In recent years, semi-parametric modeling has proven successful in describing phenomena that necessitate the modeling of non-linear structures using both parametric and nonparametric components. Partially linear varying coefficient models have emerged as a valuable alternative for modeling the effect of nonlinear interactions between a response variable and a set of covariates across diverse phenomena. In this work, we propose a novel statistical model based on the reparameterized Birnbaum-Saunders distribution, where the systematic component allows the regression coefficients to vary smoothly with respect to certain covariates. To obtain the maximum penalized likelihood estimates of the model parameters, we propose Fisher scoring and weighted backfitting algorithms based on linear spline smoothing. We conduct residual and local influence analyses to assess the potential impact of individual observations on the model fit. Finally, we present a simulation study based on Monte Carlo experiments for evaluate de maximum penalized likelihood estimators, and provide an application of the proposed model to a real-world air pollution dataset, demonstrating its effectiveness in modeling real-world phenomena. The model has been fully implemented in the R programming language.

Extreme heat is a well-established environmental hazard linked to elevated cardiovascular disease (CVD) morbidity and mortality, yet few studies evaluate temperature effects across multiple temporal scales or identify community-specific vulnerability. We analyzed neighborhood-level CVD deaths and emergency department visits linked to sociodemographic characteristics and high-resolution temperature and humidity estimates. Generalized additive models with smooth splines for temperature, humidity, age, and time estimated excess heat-related rates across temporal scales. Principal component analysis and k-means clustering classified Chicago community areas by multidimensional heat vulnerability. Higher temperatures were significantly associated with increased CVD and coronary heart disease mortality across warm-season, monthly, and daily scales but were not associated with cardiovascular emergency department visits. Peak warm-season thresholds for all CVD mortality occurred at 25.6 °C, corresponding to 20.7 excess deaths per 100 000 (SD 20.3; P<0.001). Daily peaks occurred at 39.5 °C with 0.048 excess deaths per 100 000 per day (SD 0.068; P<0.001), and a 0 to 3-day lag peak at 38 °C produced 0.049 excess deaths per 100 000 (SD 0.133; P<0.001). Coronary heart disease mortality showed similar patterns, with warm-season peaks at 27.8 °C (9.19 per 100 000; P=0.004). No statistically significant associations were observed for myocardial infarction or stroke mortality. Principal component analysis and clustering identified 3 vulnerability profiles driven by socioeconomic disadvantage, racial and ethnic composition, heat exposure, and humidity. Temperature thresholds for cardiovascular mortality vary across temporal scales and CVD subtypes, with strongest associations for all CVD and coronary heart disease mortality. Integrating temperature-mortality relationships with community vulnerability profiles may support targeted heat warning systems and neighborhood-specific adaptation strategies.

BackgroundLower respiratory infections (LRIs) are a major global contributor to morbidity and mortality, with influenza viruses being a significant cause. Despite advances in vaccination and antiviral therapies, the burden of influenza-associated LRIs remains high, particularly in low-income regions and high-risk populations. Understanding long-term trends and regional disparities is crucial for developing effective prevention strategies.MethodsUsing data from the Global Burden of Disease (GBD) 2021 study, we analyzed age-standardized mortality rates (ASMR), and disability-adjusted life years (DALYs) for influenza-associated LRIs across 21 global regions and 204 countries and territories from 1990 to 2021. Joinpoint regression was utilized to analyze temporal trends in the disease burden of influenza-associated LRIs. The relationship between influenza-associated LRIs burden and the socio-demographic index (SDI) was examined using a smoothing spline model. Frontier analysis was employed to estimate achievable outcomes based on development levels.ResultsGlobally, ASMR declined from 5.87 (95% UI: 5.33–6.40) per 100,000 population in 1990 to 1.30 (0.98–1.66) per 100,000 population in 2021, with an average annual percent change (AAPC) of -0.69% (1990–2019) and − 49.74% (2019–2021). Despite declining rates, absolute deaths increased by 0.85% annually from 1990 to 2019, reflecting population growth and aging. In 2021, Central Sub-Saharan Africa had the highest ASMR (10.84/100,000 population) and ASDR (271.71/100,000 population), while high SDI regions (e.g., High-income Asia Pacific) approached near-zero mortality. Age-specific analysis revealed bimodal burdens: children under 5 and adults ≥ 70 years faced the highest risks.ConclusionsInfluenza-associated LRIs remain a significant global health challenge, particularly in low-income and high-risk populations. While global trends indicate progress, regional disparities and the impact of demographic factors highlight the need for tailored interventions. Targeted strategies—including equitable vaccine access, healthcare system strengthening, and integrated surveillance—are critical to mitigating burden in high-risk regions and populations.Supplementary InformationThe online version contains supplementary material available at 10.1186/s12879-025-12282-7.

ObjectivesDiabetes mellitus (DM) is a common comorbidity in intensive care unit (ICU) patients. The Braden skin score (BSS) has increasingly been recognized as an indicator of patient frailty. However, the association between the BSS and clinical outcomes in critically ill diabetic patients remains unclear. This study aimed to investigate the relationship between the BSS and clinical outcomes in diabetic patients in ICU settings.MethodsA retrospective cohort of diabetic patients with measured BSS was identified from the Medical Information Mart for Intensive Care IV (MIMIC-IV) database. The primary outcomes included mortality at 30, 60, and 90 days. The association between BSS and survival outcomes was evaluated using time-dependent Cox proportional hazards model. Further validation was conducted through Kaplan-Meier survival analysis, restricted cubic spline fitting, and subgroup analyses.ResultsA total of 20,590 patients were included in this study, those with higher BSS had a 14% decreased risk of 30-day mortality (HR: 0.86, 95% CI: 0.84-0.87, p < .01). Based on cutoff values of 13, patients were categorized into two risk groups. After adjusting for covariates, time-dependent Cox proportional hazards model indicated that the high-risk group exhibited a significantly increased 30-day all-cause mortality compared with the low-risk groups (HR: 1.76, 95% CI: 1.62-1.91, p < .01). Kaplan-Meier curves consistently demonstrated poorer survival across all time points in the high-risk group. Subgroup analysis further indicated that the association between BSS and mortality was particularly pronounced in patients with cerebrovascular disease.ConclusionsA low BSS was independently linked to higher mortality among critically ill patients with diabetes, especially in those with concomitant cerebrovascular diseases. These results support the potential utility of BSS as a prognostic indicator in this population. Further validation through larger prospective studies remains necessary.

Many industrial and engineering processes monitored as time series have smooth trends that indicate normal behavior and occasionally anomalous patterns that can indicate a problem. This kind of behavior can be modeled by a smooth trend, such as a spline or Gaussian process, a disruption based on a sparser representation, and a white noise component. Our approach is to expand the process signal into two sets of basis functions: one set that uses L 2 penalties on the coefficients, and another set that uses L 1 penalties to control sparsity. From a frequentist perspective, this results in a hybrid smoother that combines cubic smoothing splines and a LASSO model. As a Bayesian hierarchical model (BHM), this is equivalent to priors resulting in a Gaussian process for the smooth component and a Laplace distribution for the anomaly coefficients. As a hybrid smoother, we propose two new ways of determining the penalty parameters which use effective degrees of freedom, and we contrast this with the BHM that uses loosely informative, inverse gamma priors. Several reformulations are used to make sampling the BHM posterior more efficient, including some novel features to orthogonalize and regularize the model basis functions. This methodology is motivated by a substantive application, offline monitoring of a water treatment process for municipal water filtration. We also test the robustness of these methods with a Monte Carlo study designed to inspect a range of trended time series under an array of conditions, and we compare this new approach to multiple existing modern methods. Both the hybrid smoother and the full BHM give comparable results with low Type I and II error rates. Besides being successful in the water treatment application, this work can be easily extended to other Gaussian process models and other process disruptions and can even be used for slightly delayed monitoring.

Bayesian multivariate smoothing spline approach for yield curve joint estimation across bond types

BackgroundPediatric cardiovascular diseases (CVDs), including congenital heart anomalies (CHAs), rheumatic heart disease (RHD), and related conditions, remain a significant health challenge in Indonesia, especially given the country’s diverse geography and disparities in healthcare access. We aim to analyze national and provincial trends in the burden of pediatric CVDs in Indonesia from 1990 to 2023 using Global Burden of Disease (GBD) data.MethodsWe conducted a retrospective observational analysis using the GBD 2023 dataset, focusing on the prevalence, mortality, and disability-adjusted life years (DALYs) of pediatric cardiovascular diseases across age groups. Trends were assessed by sex and province. The Estimated Annual Percentage Change (EAPC) was calculated for each CVD subcategory and age group by fitting a log-linear regression model to the natural logarithm of annual rates. To evaluate nonlinear temporal patterns, generalized additive models (GAMs) were applied with penalized smoothing splines for year. Poisson or negative binomial regression models were used to model mortality counts, with the latter selected when overdispersion exceeded 1.5.ResultsFrom 1990 to 2023, Indonesia showed an overall decline in DALY rates for CHAs, decreasing from 120,809.85 to 68,324.17 per 100,000, and for non-congenital CVDs, from 42,118.56 to 29,842.73 per 100,000. The most notable improvements occurred among infants and toddlers, whereas adolescents showed stagnant or rising burdens, particularly for ischemic heart disease (IHD), hypertensive heart disease (HHD), and aortic aneurysm. CHAs remained the leading contributor, with neonatal prevalence and mortality in 2023 reaching 1511.53 and 1341.68 per 100,000, respectively. Despite the overall national decline, positive EAPC values (p < 0.001) were observed for these adult-type cardiovascular conditions within the transitioning adolescent population. Regionally, the eastern provinces showed consistently higher mortality—CHA from 23.20 to 15.58 per 100,000 and non-congenital CVDs from 6.07 to 5.23 per 100,000.ConclusionCHAs remain the leading cause of pediatric CVD in Indonesia, especially among neonates, while adolescents face rising adult-type cardiovascular conditions. National improvements are uneven, with eastern provinces experiencing higher burdens due to limited access to care. These inequalities highlight the need for targeted prevention, early detection, and strengthened long-term management to ensure equitable and sustainable child cardiovascular health.

ABSTRACT Robustly modeling salinity in tidal estuaries under changing conditions remains a scientific challenge. This study focuses on the Scheldt Estuary, which faces the dual threats of saltwater intrusion and climate change, and compares the performance of three machine learning models in simulating daily salinity, including artificial neural network (ANN), random forest (RF), and support vector regression (SVR). The ANN is selected and combined with a detailed full hydrodynamic model implemented in MIKE11 via three ensemble methods, including generalized linear model (GLM), cubist regression (CUBIST), and boosted smoothing spline model (BSTSM). Results underline the effectiveness of machine learning models, showcasing the superiority of ANN, particularly in the middle and lower regions. Ensemble methods prove vital in addressing local simulation biases seen in the base models, particularly in predicting high values, with the ensemble of ANN and MIKE11 via GLM performing better downstream. This approach significantly improved predictions, reducing the root mean squared error (RMSE) by up to 20% compared to the standalone models at the downstream. In addition, the impact analysis of the external boundary conditions emphasizes the challenges with the extrapolative robustness of machine learning. The ensemble model demonstrates the potential to reduce simulation uncertainties by amalgamating predictions from base models.

BackgroundAtrial fibrillation (AF) is a prevalent arrhythmia linked to high mortality rates. The stress hyperglycemia ratio (SHR) serves as a novel marker for acute metabolic stress; however, its significance in critically ill patients with AF is not yet fully understood. This study seeks to investigate the correlation between SHR and 28-day all-cause mortality among critically ill patients diagnosed with AF.MethodsThis study utilized the Intensive Care Medicine Information Market (MIMIC-IV v2.2) database to identify and enroll 2,050 adult patients admitted to intensive care units (ICU) with AF. The SHR was calculated using the formula: SHR = inpatient blood glucose (mg/dL) / [28.7 × glycosylated hemoglobin (HbA1c) (%) − 46.7]. Patients were then divided into four groups (Q1–Q4) based on quartile SHR values. The primary outcome was 28-day all-cause mortality. Statistical analysis employed a multivariate Cox proportional hazards regression model to evaluate associations between SHR groups and mortality risk. To explore potential nonlinear relationships between SHR and mortality, restricted cubic spline (RCS) fitting was conducted. Kaplan-Meier survival curves were plotted to visually demonstrate survival differences among groups, with intergroup comparisons performed using log-rank tests. Boruta machine learning algorithms were applied for feature selection to identify key predictors. Finally, extensive sensitivity analysis and subgroup stratification analyses (categorized by age, gender, and comorbidities) were conducted to validate the robustness and reliability of core conclusions.ResultsRCS analysis revealed a U-shaped association between SHR and 28-day mortality (nonlinear P<0.001), with the lowest risk point at SHR =1.01. Compared to the Q1 group, the Q4 group (SHR ≥1.36) exhibited a significantly increased 28-day mortality risk [adjusted hazard ratio (HR) =1.89, 95% confidence interval (CI): 1.31–2.74]. Boruta algorithm identified SHR as a relatively important predictive variable, with its significance independent of confounding factors such as age and weight score. Sensitivity analyses consistently demonstrated that high SHR significantly elevated mortality risk across all subgroups (age, sex, diabetes status, etc.), with each subgroup showing HR >1 and P<0.05.ConclusionsSHR serves as an independent predictor of 28-day all-cause mortality in critically ill AF patients, and its U-shaped association highlights the critical role of metabolic stress in prognosis. Monitoring SHR may provide a clinical basis for risk stratification and individualized glucose management in AF patients.

The Oxidation Balance Score (OBS), which integrates prooxidant and antioxidant exposures from diet and lifestyle, serves as an indicator of systemic oxidative stress. This study examined the association between OBS and all-cause mortality among U.S. adults with hypertension. OBS was derived from 16 dietary nutrients and 3 lifestyle factors. The nonlinear relationship between OBS and mortality was assessed using smoothing splines. Kaplan–Meier curves, multivariable Cox regression, competing risk models, and subgroup analyses were employed to evaluate mortality risks. The results from the smoothing spline plots and Kaplan–Meier curves suggested that higher OBS levels were associated with lower all-cause mortality. After full adjustment, the Cox regression model revealed that higher OBS levels were associated with a 13% reduction in the risk of all-cause mortality among patients with hypertension compared to those with lower OBS levels (hazard ratios = 0.87, 95% confidence interval: 0.78–0.96, P = .004; P for trend = .003). Sensitivity analysis confirmed a protective association between higher OBS and 10-year mortality, indicating a 13% reduction in risk (hazard ratios = 0.87, 95% confidence interval: 0.78–0.98, P = .019; P for trend = .017). Competing risk models further confirmed that higher OBS reduced hypertension-related mortality. A nonlinear relationship exists between OBS and all-cause mortality in patients with hypertension. Higher OBS is linked to lower mortality, suggesting its potential utility in the prognostic risk assessment for hypertension.

Neonatal calves predominantly rely on colostral IgG for the passive transfer of immunity; however, little is known about their intrinsic capacity for mucosal immunoglobulin production and the developmental changes associated with their growth. To elucidate the developmental trajectory of mucosal immunity, we investigated changes in mucosal immunoglobulin concentrations and the expression levels of genes involved in immunoglobulin production and secretion across different growth stages in calves. The results demonstrated that fecal IgG and IgM levels exhibited transient peaks at 1 week of age according to smooth spline analysis, followed by sharp decreases, whereas IgA levels remained relatively stable and became the predominant isotype after 4 weeks. Gene expression analysis and immunohistochemistry revealed the localized expression of immunoglobulins in the intestinal mucosa, particularly IgA, which gradually increased with calf growth. The secretion of IgA is also thought to be facilitated by the upregulated expression of PIGR, a gene encoding the IgA transporter whose expression levels increase with calf growth. In contrast, the levels of plasma cell-recruiting chemokines and their receptors were not increased. These results suggest an important role for IgA in the mucosal defense system of the calf intestine, indicating its pivotal function in maintaining gut health following the clearance of colostral IgG.

BackgroundMental health represents a significant global health issue, with emerging evidence suggesting a link between psychological well-being and physical health outcomes, including muscle health. Subjective well-being, a key component of mental health, may influence muscle mass through lifestyle factors (e.g., nutrition, sleep) and physiological mechanisms (e.g., neuroendocrine function, inflammation). However, its specific association with low muscle mass among older Chinese adults remains unclear.MethodsThis cross-sectional study utilized data from 11,345 participants in the 2018 wave of the Chinese Longitudinal Healthy Longevity Survey. Subjective well-being was assessed using a validated and applied eight-item scale, comprising one life satisfaction item, four positive emotion items, and three negative emotion items. Low muscle mass was defined using anthropometric indicators with sex-specific thresholds for appendicular skeletal muscle mass/height². Logistic regression was employed to examine the associations between SWB and LMM, adjusting for demographic, socioeconomic, behavioral, and health-related covariates. To explore the potential nonlinear association, spline smoothing analysis and threshold effect analysis were employed. Subsequently, to ensure the robustness of the findings, several sensitivity analyses were conducted.ResultsAfter adjusting for confounding factors, participants with better subjective well-being exhibited a reduced likelihood of low muscle mass [OR = 0.82, 95% confidence interval (CI) 0.73–0.92, P value < 0.001]. Notably, this inverse association displayed nonlinear characteristics (Pfor non-linear = 0.015), with an inflection point at a subjective well-being score of 28.00. Below this threshold, no significant association was detected (OR = 1.02, 95% CI 0.98–1.06), while each unit increase above 28.00 was associated with a 4% decrease in the likelihood of low muscle mass (OR = 0.96, 95% CI 0.94–0.98). The results remained consistent across sensitivity analyses.ConclusionOur findings suggest that subjective well-being is a nonlinear modifiable determinant of low muscle mass in older adults. These results indicate that interventions aimed at enhancing subjective well-being may complement conventional strategies for regulating muscle homeostasis.Supplementary InformationThe online version contains supplementary material available at 10.1186/s12877-025-06357-y.

Daytime, nighttime, and day-night compound heatwaves and the risk of depression: A Chinese nationwide cohort.

ObjectivesInsufficient or excessive sleep and dyslipidemia are significant cardiovascular risk factors. Whilst the relationship between sleep duration and traditional lipid indices are well described, the connection to novel lipid and anthropometric indices remains unclear. This study examines these associations using National Health and Nutrition Examination Survey (NHANES) data from 2005 to 2020.MethodsThis cross-sectional study analyzed data from 9847 adults from NHANES 2005–2020, excluding those with major cardiovascular disease and cancer. Sleep duration was categorized as insufficient (< 7 h), normal (7-8 h), and excessive (> 8 h). Self-reported sleep disturbance was documented. Novel indices included non-high-density lipoprotein cholesterol to high-density lipoprotein cholesterol ratio (NHHR), Triglyceride to HDL-Cholesterol (TG/HDL), Triglyceride-Glucose (TyG) Index, Visceral Adiposity Index (VAI), Lipid Accumulation Product (LAP), Conicity Index (CI), Body-Roundness Index (BRI), A Body Shape Index (ABSI), and Weight-adjusted waist index (WWI). Generalized additive models (GAMs) with spline smoothing and threshold analysis assessed nonlinear associations, adjusting for confounders. Weighted multivariate linear regression evaluated linear associations.ResultsInsufficient sleep was associated with higher TyG combined with waist-to-height ratio (TyG–WHtR) (p = 0.003). Excessive sleep was linked to higher TyG–WHtR, CI, BRI, ABSI, and WWI (p < 0.001). Sleep disturbance was associated with elevated TyG–WHtR, TyG–WC, LAP, CI, BRI, ABSI, and WWI (p < 0.001). Threshold analysis confirmed significant changes in several indices, emphasizing the impact of both insufficient and excessive sleep.ConclusionsInsufficient, excessive sleep duration and sleep disturbance are associated with adverse lipid and anthropometric profiles, indicating increased cardiometabolic risk. Optimal sleep duration and addressing sleep disturbance could mitigate these risks. Further research is needed to understand the underlying mechanisms.

Multiple Reaction Monitoring (MRM) remains the gold standard for quantitative mass spectrometry but continues to be constrained by the limited availability of high-quality transitions and collision energy (CE) values for many biologically and chemically relevant molecules. Here, we present the METLIN 960K MRM library, a 960,000-compound transition resource derived entirely from empirically acquired MS/MS data. MRM transitions were generated in both positive and negative ionization modes using an empirical spline-based pipeline refined by AI BioSync, an XCMS enhancement that provides a framework of AI and machine-learning tools designed to decipher spectral data for biological and analytical relevance. Central to this approach is spline fitting of CE-dependent intensity profiles from experimental MS/MS data collected at four discrete energies (0, 10, 20, and 40 eV), enabling continuous CE modeling and precise prediction of optimal fragmentation conditions. Supervised learning models were used within AI BioSync to refine spline fitting across diverse chemical classes, improving reproducibility and predictive accuracy. Validation across more than 100 authentic compounds, including rare metabolites and diverse small molecules, demonstrated robust detection down to 1 nM, confirming both sensitivity and scalability. This framework also holds immediate applicability for preclinical drug development studies, where authentic metabolite and impurity standards are often unavailable. Unlike prior methods reliant on in silico fragmentation or heuristic rules, all transitions are derived directly from experimental MS/MS data using absolute intensities. The resulting precursor m/z-centric METLIN 960K MRM library (https://metlin.scripps.edu) greatly expands the chemical space accessible to targeted quantitation, providing a scalable, vendor-independent path for sensitive and specific molecular detection across research, clinical, and applied applications.

BackgroundDespite widespread vaccination, pertussis persists as a critical global public health threat, particularly for individuals under 20 years old. This study aimed to comprehensively assess the global burden of pertussis in this population, with a specific focus on disparities related to age, sex, location, and socioeconomic development.MethodsWe utilized data from the Global Burden of Disease (GBD) study 2021 to quantify the burden of pertussis including incidence, mortality, disability-adjusted life years (DALYs) among individuals under 20 years old across 204 countries and territories from 1990 to 2021. Burden estimates were stratified by age, sex, location, and socio-demographic index (SDI). Temporal trends were assessed using estimated annual percentage change (EAPC), and the association between burden metrics and SDI was evaluated via smoothing spline models and Spearman’s correlation analysis.ResultsFrom 1990 to 2021, the global incidence of pertussis in individuals under 20 years old decreased by 77.7%. Similarly, deaths and DALYs due to pertussis declined by 80.3%. In 2021, low-SDI regions reported the highest number of pertussis cases, deaths, and DALYs, whereas high-SDI regions had the lowest. Geographically, South Asia had the highest case count, and Western Sub-Saharan Africa led in deaths and DALYs. Infants had the highest incidence, mortality, and DALY rates. Gender disparities were observed, with females generally having higher rates than males, except in Eastern Sub-Saharan Africa. A negative correlation was noted between SDI and pertussis burden.ConclusionsOur study provides valuable insights into the global pertussis burden among individuals under 20 years old. Despite overall improvements, significant variations exist. Our findings emphasize the need for sustained and improved vaccination strategies such as maternal immunization, improved coverage and timeliness, and better healthcare access, to further address these inequalities.

Accurate phenological information is crucial for evaluating ecosystem dynamics and the carbon budget. As one of China’s largest terrestrial ecosystem carbon pools, Southwest China plays a significant role in achieving the “dual carbon” goals of carbon peaking and carbon neutrality. However, evergreen forests are widely distributed in this region, and phenology extraction based on vegetation indices has certain limitations, while SIF-based phenology extraction offers a viable alternative. This study first evaluated phenological results derived from three solar-induced chlorophyll fluorescence (SIF) datasets, six curve-fitting methods, and five phenological extraction thresholds at flux sites to determine the optimal threshold and SIF data for phenological indicator extraction. Secondly, uncertainties in phenological indicators obtained from the six fitting methods were quantified at the regional scale. Finally, based on the optimal phenological results, the spatiotemporal variations in phenology in Southwest China were systematically analyzed. Results show: (1) Optimal thresholds are 20% for the start of growing season (SOS) and 30% for the end of growing season (EOS), with GOSIF best for SOS and EOS, and CSIF for the peak of growing season (POS). (2) Cubic Smoothing Spline (CS) has the lowest uncertainty for SOS, while Savitzky–Golay Filter (SG) has the lowest for EOS and POS. (3) Phenology exhibits significant spatial heterogeneity, with SOS and POS generally showing an advancing trend, and EOS and length of growing season (LOS) showing a delaying (extending) trend. This study provides a reference for phenology extraction in regions with frequent cloud cover and widespread evergreen vegetation, supporting effective assessment of regional ecosystem dynamics and carbon balance.

Objective: The purpose of this study is to present a kyphosis measurement method based on quadratic spline fitting through three key vertebral landmarks: T12, T8 and T4. This approach aims to capture thoracic spine curvature more continuously and accurately than traditional methods such as the Cobb angle and circle fitting. Methods: A dataset of 560 lateral thoracic spine radiographs was retrospectively analyzed, including cases of postural kyphosis, Scheuermann’s disease, osteoporosis-induced kyphosis and ankylosing spondylitis. Two trained raters independently performed three repeated landmark annotations per image. The kyphosis angle was computed using two methods: (1) a quadratic spline fitted through the three landmarks, with the angle derived from tangent vectors at T12 and T4; and (2) a least-squares circle fit with the angle subtended between T12 and T4. Agreement with reference Cobb angles was evaluated using Pearson correlation, MAE, RMSE, ROC analysis and Bland–Altman plots. Reliability was assessed using intraclass correlation coefficients (ICC). Results: Both methods showed excellent intra- and inter-rater reliability (ICC ≥ 0.967). The spline method achieved lower MAE (5.81°), lower RMSE (8.94°) and smaller bias compared to the circle method. Both methods showed strong correlation with Cobb angles (r ≥ 0.851) and excellent classification performance (AUC > 0.950). Conclusions: Spline-based kyphosis measurement is accurate, reliable and particularly robust in cases with severe spinal deformity. Significance: This method supports automated, reproducible kyphosis assessment and may enhance clinical evaluation of spinal curvature using artificial intelligence-driven image analysis.

This article proposes two estimators for two semiparametric count regression models, namely semiparametric partially Poisson (SPPO) and semiparametric partially zero-inflated Poisson (SPZIP), via the penalized smoothing (Ps) spline and P-spline (Pb) estimations to address the common issue of nonparametric relationships between the response variable and covariates. Additionally, the SPZIP model incorporates a zero-inflation component to handle excess zeros in count data. Through extensive Monte Carlo simulations, we rigorously evaluate the performance of the proposed penalized spline estimators by comparing them against traditional parametric estimators using multiple statistical criteria, including the Akaike information criterion, Bayesian information criterion, deviance statistic, mean squared error and root mean squared error (RMSE). The results indicate that our estimators are more efficient than other estimators. Also, the SPZIP and SPPO models consistently outperform parametric (Poisson and zero-inflated Poisson) regression models, particularly in scenarios with high levels of zero inflation, demonstrating their superior ability to model complex data structures. Our findings highlight the practical utility of these models for analyzing complex count data with excess zeros and nonparametric covariate effects. A real-life data application further demonstrates the capabilities of the SPPO and SPZIP models, demonstrating their ability to provide more accurate and adaptable statistical analysis in challenging data settings. AMS Subject Classification: 62G08, 62J20, 62J05

Smith-Magenis syndrome (SMS, OMIM 182290) is a complex syndromic diagnosis marked by neurobehavioral differences and distinct facial dysmorphisms, caused by haploinsufficiency of the retinoic acid-1 (RAI1) gene either by a pathogenic sequence variant or deletion at chromosome 17p11.2 involving a portion or all of this gene. Dysmorphisms may include a broad square face and brachycephaly, heavy eyebrows, a full mouth with an everted upper lip, and early micrognathia evolving to prognathism after excessive relative mandibular growth. All patients with SMS have variable global cognitive impairment, greatest in speech/language, disturbed sleep patterns, and distinct behaviors including self-injury, food foraging, and abnormal oral intake regulation, hyperactivity, and aggression. Short stature and central obesity are common in patients with SMS, and reference curves are needed to assess growth in clinical care and research endeavors. After IRB approval, anthropometry (including length/height, weight, head circumference) was collected via direct patient encounter, parental report from external medical encounters, and extraction from medical records. Utilizing polynomial smooth splines with a B-spline basis and variable windows depending on age, sex-specific length/height and weight curves were created, including 5th, 50th and 95th percentile lines for 0 through 15 years. Head circumference data were pooled from males and females to create 5th, 50th, and 95th percentile lines for 0 through 5 years. Nearly 6000 length/height, weight, and head circumference measurements from 190 patients with SMS from birth through adulthood were gathered. Length/height and weight data were plotted against age from birth through 15 years to create new length/height-for-age and weight-for-age curves by sex. Similar processes were employed to construct head circumference-for-age curves from birth through 5 years, combining data from both sexes into one figure. Final adult height was derived from the maximum adult height for each subject over the age of 18 years. The curves included in this article represent the first set of standardized growth curves for individuals with SMS. As such, they will permit clinicians to monitor and set expectations for linear growth, weight gain, and cranial growth in individuals with SMS.