Cost-effectiveness of TOMAC therapy for medication-refractory restless legs syndrome: an updated analysis based on Extension study data.

AIMS: Patients with medication-refractory restless legs syndrome (RLS) have limited therapeutic options available for symptom relief. Tonic motor activation (TOMAC) presents a novel, non-invasive therapy for this patient population. The aim of this study was to conduct an updated cost-effectiveness analysis of TOMAC therapy based on recently available longer-term follow-up data. MATERIALS AND METHODS: A previously published decision-analytic Markov model was utilized to project strategy-specific costs and outcomes over three-years and lifetime for TOMAC compared to status quo treatment (control). Cohort characteristics were based on 24-week clinical data from the extension cohort of the RESTFUL study, which included longer-term follow-up of RESTFUL completers who were assigned to continue or discontinue TOMAC use (TOMAC and control, respectively). The primary analysis outcome was the incremental cost-effectiveness ratio (ICER) in $ per quality-adjusted life year (QALY) gained, calculated using change in International RLS Study Group Rating Scale (IRLS) score as the effect measure. Extensive sensitivity analyses were performed. RESULTS: TOMAC treatment improved IRLS by 5.9 versus control, resulting in estimated utility improvement of +0.05. Over three-years and lifetime, TOMAC added 0.14 and 0.73 QALYs, at incremental costs of $6,751 and $27,440, resulting in projected ICERs of $47,609 and $37,823 per QALY gained, respectively. TOMAC was found to be cost-effective across all tested sensitivity analyses. LIMITATIONS AND CONCLUSION: The inclusion of longer follow-up data in the current analysis confirms earlier exploratory cost-effectiveness findings and suggest TOMAC therapy may provide a high-value treatment option for patients with medication-refractory RLS.

Restless Legs Syndrome (RLS) is a is a neurological disorder, usually chronic, that causes an overwhelming urge to move one's legs, with pronounced implications for patients' quality of life. While pharmaceutical treatment options exist, a substantial proportion of patients are considered refractory to drug treatment. Tonic motor activation (TOMAC) therapy is a novel non-invasive neurostimulation approach that was recently cleared for market in the United States. This study sought to provide an updated economic analysis based on recently available data with longer follow-up. The findings of this study, based on data from the RESTFUL Extension study, suggest TOMAC therapy can be a high-value treatment alternative for refractory patients, providing meaningful quality of life improvement at costs that render it cost-effective in the United States. Future data with further extended follow-up will be useful to further broaden the evidence base underpinning these findings.

Development of decision tree classification algorithms in predicting mortality of COVID-19 patients.

INTRODUCTION: The accurate prediction of COVID-19 mortality risk, considering influencing factors, is crucial in guiding effective public policies to alleviate the strain on the healthcare system. As such, this study aimed to assess the efficacy of decision tree algorithms (CART, C5.0, and CHAID) in predicting COVID-19 mortality risk and compare their performance with that of the logistic model. METHODS: This retrospective cohort study examined 5080 cases of COVID-19 in Babol, a city in northern Iran, who tested positive for the virus via PCR from March 2020 to March 2022. In order to check the validity of the findings, the data was randomly divided into an 80% training set and a 20% testing set. The prediction models, such as Logistic regression models and decision tree algorithms, were trained on the 80% training data and tested on the 20% testing data. The accuracy of these methods for the test samples was assessed using measures like ROC curve, sensitivity, specificity, and AUC. RESULTS: The findings revealed that the mortality rate for COVID-19 patients who were admitted to hospitals was 7.7%. Through cross validation, it was determined that the CHAID algorithm outperformed other decision tree and logistic regression algorithms in specificity, and precision but not sensitivity in predicting the risk of COVID-19 mortality. The CHAID algorithm demonstrated a specificity, precision, accuracy, and F-score of 0.98, 0.70, 0.95, and 0.52 respectively. All models indicated that factors such as ICU hospitalization, intubation, age, kidney disease, BUN, CRP, WBC, NLR, O2 sat, and hemoglobin were among the factors that influenced the mortality rate of COVID-19 patients. CONCLUSIONS: The CART and C5.0 models had outperformed in sensitivity but CHAID demonstrates a better performance compared to other decision tree algorithms in specificity, precision, accuracy and shows a slight improvement over the logistic regression method in predicting the risk of COVID-19 mortality in the population under study.

Microbial bacterioruberin: The new C50 carotenoid player in food industries.

The demand for natural products has significantly increased, driving interest in carotenoids as bioactive compounds for both human and animal consumption. Carotenoids, natural pigments with several biological properties, like antioxidant and antimicrobial, are increasingly preferred over synthetic colorants by the consumers (chemophobia). The global carotenoid market is projected to reach US$ 2.45 billion by 2034, driven by consumer preferences for natural ingredients and regulatory restrictions on synthetic products. Among carotenoids, bacterioruberin (BR), a C50 carotenoid naturally found in microbial hyperhalophilic archaea and in moderate halophilic archaea, stands out for its exceptional antioxidant capabilities, surpassing even well-known carotenoids like astaxanthin. BR's and its derivatives unique structure, with 13 conjugated double bonds and four -OH groups, contributes to its potent antioxidant activity and potential applications in food, feed, supplements, pharmaceuticals, and cosmeceuticals. This review explores BR's chemical and biological properties, upstream and downstream technologies, analytical techniques, market applications, and prospects in the colorants industry. While BR is not intended to replace existing carotenoids, its inclusion enriches the range of natural products available to meet the rising demand for natural alternatives. Furthermore, BR's promising antioxidant capacity positions it as a key player in the future carotenoid market, offering diverse industries a natural and potent alternative for several applications.

Exploring a distinct group of analytical functions linked with Bernoulli's Lemniscate using the q-derivative.

This research presents a new group of mathematical functions connected to Bernoulli's Lemniscate, using the q-derivative. Expanding on previous studies, the research concentrates on determining coefficient approximations, the Fekete-Szego functional, Zalcman inequality, Krushkal inequality, along with the second and third Hankel determinants for this recently established collection of functions. Additionally, the study derives the Fekete-Szego inequality for the function ξ f ( ξ ) and obtains the inverse function f - 1 ( ξ ) for this specific class. This research advances our understanding in this area and suggests for further exploration.

A note on heat kernel of graphs.

Consider a simple undirected connected graph G, with D ( G ) and A ( G ) representing its degree and adjacency matrices, respectively. Furthermore, L ( G ) = D ( G ) - A ( G ) is the Laplacian matrix of G, and H t = exp ⁡ ( - t L ( G ) ) is the heat kernel (HK) of G, with t > 0 denoting the time variable. For a vertex u ∈ V ( G ) , the uth element of the diagonal of the HK is defined as H t ( u , u ) = ( exp ⁡ ( - t L ( G ) ) ) u u = ∑ k = 0 ∞ ( ( - t L ( G ) ) k ) u u k ! , and H E ( G ) = ∑ i = 1 n e - t λ i = ∑ u = 1 n H t ( u , u ) is the HK trace of G, where λ 1 , λ 2 , ⋯ , λ n denote the eigenvalues of L ( G ) . This study provides new computational formulas for the HK diagonal entries of graphs using an almost equitable partition and the Schur complement technique. We also provide bounds for the HK trace of the graphs.

Novel machine-learning prediction tools for overall survival of patients with chondrosarcoma: Based on recursive partitioning analysis.

BACKGROUND: Chondrosarcoma (CHS), a bone malignancy, poses a significant challenge due to its heterogeneous nature and resistance to conventional treatments. There is a clear need for advanced prognostic instruments that can integrate multiple prognostic factors to deliver personalized survival predictions for individual patients. This study aimed to develop a novel prediction tool based on recursive partitioning analysis (RPA) to improve the estimation of overall survival for patients with CHS. METHODS: Data from the Surveillance, Epidemiology, and End Results (SEER) database were analyzed, including demographic, clinical, and treatment details of patients diagnosed between 2000 and 2018. Using C5.0 algorithm, decision trees were created to predict survival probabilities at 12, 24, 60, and 120 months. The performance of the models was assessed through confusion scatter plot, accuracy rate, receiver operator characteristic (ROC) curve, and area under ROC curve (AUC). RESULTS: The study identified tumor histology, surgery, age, visceral (brain/liver/lung) metastasis, chemotherapy, tumor grade, and sex as critical predictors. Decision trees revealed distinct patterns for survival prediction at each time point. The models showed high accuracy (82.40%-89.09% in training group, and 82.16%-88.74% in test group) and discriminatory power (AUC: 0.806-0.894 in training group, and 0.808-0.882 in test group) in both training and testing datasets. An interactive web-based shiny APP (URL: https://yangxg1209.shinyapps.io/chondrosarcoma_survival_prediction/) was developed, simplifying the survival prediction process for clinicians. CONCLUSIONS: This study successfully employed RPA to develop a user-friendly tool for personalized survival predictions in CHS. The decision tree models demonstrated robust predictive capabilities, with the interactive application facilitating clinical decision-making. Future prospective studies are recommended to validate these findings and further refine the predictive model.

Certain inequalities related with Hankel and Toeplitz determinant for q-starlike functions.

In the present article, we prove the sharp upper bounds for the second order Hankel determinants |H2(1)|,|H2(2)| and related functionals |a2a3-a4|, |a2a5-a3a4| for q-starlike functions. An upper bound for the third order Hankel determinant |H3(1)| along with the sharp upper bounds for Toeplitz determinant |Tm(n)|, where (m,n)∈{(2,2),(2,3),(3,1),(3,2)} are attained. Many known results are also obtained as corollaries of our main results.

Image edge detection enhancement using coefficients of Sakaguchi type functions mapped onto petal shaped domain.

This research introduces a new approach to elevate the precision of image edge detection through a new algorithm rooted in the coefficients derived from the subclass SCt,ρ (CSKP model). Our method employs convolution operations on input image pixels, utilizing the CSKP mask window in eight distinct directions, fostering a comprehensive and multi-directional analysis of edge features. To gauge the efficacy of our algorithm, image quality is assessed through perceptually significant metrics, including contrast, correlation, energy, homogeneity, and entropy. The study aims to contribute a valuable tool for diverse applications such as computer vision and medical imaging by presenting a robust and innovative solution to enhance image edge detection. The results demonstrate notable improvements, affirming the potential of the proposed algorithm to advance the current state-of-the-art in image processing.

Spectral norm and energy of a digraph with respect to a VDB topological index.

The set of singular values of a digraph with respect to a vertex-degree based topological index is the set of all singular values of its general adjacency matrix. The spectral norm is the largest singular value and the energy the sum of the singular values. In this paper we characterize the digraphs which have exactly one singular value different from zero and the digraphs for which all singular values are equal. As a consequence, we deduce sharp upper and lower bounds for the spectral norm and energy of digraphs. In addition to being a natural generalization, proving the results in the general setting of digraphs allows us to deduce new results on graph energy.

The prognostic value of peak oxygen uptake in obstructive hypertrophic cardiomyopathy: a literature review to inform economic model development.

AIMS: Patients with obstructive hypertrophic cardiomyopathy (oHCM) experience significant clinical burden which is associated with a high economic burden. Peak oxygen uptake (pVO2), measured by cardiopulmonary exercise testing, is used to quantify functional capacity, and has been studied as a primary endpoint in recent clinical trials. This study aimed to gather evidence to consolidate the prognostic value of pVO2 in oHCM and to assess whether it is feasible to predict health outcomes in an economic model based on changes in pVO2. METHODS: A targeted literature review was conducted in MEDLINE (via PubMed) and Embase databases to identify evidence on the prognostic value of pVO2 as a surrogate health outcome to support future oHCM economic model development. Following screening, study characteristics, population characteristics, and pVO2 prognostic association data were extracted. RESULTS: A total of 4,687 studies were identified. In total, 3,531 and 538 studies underwent title/abstract and full-text screening, respectively, of which 151 were included and nine of these were in hypertrophic cardiomyopathy (HCM); only three studies focused on oHCM. The nine HCM studies consisted of one systematic literature review and eight primary studies reporting on 27 potentially predictive relationships from a pVO2-based metric with clinical outcomes including all-cause mortality, cardiovascular mortality, sudden cardiac death, transplant, paroxysmal, and permanent atrial fibrillation. pVO2 was described as a predictor of single and composite endpoints, in three and six studies, respectively, with one study reporting on both. LIMITATIONS: This study primarily uses systemic literature review methods but does not qualify as one due to not entailing parallel reviewers during title-abstract and full-text stages of review. CONCLUSION: The findings of this study suggest pVO2 is predictive of multiple health outcomes, providing a rationale to use pVO2 in the development of an economic model.

Obstructive hypertrophy cardiomyopathy (oHCM) is a condition where the heart muscle thickens, obstructing blood flow and potentially impacting health. Peak oxygen uptake (pVO2) measures the highest amount of oxygen consumption during peak exercise and serves as an indicator of fitness. pVO2 can be used to assess heart health and predict severe conditions and death, acting as a surrogate endpoint. Surrogate endpoints are valuable in drug investigations since they allow earlier decisions on drug approval and funding before longer-term patient follow-up is available.This study reviewed evidence on the relationship between pVO2 values in patients with heart disease and the risk of becoming sicker or dying. Our goal was to assess if these relationships had been established and whether it is feasible to use them to predict future treatment benefits and support economic evaluations of new treatments. Our review found that most studies reported on patients with heart failure, with only nine focusing on HCM. Evidence indicates that low pVO2 values in patients with heart disease are linked to an increased risk of developing other heart conditions, needing a heart transplant, or dying.

Dynamic Shrinkage Priors for Large Time-Varying Parameter Regressions Using Scalable Markov Chain Monte Carlo Methods.

Time-varying parameter (TVP) regression models can involve a huge number of coefficients. Careful prior elicitation is required to yield sensible posterior and predictive inferences. In addition, the computational demands of Markov Chain Monte Carlo (MCMC) methods mean their use is limited to the case where the number of predictors is not too large. In light of these two concerns, this paper proposes a new dynamic shrinkage prior which reflects the empirical regularity that TVPs are typically sparse (i.e. time variation may occur only episodically and only for some of the coefficients). A scalable MCMC algorithm is developed which is capable of handling very high dimensional TVP regressions or TVP Vector Autoregressions. In an exercise using artificial data we demonstrate the accuracy and computational efficiency of our methods. In an application involving the term structure of interest rates in the eurozone, we find our dynamic shrinkage prior to effectively pick out small amounts of parameter change and our methods to forecast well.

The accurate diagnosis for COVID-19 variants using nearly initial-rough sets.

The rapid evolution of rough-set theory has prompted the need for enhanced methodologies in medical diagnostics, particularly regarding COVID-19 variant detection. This study introduces refined mathematical techniques based on topological structures (called nearly initial-rough sets) derived directly from initial-rough sets. Four categories of rough-set methodologies are presented, demonstrating heightened accuracy through comprehensive comparisons against existing methods. By leveraging these techniques, a rule-based classification system for COVID-19 variants is established, achieving 100 % accuracy measures through rigorous testing against real-world and computer-generated data. The implications of these advancements in medical diagnosis hold promise for future research, offering accessible and precise tools for variant identification and prediction. Using a medical application as a case study, we demonstrate superiority through comparative analyses, aligning mathematical results with medical data and showcasing the potential for broader applications beyond experts in topology. Furthermore, the study outlines an algorithm simplifying implementation, particularly in MATLAB, and suggests future explorations in medical, economic, and diverse theoretical frameworks to enhance applicability.

Bacterioruberin: Biosynthesis, Antioxidant Activity, and Therapeutic Applications in Cancer and Immune Pathologies.

Halophilic archaea, also termed haloarchaea, are a group of moderate and extreme halophilic microorganisms that constitute the major microbial populations in hypersaline environments. In these ecosystems, mainly aquatic, haloarchaea are constantly exposed to ionic and oxidative stress due to saturated salt concentrations and high incidences of UV radiation (mainly in summer). To survive under these harsh conditions, haloarchaea have developed molecular adaptations including hyperpigmentation. Regarding pigmentation, haloarchaeal species mainly synthesise the rare C50 carotenoid called bacterioruberin (BR) and its derivatives, monoanhydrobacterioruberin and bisanhydrobacterioruberin. Due to their colours and extraordinary antioxidant properties, BR and its derivatives have been the aim of research in several research groups all over the world during the last decade. This review aims to summarise the most relevant characteristics of BR and its derivatives as well as describe their reported antitumoral, immunomodulatory, and antioxidant biological activities. Based on their biological activities, these carotenoids can be considered promising natural biomolecules that could be used as tools to design new strategies and/or pharmaceutical formulas to fight against cancer, promote immunomodulation, or preserve skin health, among other potential uses.

Value of next generation sequencing (NGS) testing in advanced cancer patients.

OBJECTIVE: The availability of targeted therapies for oncology patients is increasing. Available genomic tests to identify treatment-eligible patients include single gene tests and gene panel tests, including the whole-exome, whole-transcriptome OncoExTra test. We assessed the costs and clinical benefits of test choice. METHODS: A Microsoft Excel-based model was developed to evaluate test choice in patients with advanced/metastatic non-small cell lung cancer (NSCLC), breast, prostate, and colorectal cancer. Treatment pathways were based on NCCN guidelines and medical expert opinion. Inputs were derived from published literature. Annual economic results and lifetime clinical results with OncoExTra testing were projected per-tested-patient and compared with single gene testing and no testing. Separately, results were estimated for a US health plan without the OncoExTra test and with its use in 5% of patients. RESULTS: Compared with no genomic testing, OncoExTra test use increased costs by $4,915 per patient; however, 82%-92% of individuals across tumour types were identified as eligible for targeted therapy or a clinical trial. Compared with single gene testing, OncoExTra test use decreased costs by $9,966 per-patient-tested while increasing use of approved or investigational targeted therapies by 20%. When considering a hypothetical health plan with 1 million members, 858 patients were eligible for genomic testing. Using the OncoExTra test in 5% of those eligible, per-member per-month costs decreased by $0.003, ranging from cost-savings of $0.026 in NSCLC patients to a $0.009 increase in prostate cancer patients. Cost-savings were driven by reduced treatment costs with increased clinical trial enrolment and reduced direct and indirect medical costs associated with targeted treatments. LIMITATIONS: Limitations include the required simplifications in modelling complex conditions that may not fully reflect evolving real-world testing and treatment patterns. CONCLUSIONS: Compared to single-gene testing, results indicate that using next generation sequencing test such as OncoExTra identified more actionable alterations, leading to improved outcomes and reduced costs.

Relations between ordinary energy and energy of a self-loop graph.

Let G be a graph on n vertices with vertex set V(G) and let S⊆V(G) with |S|=α. Denote by GS, the graph obtained from G by adding a self-loop at each of the vertices in S. In this note, we first give an upper bound and a lower bound for the energy of GS (E(GS)) in terms of ordinary energy (E(G)), order (n) and number of self-loops (α). Recently, it is proved that for a bipartite graph GS, E(GS)≥E(G). Here we show that this inequality is strict for an unbalanced bipartite graph GS with 0<α

Characterizations of generalized Robertson-Walker spacetimes concerning gradient solitons.

In this article, we examine gradient type Ricci solitons and (m,τ)-quasi Einstein solitons in generalized Robertson-Walker (GRW) spacetimes. Besides, we demonstrate that in this scenario the GRW spacetime presents the Robertson-Walker (RW) spacetime and the perfect fluid (PF) spacetime presents the phantom era. Consequently, we show that if a GRW spacetime permits a gradient τ-Einstein solitons, then it also represents a PF spacetime under certain condition.

Computing the Laplacian spectrum and Wiener index of pentagonal-derivation cylinder/Möbius network.

The Laplacian spectrum significantly contributes the study of the structural features of non-regular networks. Actually, it emphasizes the interaction among the network eigenvalues and their structural properties. Let Pn(Pn') represent the pentagonal-derivation cylinder (Möbius) network. In this article, based on the decomposition techniques of the Laplacian characteristic polynomial, we initially determine that the Laplacian spectra of Pn contain the eigenvalues of matrices LR and LS. Furthermore, using the relationship among the coefficients and roots of these two matrices, explicit calculations of the Kirchhoff index and spanning trees of Pn are determined. The relationship between the Wiener and Kirchhoff indices of Pn is also established.

Gluing constructions for Lorentzian length spaces.

We introduce an analogue to the amalgamation of metric spaces into the setting of Lorentzian pre-length spaces. This provides a very general process of constructing new spaces out of old ones. The main application in this work is an analogue of the gluing theorem of Reshetnyak for CAT(k) spaces, which roughly states that gluing is compatible with upper curvature bounds. Due to the absence of a notion of spacelike distance in Lorentzian pre-length spaces we can only formulate the theorem in terms of (strongly causal) spacetimes viewed as Lorentzian length spaces.

Several Zagreb indices of power graphs of finite non-abelian groups.

Molecular topology can be described by using topological indices. These are quantitative measures of the essential structural features of a proposed molecule calculated from its molecular structure. It is a numerical value obtained from a molecular configuration that reflects the significant physical characteristics of the suggested molecule. Numerous physical properties, chemical reactivity, and biological activity are correlated with the chemical composition using an algebraic number. The power graph P(G) of a finite group G is a graph whose vertex set is G and in which two distinct vertices are connected by an edge when one element is an integral power of the other. This article investigates a wide range of degree-based topological descriptors for power graphs of various finite groups. We find numerous Zagreb indices (given in Table 1) of power graphs of finite non-cyclic and cyclic groups, dihedral, and generalized quaternion groups.

Steady solution and its stability of a mathematical model of diabetic atherosclerosis.

Atherosclerosis is a leading cause of death worldwide. Making matters worse, nearly 463 million people have diabetes, which increases atherosclerosis-related inflammation. Diabetic patients are twice as likely to have a heart attack or stroke. In this paper, we consider a simplified mathematical model for diabetic atherosclerosis involving LDL, HDL, glucose, insulin, free radicals (ROS), ß cells, macrophages and foam cells, which satisfy a system of partial differential equations with a free boundary, the interface between the blood flow and the plaque. We establish the existence of small radially symmetric stationary solutions to the model and study their stability. Our analysis shows that the plague will persist due to hyperglycemia even when LDL and HDL are in normal range, hence confirms that diabetes increase the risk of atherosclerosis.