0, 95% CI: 1.1–139.0). Exposure to group A streptococcal (GAS)-like illnesses such as impetigo, pharyngitis, and scarlet fever was reported in 8 (44%) cases and 15 (15%) controls (OR: 7.1, 95% CI: 1.8–29.0). Our findings are in line with previous studies by identifying varicella as a risk factor for iGAS among young children and highlight the association with non-invasive GAS infections in the community as a possible source of transmission.