The Jarque–Bera test is commonly used in statistics and econometrics to test the hypothesis that sample elements adhere to a normal distribution with an unknown mean and variance. This paper proposes several modifications to this test, allowing for testing hypotheses that the considered sample comes from: a normal distribution with a known mean (variance unknown); a normal distribution with a known variance (mean unknown); a normal distribution with a known mean and variance. For given significance levels, $\alpha =0.05$ and $\alpha =0.01$, we compare the power of our normality test with the most well-known and popular tests using the Monte Carlo method: Kolmogorov–Smirnov (KS), Anderson–Darling (AD), Cramér–von Mises (CVM), Lilliefors (LF), and Shapiro–Wilk (SW) tests. Under the specific distributions, 1000 datasets were generated with the sample sizes $n=25,50,75,100,150,200,250,500,$ and 1000. The simulation study showed that the suggested tests often have the best power properties. Our study also has a methodological nature, providing detailed proofs accessible to undergraduate students in statistics and probability, unlike the works of Jarque and Bera.

Aim. To compare the long-term outcomes of the catheter ablation (CA) using remote magnetic-guided navigation (RMN) and manual radiofrequency CA (MAN) in patients with congenital heart defect (CHD) and incisional atrial tach-yarrhythmias (AT).Methods. In this retrospective study cohort, 67 patients were included with CHD and AT. CHD were classified based on complexity (simple, moderate, and complex) according to ACC/AHA guidelines 2008. Fifty-seven (85%) patients underwent at least one surgical procedure for CHD correction before CA. The patients were divided into the two groups regarding CA approach: the MAN group (n=42) and the RMN group (n=25). The primary endpoitnts was long-term freedom from any AT, including atrial fibrillation. Key secondary endpoints included perioperative and late complications. To compare freedom from any AT between the groups, 1:3 propensity score matching was applied, and 63 patients were matched. The matching was exact on CHD complexity. The weighted matched observations were assessed with univariate Cox regression with any AT as the outcome.Results. The median follow-up period was 20 months. In the matched MAN and RMN groups, 92.3% and 83.3% patients, respectively, had incisional АТ (p=0.27), the other patients having additionally AF. The mean fluoroscopy time was statistically significant lower in the RMN group compared with MAN (р=0.009) with longer procedural duration in the RMN group (p<0.001). There was no statistically significant difference in perioperative and late complications. The freedom from any AT 36 months after CA was 78.9% in the matched RMN group and 47.2% in the matched MAN group. The comparison of freedom from any AT between the groups yielded p=0.040, hazard ration 0.32 [95% confidence interval 0.11; 0.95].Conclusion. RMN CA was superior over manual CA with respect to long-term freedom from AT in patients with CHD with similar safety profile.

Introduction: Pulmonary vein ostia isolation (PVI) is the main method for catheter ablation (CA) in patients with atrial fibrillation (AF) who are refractory to antiarrhythmic drug therapy (AAD). The data regarding comparison of the remote magnetic-guided navigation (RMN) and manual (MAN) radiofrequency ablation approaches for PVI in patients with AF and enlarged left atrium (LA) are limited.Objective: The study was aimed to comparison of the safety and long-term efficacy of the radiofrequency CA associated with RMN and MAN using in patients with AF and enlarged LA.Methods: The retrospective cohort included 534 patients (mean age 59.2 ± 8.7 years, 41.6% female) with different AF forms and LA >4.5 cm who underwent PVI between 2016 and 2019. The patients were divided into two groups: the RMN group (n = 267) and MAN group (n = 267). The primary safety objective was associated with preventing perisurgical complications, and the primary efficacy objective was disengagement from AF / atrial flutter (AFl) / AT (atrial tachycardia), lasting > 30 seconds, in the 3-month period after the index procedure without AAD. The comparison of the results with 1:1 propensity score matching (PSM) was applied on the basis of 11 covariates. After PSM, 235 patients were selected for each group. The entire cohort was additionally divided into the subgroups of paroxysmal AF (n = 355) and non-paroxysmal AF (n = 179) to increase efficacy assessment. After PSM, 310 and 136 patients with paroxysmal and non-paroxysmal AF were analyzed, respectively.Results: In the entire cohort after PSM (n = 470) patients were balanced completely according to AF forms. The mean values of LA diameter were 4.98 ± 0.61 cm and 4.94 ± 0.58 cm in the RMN and MAN groups, respectively. The long-term efficacy assessment was performed in 448 patients of the both groups excluding 22 (4.7%) patients due to failed contacts. The median follow-up period was 24 months (minimum 3 and maximum 72 months). In the matched cohorts, perisurgical complications were detected in 11 (4.7%) patients of the MAN group and 2 (0.9%) patients of the RMN group (Р = 0.021, OR = 5.7; 95% CI [1.22, 53.5]). The disengagement from AF/AFl/AT after 36 months of the follow up amounted to 62.6% in the RMN group and 47.9% in the MAN group (for entire follow up, P = 0.005, HR = 1.54; 95% CI [1.14, 2.08]). For paroxysmal AF subgroup (n = 310), the disengagement from AF/AFl/AT after 36 months of the follow was 67.1% in the RMN group and 60.6% in the MAN group (for entire follow up, P = 0.15, HR = 1.34; 95% CI [0.90, 1.98]). In the non-paroxysmal AF subgroup (n = 136), the disengagement from AF/AFl/AT after 36 months of the follow up was higher in the RMN group as compared to the MAN group (59.6% and 30.4%, respectively, for entire follow up, P = 0.005, HR = 2.01; 95% CI [1.23, 3.29]) predominantly due to persistent AF.Conclusion: The present propensity-score matching study evidentiated that RMN CA was superior over manual CA for the interventional treatment of patients with AF and enlarged LA with respect to perisurgical complications and long-term disengagement from AF/AFl/AT predominantly due to non-paroxysmal AF. Prospective randomized studies are recommended for the comparison of the outcomes related to RMN and manual CA in patients with AF and enraged LA. Received 24 April 2024. Accepted 8 May 2024. Funding: Work by P.S. Ruzankin and S.E. Khrushchev was carried out within the framework of the state assignment of the Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences, project FWNF-2024-0001. Conflict of interest: The authors declare no conflict of interest. Contribution of the authorsConception and study design: A.B. Romanov, V.V. Beloborodov, V.V. Shabanov, A.G. FilippenkoData collection and analysis: V.V. Beloborodov, A.B. Romanov, D.A. Elesin, V.A. Boboshko, V.V. Shabanov, A.G. Filippenko Statistical analysis: P.S. Ruzankin, S.Ye. Khrushchev, A.B. RomanovDrafting the article: A.B. Romanov, V.V. Beloborodov, P.S. Ruzankin, S.Ye. KhrushchevCritical revision of the article: A.B. Romanov, V.V. Beloborodov, P.S. Ruzankin, S.Ye. KhrushchevFinal approval of the version to be published: A.B. Romanov, V.V. Beloborodov, V.V. Shabanov, A.G. Filippenko, D.A. Elesin, V.A. Boboshko, S.Ye. Khrushchev, P.S. Ruzankin

Introduction. Magnetic resonance imaging allows for the assessment of overall and regional myocardial contractility of the left ventricle, and the use of contrast enhancement evaluates the depth of wall damage, which together serve as important prognostic criteria for the improvement of myocardial contractile function in the postoperative period. Objective. To determine the diagnostic capabilities of magnetic resonance imaging in post-infarction cardiac aneurysms. Methods. For inclusion in the prospective observational study, 160 patients with post-infarction heart aneurysms were assessed. Preoperative modeling of the left ventricle cavity was performed on all patients. Results. Magnetic resonance imaging reliably detects a greater number of segments with impaired kinetic function compared to echocardiography. In the assessment of local contractility using delayed contrast enhancement, a higher number of segments with impaired kinetics were identified. On average, each patient had 4.40 ± 0.95 segments with abnormal kinetics. The average difference in the number of segments amounted to 68 segments [60; 87]. A negative correlation was observed between the depth of myocardial damage and the type of local contractility impairment: as the transmurality index increased, the number of segments with hypokinesis decreased (r = –0.74; p = 0.032), while the number of segments with akinesis increased (r = 0.82; p = 0.026). In terms of diagnostic performance, MRI demonstrated superior sensitivity and specificity for diagnosing postinfarction left ventricular aneurysm, with values of 97.6 % and 100 %, respectively, compared to echocardiography, which had sensitivity and specificity values of 68.5 % and 8.3 %, respectively. Conclusion. Magnetic resonance imaging reliably detects a greater number of segments with impaired kinetic function compared to echocardiography. It allows for the reliable detection of a greater number of segments with kinetic impairment compared to echocardiography. The use of MRI with delayed contrast enhancement increases the informativeness of the method. This technique is safe and does not increase hospital mortality.

The authors studied heterogeneous samples (for a number of statistical populations) taken from finite mixtures of probability distribu- tions, which reflect a number of socio-economic characteristics of the Russian society, using the information resources of the Federal State Statistics Service; in this case the number of mixing distributions (components), as well as their corresponding weights and parameters, may be unknown. In terms of content, the problem of separation (decomposition) of mixtures can be reduced to estimating unknown parameters of mixing distributions and their weights.The article considers and discusses methods for solving this problem, their advantages and disadvantages, conditions and areas of application. In the study the decomposition of mixtures of probability distributions on the population of subjects of the RussianFederation was carried out according to three interrelated statistical indicators – the unemployment rate, the poverty rate, the level of violence. These indicators can be considered as statistical measure of achieving sustainable development goals at the regional level and, at the same time, measures of socio-economic «health» of territory. Typologies of subjects of the Russian Federation were carried out according to the listed indicators. A cross-comparison of the results of the obtained typological groupings was performed, which also made it possible to identify the subjects of the Russian Federation that differ in both negative and positive trends in the context of the indicators under consideration.The authors underline that the results of the study can be used by the authorities to develop specific measures for the socio-economic development of Russia and its regions.

Background: Presently, the availability of single-stage surgical correction of mitral valve disease combined with atrial fibrillation (AF) via a mini-access approach remains limited. Moreover, the comparative effectiveness of this procedure versus conventional sternotomy (CS) remains poorly understood. Thus, this study aimed to conduct a comparative assessment of the efficacy and safety of concomitant mitral valve surgery and AF ablation via a minimally invasive approach (minimally invasive cardiac surgery, MICS group) versus the standard sternotomy approach (CS group). Methods: An extensive literature search was performed to identify relevant studies. Additionally, for comparative analysis, we included isolated studies where the combined intervention was conducted exclusively via either minimally invasive or CS as the primary access. Results: Freedom from atrial arrhythmia (AA) for MICS and CS was 94.52% [95% CI 91.52, 96.50] vs. 80.76% [95% CI 67.19, 89.59] and 86.22% [95% CI 80.13, 90.66] vs. 86.33% [95% CI 79.39, 91.19] at 1 and 2 years, respectively, with no statistically significant differences. Meanwhile, cardiopulmonary bypass (CPB) and aortic cross-clamp (ACC) times were significantly longer in the MICS group compared to CS (CPB: 151.50 vs. 120.01 min; ACC: 112.36 vs. 101.43 min; p < 0.001). There were no differences in mortality between groups (p = 0.709). The rate of pacemaker implantation was significantly higher in the CS group (MICS: 3.32% [95% CI 1.58, 6.87] vs. CS: 5.20% [95% CI 2.80, 9.46]; p < 0.001). Conclusion: This meta-analysis found that the minimally invasive approach was associated with longer CPB and ACC times but a lower rate of pacemaker implantation, with no significant differences observed in mortality and freedom from AA at 1 and 2 years. The PROSPERO registration: CRD42024570022, https://www.crd.york.ac.uk/PROSPERO/view/CRD42024570022.