Search Results (9)

This paper develops a unified asymptotic theory for conditional single-index U-statistics and the associated conditional U-processes in the setting of locally stationary functional time series subject to missing-at-random response mechanisms. The proposed framework addresses, within a single nonparametric inferential architecture, three major sources of complexity in modern functional data analysis: infinite-dimensional covariates, smoothly time-varying stochastic dynamics, and incomplete response observations. The methodology is based on a class of kernel-type estimators combining temporal localization, functional single-index smoothing, and inverse-propensity correction. Temporal localization captures the gradual evolution of the underlying regression structure, the single-index projection provides an effective dimension-reduction mechanism for functional covariates, and the propensity adjustment restores the target conditional functional under the MAR sampling scheme. The principal contribution of the paper is the establishment of weak convergence, in a suitable space of bounded functions, for the resulting propensity-adjusted conditional U-process indexed by a general class of measurable kernels. Under absolute regularity conditions, local stationarity assumptions, small-ball probability requirements, entropy restrictions of VC type, and uniform consistency of the propensity-score estimator, the normalized process is shown to converge weakly to a tight centered Gaussian process. The limiting covariance structure explicitly reflects the interaction between temporal smoothing, functional concentration, dependence, and the random loss of responses. In parallel, uniform convergence rates are derived for the associated conditional single-index U-statistic estimators, thereby quantifying the respective contributions of smoothing bias, stochastic fluctuation, local-stationarity approximation error, and missingness-induced variance inflation. A substantial part of the analysis is devoted to the technical difficulties created by the simultaneous presence of dependence, nonstationarity, functional covariates, and incomplete observations. The proofs combine Hoeffding-type decompositions adapted to weighted incomplete data, blocking and coupling arguments for absolutely regular triangular arrays, refined entropy bounds for kernel-indexed function classes, and small-ball probability techniques for functional covariates. The MAR mechanism is incorporated via inverse-propensity weighting, and its effects on the effective sample size, asymptotic variance, and bias structure are made explicit. The theory also provides a rigorous foundation for bandwidth selection through blocked, propensity-adjusted cross-validation and clarifies its relation to the corresponding oracle risk. The proposed framework encompasses a broad class of statistical learning and inference problems involving pairwise or higher-order functionals of functional time series. In particular, it applies to conditional Kendall-type functionals, discrimination problems, metric learning with incomplete labels, and conditional independence testing under local stationarity. A simulation study illustrates the finite-sample behavior of the proposed estimators and supports the theoretical findings across varying regimes of temporal nonstationarity, serial dependence, functional concentration, and response missingness. Overall, the results provide a mathematically rigorous and methodologically flexible foundation for inference from evolving functional data when dependence, infinite dimensionality, and incomplete observation are present simultaneously. Full article

Background: Erectile dysfunction (ED) is a disease whose occurrence is steadily increasing worldwide. This pathology is multifactorial and often combined with other diseases. ED of organic genesis in 50–80% of men is vasculogenic. Methods: A survey was conducted of 88 men (aged 44 to 62) who complained of erectile dysfunction. It consisted of a questionnaire administered according to the protocols “International Index of Erectile Function” and “Aging Male Screening”, and was followed by a color Doppler ultrasound (Logiq 9 ExpertGE with a 7 MHz linear transducer using B mode) and penile scintigraphy (single-photon emission computed tomography). The procedures were initially performed at rest, then during pharmacologically induced erection, which was achieved through the intake of phosphodiesterase-5 (PDE5) inhibitors. Patients who did not respond to pharmacological stimulation and had IIEF scores below 5–7 were offered surgical treatment—penile prosthesis followed by histological examination of the tissue of the corpus cavernosum. Statistical analysis was carried out using Microsoft Excel and STATISTICA 10.0 software. The Mann–Whitney U test was used to assess differences between quantitative variables, with the significance level set at p ≤ 0.05. Results: Penile scintigraphy shows high sensitivity (85.2%) and specificity (83.3%), outperforming color Doppler ultrasonography in detecting vasculogenic ED. Conclusion: Penile scintigraphy is demonstrated to be a highly informative method, allowing us to analyze the condition of the magistral and organ blood flow, as well as the microcirculatory bed of the cavernous bodies of the penis. This improves the effectiveness of this method in diagnosing various types of vasculogenic erectile dysfunction (ED), which opens opportunities for its use together with ultrasound examination when the latter is less informative. Full article

Background: Transradial access may affect health-related quality of life (QoL) in cerebral diagnostic angiography. However, its assessment is methodologically challenging, as repeated measurements can be influenced by response shift. To mitigate this bias, a retrospective cross-sectional study was designed using a then-test approach, allowing patients to reflect on their post procedural status at a single time point. Methods: Quality of life was assessed using the 12-Item Short Form Health Survey (SF-12). A then-test approach was also employed, whereby patients were asked to retrospectively indicate whether they perceived their condition as worse following the procedure. The survey yielded Physical (PCS) and Mental Component Summary (MCS) scores, standardized to a mean of 50 (range of 0–100), with lower values indicating greater health-related limitations. Group differences were analyzed using the Mann–Whitney U test. Associations between PCS and MCS, respectively, and clinical variables were assessed using multiple linear regression models. Results: Forty patients underwent diagnostic cerebral angiography over a 15-month observation period. Applying a then-test design, Group A included the 12.5% (n = 5) of patients who reported feeling worse post-procedure while Group B comprised the remaining 87.5% (n = 35). QoL scores were significantly lower in Group A (Mdn = 28.6) compared to B (Mdn = 46.7) for both PCS scores (p = 0.007) and MCS scores (45.3 vs. 54.6, p = 0.018). In the multiple linear regression analysis, no statistically significant associations were found between the PCS or MCS scores and any clinical variable, including age, sex, body mass index (BMI), procedure duration, dose area product, access site, prior neurosurgical history, and fluoroscopy time (p > 0.05). Conclusions: Transradial access for diagnostic cerebral angiography may affect QoL, as assessed using the SF-12 questionnaire. Applying the then-test approach, the group of patients who reported feeling worse after the procedure (12.5%) showed significantly lower physical and mental health scores. These findings underscore the need for prospective studies to further investigate patient-reported outcomes. Full article

Background and Objectives: Psoriatic arthritis (PsA) is a chronic rheumatic disease that is frequently associated with fibromyalgia (FM). The coexistence of FM complicates the evaluation of PsA disease activity and the planning of treatment strategies, as the two conditions share many overlapping clinical symptoms. To investigate the contribution of demographic factors and available serum biomarkers of inflammation and autoimmunity in characterizing the heterogeneity among patients meeting the classification criteria for both PsA and FM. Materials and Methods: This cross-sectional, single-center study involved 1547 adult patients evaluated between January 2017 and December 2024 who met the CASPAR criteria for PsA. A patient subgroup also met the 2016 ACR criteria for FM. Demographic data, serum inflammatory markers such as C-reactive protein (CRP) and erythrocyte sedimentation rate (ESR), and autoimmunity markers including antinuclear antibodies (ANA), rheumatoid factor (RF), and anti-citrullinated protein antibodies (ACPA) were evaluated. Statistical analyses included chi-square tests, t-tests, Mann–Whitney U tests, and multivariate logistic regression to identify independent predictors associated with the coexistence of PsA and FM. Results: A total of 254 patients (16.42%) were diagnosed with concomitant FM. Compared to patients with PsA alone, those with concurrent PsA and FM showed significantly lower C-reactive protein (CRP) levels (0.39 ± 0.74 vs. 2.88 ± 12.31 mg/dL; p < 0.001) and a higher frequency of antinuclear antibody (ANA) positivity (13.57% vs. 5.78%; p < 0.001). No significant differences were observed in rheumatoid factor (RF) or anti-citrullinated protein antibody (ACPA) positivity between the groups. Multivariate logistic regression identified female sex, ANA positivity, CRP levels ≤ 0.5 mg/dL, and elevated body mass index (BMI) as independent predictors of the presence of concomitant FM. Conclusions: Patients with concomitant PsA and FM have a distinct demographic and serological profile, suggesting the existence of a clinically significant subgroup within the PsA population. Recognition of these differences may improve diagnostic accuracy and support the development of personalized, non-immunosuppressive therapeutic strategies for this subgroup of patients. Full article

U-statistics are fundamental in modeling statistical measures that involve responses from multiple subjects. They generalize the concept of the empirical mean of a random variable X to include summations over each m-tuple of distinct observations of X. W. Stute introduced conditional U-statistics, extending the Nadaraya–Watson estimates for regression functions. Stute demonstrated their strong pointwise consistency with the conditional expectation $r^{\left(m\right)}(\phi ,\mathbf{t})$, defined as $\mathbb{E}\left[\phi (Y_1,\dots ,Y_m)\right|(X_1,\dots ,X_m)=\mathbf{t}]$ for $\mathbf{t}\in {\mathcal{X}}^m$. This paper focuses on estimating functional single index (FSI) conditional U-processes for regular time series data. We propose a novel, automatic, and location-adaptive procedure for estimating these processes based on k-Nearest Neighbor (kNN) principles. Our asymptotic analysis includes data-driven neighbor selection, making the method highly practical. The local nature of the kNN approach improves predictive power compared to traditional kernel estimates. Additionally, we establish new uniform results in bandwidth selection for kernel estimates in FSI conditional U-processes, including almost complete convergence rates and weak convergence under general conditions. These results apply to both bounded and unbounded function classes, satisfying certain moment conditions, and are proven under standard Vapnik–Chervonenkis structural conditions and mild model assumptions. Furthermore, we demonstrate uniform consistency for the nonparametric inverse probability of censoring weighted (I.P.C.W.) estimators of the regression function under random censorship. This result is independently valuable and has potential applications in areas such as set-indexed conditional U-statistics, the Kendall rank correlation coefficient, and discrimination problems. Full article

In his work published in (Ann. Probab. 19, No. 2 (1991), 812–825), W. Stute introduced the notion of conditional U-statistics, expanding upon the Nadaraya–Watson estimates used for regression functions. Stute illustrated the pointwise consistency and asymptotic normality of these statistics. Our research extends these concepts to a broader scope, establishing, for the first time, an asymptotic framework for single-index conditional U-statistics applicable to locally stationary random fields $\{{\mathbf{X}}_{s,A_n}:sin{R}_n\}$ observed at irregularly spaced locations in $R_n$, a subset of ${\mathbb{R}}^d$. We introduce an estimator for the single-index conditional U-statistics operator that accommodates the nonstationary nature of the data-generating process. Our method employs a stochastic sampling approach that allows for the flexible creation of irregularly spaced sampling sites, covering both pure and mixed increasing domain frameworks. We establish the uniform convergence rate and weak convergence of the single conditional U-processes. Specifically, we examine weak convergence under bounded or unbounded function classes that satisfy specific moment conditions. These findings are established under general structural conditions on the function classes and underlying models. The theoretical advancements outlined in this paper form essential foundations for potential breakthroughs in functional data analysis, laying the groundwork for future research in this field. Moreover, in the same context, we show the uniform consistency for the nonparametric inverse probability of censoring weighted (I.P.C.W.) estimators of the regression function under random censorship, which is of its own interest. Potential applications of our findings encompass, among many others, the set-indexed conditional U-statistics, the Kendall rank correlation coefficient, and the discrimination problems. Full article

Arm swing during gait has been positively related to gait stability and gait efficiency, particularly in the presence of neurological disorders that affect locomotion. However, most gait studies have focused on lower extremities, while arm swing usually remains ignored. In addition, these studies are mostly based on costly, highly-specialized vision systems or on wearable devices which, despite their popularity among researchers and specialists, are still relatively uncommon for the general population. This work proposes a way of estimating arm swing asymmetry from a single 2D gait video. First, two silhouette-based representations that separately capture motion data from both arms were built. Second, a measure to quantify arm swing energy from such a representation was introduced, producing two side-dependent motion measurements. Third, an arm swing asymmetry index was obtained. The method was validated on two public datasets, one with 68 healthy subjects walking normally and one with 10 healthy subjects simulating different styles of arm swing asymmetry. The validity of the asymmetry index at capturing different arm swing patterns was assessed by two non-parametric tests: the Mann–Whitney U test and the Wilcoxon signed-rank test. The so-called physiological asymmetry was observed on the normal gait sequences of both datasets in a statistically similar way. The asymmetry index was able to fairly characterize the different levels of asymmetry simulated in the second set. Results show that it is possible to estimate the arm swing asymmetry from a single 2D gait video, with enough sensitivity to discriminate anomalous patterns from normality. This opens the door to low-cost easy-to-use mobile applications to assist clinicians in monitoring gait condition in primary care (e.g., in the elderly), when more accurate and specialized technologies are often not available. Full article

Gout is an inflammatory condition caused by elevated serum urate (SU), a condition known as hyperuricemia (HU). Genetic variations, including single nucleotide polymorphisms (SNPs), can alter the function of urate transporters, leading to differential HU and gout prevalence across different populations. In the United States (U.S.), gout prevalence differentially affects certain racial groups. The objective of this proposed analysis is to compare the frequency of urate-related genetic risk alleles between Europeans (EUR) and the following major racial groups: Africans in Southwest U.S. (ASW), Han-Chinese (CHS), Japanese (JPT), and Mexican (MXL) from the 1000 Genomes Project. The Ensembl genome browser of the 1000 Genomes Project was used to conduct cross-population allele frequency comparisons of 11 SNPs across 11 genes, physiologically involved and significantly associated with SU levels and gout risk. Gene/SNP pairs included: ABCG2 (rs2231142), SLC2A9 (rs734553), SLC17A1 (rs1183201), SLC16A9 (rs1171614), GCKR (rs1260326), SLC22A11 (rs2078267), SLC22A12 (rs505802), INHBC (rs3741414), RREB1 (rs675209), PDZK1 (rs12129861), and NRXN2 (rs478607). Allele frequencies were compared to EUR using Chi-Square or Fisher’s Exact test, when appropriate. Bonferroni correction for multiple comparisons was used, with p < 0.0045 for statistical significance. Risk alleles were defined as the allele that is associated with baseline or higher HU and gout risks. The cumulative HU or gout risk allele index of the 11 SNPs was estimated for each population. The prevalence of HU and gout in U.S. and non-US populations was evaluated using published epidemiological data and literature review. Compared with EUR, the SNP frequencies of 7/11 in ASW, 9/11 in MXL, 9/11 JPT, and 11/11 CHS were significantly different. HU or gout risk allele indices were 5, 6, 9, and 11 in ASW, MXL, CHS, and JPT, respectively. Out of the 11 SNPs, the percentage of risk alleles in CHS and JPT was 100%. Compared to non-US populations, the prevalence of HU and gout appear to be higher in western world countries. Compared with EUR, CHS and JPT populations had the highest HU or gout risk allele frequencies, followed by MXL and ASW. These results suggest that individuals of Asian descent are at higher HU and gout risk, which may partly explain the nearly three-fold higher gout prevalence among Asians versus Caucasians in ambulatory care settings. Furthermore, gout remains a disease of developed countries with a marked global rising. Full article

Background and objectives: In hospitalized children, acute kidney injury (AKI) remains to be a frequent and serious condition, associated with increased patient mortality and morbidity. Identifying early biomarkers of AKI and patient groups at the risk of developing AKI is of crucial importance in current clinical practice. Specific human protein urinary neutrophil gelatinase-associated lipocalin (uNGAL) and interleukin 18 (uIL-18) levels have been reported to peak specifically at the early stages of AKI before a rise in serum creatinine (sCr). Therefore, the aim of our study was to determine changes in uNGAL and uIL-18 levels among critically ill children and to identify the patient groups at the highest risk of developing AKI. Materials and methods: This single-center prospective observational study included 107 critically ill children aged from 1 month to 18 years, who were treated in the Pediatric Intensive Care Unit (PICU) of Lithuanian University of Health Sciences Hospital Kauno Klinikos from 1 December 2013, to 30 November 2016. The patients were divided into two groups: those who did not develop AKI (Group 1) and those who developed AKI (Group 2). Results: A total of 68 (63.6%) boys and 39 (36.4%) girls were enrolled in the study. The mean age of the patients was 101.30 ± 75.90 months. The mean length of stay in PICU and hospital was 7.91 ± 11.07 and 31.29 ± 39.09 days, respectively. A total of 32 (29.9%) children developed AKI. Of them, 29 (90.6%) cases of AKI were documented within the first three days from admission to hospital. In all cases, AKI was caused by diseases of non-renal origin. There was a significant association between the uNGAL level and AKI between Groups 1 and 2 both on day 1 (p = 0.04) and day 3 (p = 0.018). Differences in uNGAL normalized to creatinine in the urine (uCr) (uNGAL/uCr) between the groups on days 1 and 3 were also statistically significant (p = 0.007 and p = 0.015, respectively). uNGAL was found to be a good prognostic marker. No significant associations between uIL-18 or Uil-18/uCr and development of AKI were found. However, the uIL-18 level of >69.24 pg/mL during the first 24 h was associated with an eightfold greater risk of AKI progression (OR = 8.33, 95% CI = 1.39–49.87, p = 0.023). The AUC for uIL-18 was 73.4% with a sensitivity of 62.59% and a specificity of 83.3%. Age of <20 months, Pediatric Index of Mortality 2 (PIM2) score of >2.5% on admission to the PICU, multiple organ dysfunction syndrome with dysfunction of three and more organ systems, PICU length of stay more than three days, and length of mechanical ventilation of >five days were associated with a greater risk of developing AKI. Conclusions: Significant risk factors for AKI were age of <20 months, PIM2 score of >2.5% on admission to the PICU, multiple organ dysfunction syndrome with dysfunction of 3 and more organ systems, PICU length of stay of more than three days, and length of mechanical ventilation of > five days. uNGAL was identified as a good prognostic marker of AKI. On admission to PICU, uNGAL should be measured within the first three days in patients at the risk of developing AKI. The uIL-18 level on the first day was found to be as a biomarker predicting the progression of AKI. Full article