Smoothing Spline Research Articles

A Tale of NGC 3785: The formation of an ultra-diffuse galaxy at the end of the longest tidal tail

We present the discovery of an extended and faint tail observed in the isolated environment associated with galaxy NGC\,3785. This study additionally provides observational evidence supporting the formation of ultra-diffuse galaxies (UDGs) at the end of the tail. We utilized the Gnuastro software to detect and analyze the low surface brightness structures in the optical $g$- and $r$-bands using data from the Dark Energy Camera Legacy Survey. We created a detection map to identify the faint tail and measured its length using cubic spline fitting. Additionally, we found 84 star-forming clumps along the tail and performed photometric analysis on the tail portion after applying a significance threshold on the signal-to-noise ratio . We have measured the projected length of the tail, which is sim 390 kpc. We propose that this tail arises from the interaction of the NGC\,3785 with a gas-rich galaxy, which ends up as a UDG at the end of the tail.

Three-dimensional visualization of large-area, nanoscale topography measurements

High-resolution metrology is a critical area of development for nanoscale manufacturing, especially as it affects production throughput and fabrication quality. Atomic force microscopy (AFM) is one of the most popular tools for nanometrology, and high-resolution AFM often requires a significant time commitment and produces datasets of several million points. It is therefore critical for the development of data processing techniques to keep pace with the requirements of analyzing this type of data, and for these techniques to be portable as miniaturization in AFM is becoming more common. This work presents a data fitting algorithm designed for reducing the parameters of large-area data sets which utilizes well-established spline fitting techniques. In this paper we show that basis-spline fitting can be used to accurately represent large AFM data sets, including data sets with noisy data and sharp features, while achieving at least 90% parameter reduction in all test cases.

Wind Power Curve Model Combining Smoothed Spline with First-Order Moments and Density-Adjusted Wind Speed Strategy

Given the variety of potential application scenarios, it is crucial to develop wind power curves that are more accurate, smoother, efficient, and applicable across a wider range of contexts. To this end, a wind power curve model combining smoothed spline with first-order moments (FOM) and density-adjusted wind speed (DAWS) strategy is proposed in this paper. First, the DAWS strategy is employed to consider the influence of meteorological factors on the wind power curve by adjusting wind speed. This strategy reduces the root mean square error (RMSE) by 5.81%-6.17% and the mean absolute error (MAE) by 5.84%-6.44% without adding complexity to the model. Secondly, FOM is proposed as a substitute for the original data during the modeling process. This approach reduces the number of operations on the similar data, resulting in a reduction of modeling time by 48.11%-99.89%. Furthermore, the impact on model accuracy is minimal. Finally, a the wind power curve model based on smooth spline is constructed, which exhibits superior smoothness, a broader range of generalizability, enhanced model accuracy, and reductions in RMSE by 5.67%-23.87% and MAE by 4.79%-22.35% in comparison to the control method.

Optimal knots for smoothing splines and adaptive smoothing splines in generalized linear models: Design approach

Smoothing splines play a crucial role as a prevalent tool for estimating unknown functions in non parametric regression. In fitting functions with varying roughness, adaptive smoothing splines provide the flexibility to adjust the smoothing parameter adaptively with the changes over the predictor variable within specific intervals, facilitating accommodation for changing roughness. Despite its intuitive appeal and high flexibility, the implementation of this estimator poses challenges, especially in the absence of specified knot numbers, knot locations, and certain simplifying assumptions on the smoothing parameter. D-optimal designs are considered to specify the knot locations in this models. The prior information from data as the prior curvature knowledge can be useful for this optimization problem. For this purpose, the smoothing parameter in this optimization problem can be considered as a function based on the prior curvature. We apply this method to responses from the exponential family of distributions. The mathematical expression of the estimator of the curve in a generalized linear mixed model enables us to derive an information matrix. The derived information matrix and hence the optimum design will depend on the values of the model’s unknown parameters. In such situations, numerical techniques should be considered for evaluating and optimizing this criterion.

Dietary inflammatory index and all-cause mortality in adults with COPD: a prospective cohort study from the NHANES 1999-2018.

Chronic inflammation is closely linked to Chronic Obstructive Pulmonary Disease (COPD); however, the impact of the Dietaryq Inflammatory Index (DII) on mortality among COPD patients remains uncertain. To assess the correlation between the DII and all-cause mortality in COPD patients using data from the National Health and Nutrition Examination Survey (NHANES). We conducted a retrospective cohort study on 1,820 COPD patients from the NHANES dataset (1999-2018). The influence of DII on mortality was evaluated using multivariate Cox regression, smoothing spline fitting, and threshold effect analysis. Additionally, Kaplan-Meier survival analysis was performed to compare survival curves among different DII groups. Subgroup analyses and E-values identified sensitive cohorts and assessed unmeasured confounding. Over an average follow-up of 91 months, multivariate Cox regression models revealed a significant positive correlation between DII scores and mortality risk, with each unit increase in DII associated with a 10% higher risk of death (HR: 1.10, 95% CI: 1.03-1.16; P = 0.002). Among the DII tertiles, individuals in the second tertile (T2: 1.23-2.94) experienced a 67% increase in mortality risk compared to those in the lowest tertile (T1: -5.28-1.23) (HR: 1.67, 95% CI: 1.26-2.21; p < 0.001). The third tertile (T3) did not show a statistically significant increase in mortality risk (HR: 1.30, 95% CI: 0.98-1.72; p=0.074). A restricted cubic spline analysis indicated a significant nonlinear association between DII and all-cause mortality (p = 0.021). Threshold effect analysis further revealed that below a DII of 2.19, there was a significant increase in all-cause mortality risk (HR = 1.19, 95% CI: 1.07-1.33; p = 0.002), while at or above this threshold, the risk increase was not statistically significant (HR=0.89, 95% CI: 0.68-1.15; p = 0.380). Kaplan-Meier analysis revealed significant differences in survival curves among DII tertiles (p < 0.001), with the lowest DII tertile showing the highest survival probability. Both subgroup and sensitivity analyses confirmed the robustness of these findings. DII is positively correlated with mortality risk in COPD patients, showing nonlinear characteristics and threshold effects, underscoring its prognostic value.

Forward variable selection enables fast and accurate dynamic system identification with Karhunen-Loève decomposed Gaussian processes

A promising approach for scalable Gaussian processes (GPs) is the Karhunen-Loève (KL) decomposition, in which the GP kernel is represented by a set of basis functions which are the eigenfunctions of the kernel operator. Such decomposed kernels have the potential to be very fast, and do not depend on the selection of a reduced set of inducing points. However KL decompositions lead to high dimensionality, and variable selection thus becomes paramount. This paper reports a new method of forward variable selection, enabled by the ordered nature of the basis functions in the KL expansion of the Bayesian Smoothing Spline ANOVA kernel (BSS-ANOVA), coupled with fast Gibbs sampling in a fully Bayesian approach. It quickly and effectively limits the number of terms, yielding a method with competitive accuracies, training and inference times for tabular datasets of low feature set dimensionality. Theoretical computational complexities are O ( N P 2 ) in training and O ( P ) per point in inference, where N is the number of instances and P the number of expansion terms. The inference speed and accuracy makes the method especially useful for dynamic systems identification, by modeling the dynamics in the tangent space as a static problem, then integrating the learned dynamics using a high-order scheme. The methods are demonstrated on two dynamic datasets: a ‘Susceptible, Infected, Recovered’ (SIR) toy problem, along with the experimental ‘Cascaded Tanks’ benchmark dataset. Comparisons on the static prediction of time derivatives are made with a random forest (RF), a residual neural network (ResNet), and the Orthogonal Additive Kernel (OAK) inducing points scalable GP, while for the timeseries prediction comparisons are made with LSTM and GRU recurrent neural networks (RNNs) along with the SINDy package.

Nonlinear association between remnant cholesterol and reversion from impaired fasting glucose to normoglycemia: a multicenter cohort study

BackgroundRemnant cholesterol (RC), a potent atherogenic lipid, has been shown to be strongly correlated with insulin resistance and the pathogenesis of diabetes mellitus. However, the relationship between RC and normoglycemia reversal in individuals with impaired fasting glucose (IFG) is crucial and remains unclear. This investigation, which aimed to clarify this association, is important for understanding and potentially improving the management of diabetes.MethodThis study, which included 15,019 IFG participants from 11 Chinese cities between 2010 and 2016, was conducted with a rigorous research process. Cox regression analysis revealed intriguing findings regarding the relationship between RC and normoglycemia reversal in individuals with IFG. Potential nonlinear associations were further explored via smooth curve-fitting techniques and 4-knot restricted cubic spline functions, ensuring a comprehensive analysis. To examine the validity of the results, an array of subgroup and sensitivity analyses were conducted, further bolstering the robustness of the findings.ResultsBy the end of the 2.89-year median follow-up period, 6,483 of the 15,019 IFG participants (43.17%) had reverted to normoglycemia. The findings, which reveal that increased RC levels are inversely associated with the likelihood of normoglycemia reversal, are novel and significant. According to the fully adjusted Cox proportional hazards model analysis, an increase of one standard deviation in RC was associated with a 20% decrease in the likelihood of normoglycemia reversal among IFG participants (HR: 0.80, 95% CI: 0.77–0.82). A nonlinear association between RC and normoglycemia reversal was observed, with an inflection point at 41.37 mg/dL. This suggests that the growth rate of the likelihood of reversion decreased and stabilized after the inflection point was reached. Moreover, significant interactions were observed between the age groups, providing a more nuanced understanding of this complex relationship.ConclusionAmong Chinese adults with IFG, RC exhibited a negative nonlinear relationship with the probability of normoglycemia reversal. When RC levels reached or exceeded 41.38 mg/dL, the probability of achieving normoglycemia progressively diminished and subsequently stabilized. Maintaining RC levels below 41.38 mg/dL can significantly improve the probability of normoglycemia reversal among individuals with IFG, especially those aged 60 years or older.

Exploring the unique association between high-density lipoprotein cholesterol and vitamin D deficiency in adults aged 20–59: findings based on the NHANES database

BackgroundSerum lipids are highly heritable and play an important role in cardiovascular and metabolic health. However, the relationship between high-density lipoprotein cholesterol (HDL-C) and serum 25-hydroxyvitamin D [25(OH)D] levels is unclear. This study aims to explore the association between serum 25(OH)D levels and HDL-C in adults aged 20–59.MethodsThis cross-sectional study was based on data from the National Health and Nutrition Examination Survey (NHANES). Multivariable logistic regression was used to assess the relationship between HDL-C and serum 25(OH)D, with further analysis using smooth spline fitting and generalized additive models.ResultsA total of 28,084 adults were included in the study. After adjusting for multiple variables, we found a significant positive correlation between HDL-C and serum 25(OH)D levels (β = 8.3, 95% CI: 7.24–9.35, p < 0.001). Stratified subgroup analysis by gender showed that females consistently exhibited a positive correlation (β = 10.12, 95% CI: 9.07–11.18, p < 0.001), while males demonstrated an inverted U-shaped relationship between HDL-C and serum 25(OH)D.ConclusionIn the population aged 20–59, HDL-C levels are significantly associated with serum 25(OH)D levels. Clinically, simultaneous monitoring of HDL-C and vitamin D is recommended to better assess and manage cardiovascular health. Increasing vitamin D intake should be considered, especially for males with low HDL-C levels, to prevent related health issues.

Non-linear relationship between age and subfoveal choroidal thickness in Chinese patients with proliferative diabetic retinopathy.

No study has investigated the change regularity between age and subfoveal choroidal thickness (SFCT) in proliferative diabetic retinopathy (PDR). To investigate the relationship between the SFCT and age in Chinese patients with PDR. This was a cross-sectional retrospective study. The participants were hospitalized individuals with type 2 diabetes who underwent vitrectomy for PDR. Con-tralateral eyes that met the criteria were included in the study. All necessary laboratory tests were performed at the time of admission. Central macular thickness (CMT) and SFCT were two quantitative assessments made using enhanced depth imaging optical coherence tomography. CMT was measured automatically and SFCT was measured manually with digital calipers provided by the Heidelberg Eye Explorer software. The final analysis included a total of 234 individuals with PDR. The average age was 55.60 years old ± 10.03 years old, and 57.69% of the population was male. Univariate analysis revealed a significant negative connection between age and SFCT in patients with PDR [β = -2.44, 95% confidence interval (95%CI): -3.46 to -1.42; P < 0.0001]. In the fully adjusted model, the correlation between SFCT and age remained steady (β = -1.68, 95%CI: -2.97 to -0.39; P = 0.0117). Spline smoothing showed that the relationship between SFCT and age in patients with PDR was non-linear, with an inflection point at 54 years of age. Our findings suggest that age is a key determinant of choroidal thickness. The non-linear link between SFCT and age in PDR patients should be taken into account.

Manufacturing design of plain milling technology of spline shaft by formed disc-type milling cutter

Abstract The spline fittings are widely used in different mechanical constructions where high load transmission is required from a shaft to a spline plate or a tooth gear or other internal cylindrical element. In many cases a key joint connection can not bear the load that we want to transform. In this case the application of double key could give solution. But sometimes it does not give solution due to the high load that is why spline fitting should be used. This publication focuses for the manufacturing of the spline shaft with plain milling technology. The type of the tool is a formed disc type milling cutter. Since more splines are around the perimeter of the shaft the repetition of the milling process is needed in the function of the number of the splines. All of the manufacturing parameters will be determined that are needed for a complex technological analysis such as cutting forces, machining times, speeds, etc. The chip volume will be approximated by volume constancy since the separated chip volume is a quite complex geometric body. I will prescribe initial technological parameters and define existing shaft geometries for which I will determine the technological parameters to show and analyze the correlations between the technological parameters and the variable for each shaft.

A NONPARAMETRIC MIXED-EFFECTS MIXTURE MODEL FOR PATTERNS OF CLINICAL MEASUREMENTS ASSOCIATED WITH COVID-19.

Some patients with COVID-19 show changes in signs and symptoms such as temperature and oxygen saturation days before being positively tested for SARS-CoV-2, while others remain asymptomatic. It is important to identify these subgroups and to understand what biological and clinical predictors are related to these subgroups. This information will provide insights into how the immune system may respond differently to infection and can further be used to identify infected individuals. We propose a flexible nonparametric mixed-effects mixture model that identifies risk factors and classifies patients with biological changes. We model the latent probability of biological changes using a logistic regression model and trajectories in the latent groups using smoothing splines. We developed an EM algorithm to maximize the penalized likelihood for estimating all parameters and mean functions. We evaluate our methods by simulations and apply the proposed model to investigate changes in temperature in a cohort of COVID-19-infected hemodialysis patients.

Adaptive methods with [formula omitted] splines for multi-patch surfaces and shells

We introduce an adaptive isogeometric method for multi-patch surfaces and Kirchhoff–Love shell structures with hierarchical splines characterized by C1 continuity across patches. We extend the construction of smooth hierarchical splines from the multi-patch planar setting to analysis suitable G1 surfaces. The adaptive scheme to solve fourth order partial differential equations is presented in a general framework before showing its application for the numerical solution of the bilaplacian and the Kirchhoff–Love model problems. A selection of numerical examples illustrates the performance of hierarchical adaptivity on different multi-patch surface configurations.

A Robust Wind Turbine Component Health Status Indicator

Wind turbine components’ failure prognosis allows wind farm owners to apply predictive maintenance techniques to their fleets. Determining the health status of a turbine’s component typically requires verifying many variables that should be monitored simultaneously. The scope of this study is the selection of the more relevant variables and the generation of a health status indicator (Failure Index) to be considered as a decision criterion in Operation and Maintenance activities. The proposed methodology is based on Gaussian Mixture Copula Models (GMCMs) combined with a smoothing method (Cubic spline smoothing) to define a component’s health index based on the previous behavior and relationships between the considered variables. The GMCM allows for determining the component’s status in a multivariate environment, providing the selected variables’ joint probability and obtaining an easy-to-track univariate health status indicator. When the health of a component is degrading, anomalous behavior becomes apparent in certain Supervisory Control and Data Acquisition (SCADA) signals. By monitoring these SCADA signals using this indicator, the proposed anomaly detection method could capture the deviations from the healthy working state. The resulting indicator shows whether any failure is likely to occur in a wind turbine component and would aid in a preventive intervention scheduling.

An Improved CH4 Profile Retrieving Method for Ground-Based Differential Absorption Lidar

Range-resolved CH4 concentration measurement is important prior data for atmospheric physical and chemical models. Ground-based differential absorption lidar (DIAL) can measure the vertical distribution of CH4 concentration in the atmosphere. The traditional method uses lidar observational data and the lidar equation to calculate profiles, but the inversion accuracy is greatly affected by noise. Although some denoising methods can improve accuracy at low altitudes, the low signal-to-noise ratio caused by the effect of aerosol Mie scattering and lower aerosol concentrations at high altitudes cannot be solved. Here, an improved cubic smoothing spline fitting CH4 concentration profile inversion method is proposed to address this challenge. By adding a penalty term of the second derivative of the conventional cubic spline function to the objective function, this penalty term acts to smooth the fitting, allowing the fitting function to avoid necessarily passing through those noisy sampling points. This avoids the large fluctuations caused by noisy sampling points, effectively suppresses noise, captures signals with lower noise levels, and thereby enhances the inversion accuracy of the profiles. Simulations and case studies demonstrated the superiority of the proposed method. Compared with the traditional method, cubic smoothing spline fitting can reduce the mean error of the whole CH4 profile by 85.54%. The standard deviation of CH4 concentration retrieved is 3.59 ppb–90.29 ppb and 0.01 ppb–6.75 ppb smaller than the traditional method and Chebyshev fitting, respectively. Three real cases also indicate that the CH4 concentration retrieved by cubic smoothing spline fitting is more consistent with in-situ measurements. In addition, long-term DIAL observations have also revealed notable diurnal and seasonal trends in CH4 concentration at observation sites.

Examination of nonlinear associations between pulse pressure index and incident prediabetes susceptibility: a 5-year retrospective cohort investigation

Prediabetes and related complications constitute significant public health burdens globally. As an indicator closely associated with abnormal glucose metabolism and atherosclerosis, the utility of Pulse Pressure Index (PPI) as a prediabetes risk marker has not been explored. We performed a retrospective cohort analysis to investigate this putative association between PPI and prediabetes hazard. Our analysis encompassed 183,517 Chinese adults ≥ 20 years registered within the Rich Healthcare Group 2010–2016. PPI was defined as (systolic blood pressure − diastolic blood pressure)/systolic blood pressure. The relationship between PPI and prediabetes risk was assessed via Cox proportional hazards regression modeling. Non-linearity evaluations applied cubic spline fitting approaches alongside smooth curve analysis. Inflection points of PPI concerning prediabetes hazard were determined using two-piecewise Cox models. During a median follow-up of 3 years (2.17–3.96 years), new-onset prediabetes was documented in 20,607 patients (11.23%). Multivariate regression analysis showed that PPI was an independent risk factor for prediabetes, and the risk of prediabetes increased by 0.6% for every 1% increase in PPI (Hazard Ratio [HR]: 1.006, 95% Confidence Interval [CI] 1.004–1.008, P < 0.001). This association was non-significant for PPI ≤ 37.41% yet exhibited a sharp upsurge when PPI surpassed 37.41% (HR: 1.013, 95% CI 1.005–1.021, P = 0.0029). Our analysis unveils a positive, non-linear association between PPI and future prediabetes risk. Within defined PPI ranges, this relationship is negligible but dramatically elevates beyond identified thresholds.

Association of apolipoprotein A1 levels with lumbar bone mineral density and β-CTX in osteoporotic fracture individuals: a cross-sectional investigation.

The relationship between the levels of high-density lipoprotein (HDL) and bone mineral density (BMD) is controversial. Furthermore, the specific role of apolipoprotein A1 (APOA1), a primary HDL component, in regulating BMD remains unclear. This study aimed to elucidate the correlation between APOA1 levels and lumbar BMD in patients with osteoporotic fracture (OPF) for novel insights into potential therapeutic strategies against osteoporosis. This study included 587 OPF patients enrolled at the Kunshan Hospital, Affiliated with Jiangsu University between January 2017 and July 2022. The patient's serum APOA1 levels were determined, followed by the assessment of lumbar BMD and C-terminal telopeptide of type I collagen (β-CTX) as outcome variables. The association of APOA1 levels with lumbar BMD and β-CTX was assessed via Generalized Estimating Equations (GEE) and spline smoothing plot analyses. A generalized additive model (GAM) helped ascertain non-linear correlations. Moreover, a subgroup analysis was also conducted to validate the result's stability. It was observed that APOA1 levels were positively correlated with lumbar BMD (β = 0.07, 95% CI: 0.02 to 0.11, p = 0.0045), indicating that increased APOA1 levels were linked with enhanced lumbar BMD. Furthermore, APOA1 levels were negatively related to β-CTX (β = -0.19, 95% CI: -0.29 to -0.09, p = 0.0003), suggesting APOA1 might reduce osteolysis. In addition, these findings were robustly supported by subgroup and threshold effect analyses. This study indicated that increased APOA1 levels were correlated with enhanced lumbar BMD and decreased osteolysis in OPF patients. Therefore, APOA1 may inhibit osteoclast activity to prevent further deterioration in osteoporotic patients. However, further research I warranted to validate these conclusions and elucidate the underlying physiologies.

Spatiotemporal methods for estimating subsurface ocean thermal response to tropical cyclones

Abstract. Tropical cyclones (TCs), driven by heat exchange between the air and sea, pose a substantial risk to many communities around the world. Accurate characterization of the subsurface ocean thermal response to TC passage is crucial for accurate TC intensity forecasts and an understanding of the role that TCs play in the global climate system. However, that characterization is complicated by the high-noise ocean environment, correlations inherent in spatiotemporal data, relative scarcity of in situ observations, and the entanglement of the TC-induced signal with seasonal signals. We present a general methodological framework that addresses these difficulties, integrating existing techniques in seasonal mean field estimation, Gaussian process modeling, and nonparametric regression into an ANOVA decomposition model. Importantly, we improve upon past work by properly handling seasonality, providing rigorous uncertainty quantification, and treating time as a continuous variable, rather than producing estimates that are binned in time. This ANOVA model is estimated using in situ subsurface temperature profiles from the Argo fleet of autonomous floats through a multistep procedure, which (1) characterizes the upper-ocean seasonal shift during the TC season, (2) models the variability in the temperature observations, and (3) fits a thin-plate spline using the variability estimates to account for heteroskedasticity and correlation between the observations. This spline fit reveals the ocean thermal response to the TC passage. Through this framework, we obtain new scientific insights into the interaction between TCs and the ocean on a global scale, including a three-dimensional characterization of the near-surface and subsurface cooling along the TC storm track and the mixing-induced subsurface warming on the track's right side.

Association between serum osmolality and 28-day all-cause mortality in patients with heart failure and reduced ejection fraction: a retrospective cohort study from the MIMIC-IV database.

Previous studies have not thoroughly explored the impact of serum osmolality levels on early mortality in heart failure and reduced ejection fraction (HFrEF) patients. The purpose of this study was to investigate the relationship between serum osmolality levels and early all-cause mortality in patients with HFrEF. The open access MIMIC-IV database was the source of data for our study. We collected demographic data, vital signs, laboratory parameters, and comorbidities of the included patients and divided them into 3 groups based on their initial serum osmolality on admission, with the primary outcome being all-cause mortality within 28 days of admission. Smoothing Spline Fitting Curve, the Kaplan-Meier survival curve, and Threshold effect analysis were used to assess the relationship between serum osmolality and early mortality in HFrEF patients. A total of 6228 patients (55.31% male) were included. All-cause mortality within 28 days on admission was 18.88% in all patients. After adjusting for confounders, higher serum osmolality levels were independently associated with an increased risk of 28-days all-cause mortality compared with the reference group (Reference group Q2: 290-309 mmol/L, Q4: HR, 1.82 [95% CI 1.19-2.78] P<0.05, Q5: HR, 1.99 [95% CI 1.02-3.91] P<0.05). Smooth spline fitting revealed a U-shaped association between serum osmolality and 28-days all-cause mortality. Further threshold effect analysis results suggested that each unit increase in serum osmolality level was associated with a 2% increase in 28-days all-cause mortality when serum osmolality levels were ≥ 298.8 mmol/L (HR, 1.019 [95% CI 1.012-1.025] P<0.05). A U-shaped correlation between initial serum osmolality and 28-days all-cause mortality in HFrEF patients was identified, revealing higher osmolality levels significantly increase mortality risk. These results underscore serum osmolality's critical role in early mortality among HFrEF patients, highlighting the need for further, larger-scale studies for validation.

Triglyceride-glucose index is associated with the risk of impaired fasting glucose in Chinese elderly individuals

The association between the triglyceride-glucose (TyG) index and impaired fasting glucose (IFG) in elderly individuals remains uncertain. Our study aimed to explore the association between the TyG index and the risk of future IFG in this population. This retrospective cohort study included 17,746 elderly individuals over 60. In this population, Cox regression models proportional to hazards, along with smooth curve fitting and cubic spline functions, were employed to examine the association between the baseline TyG index and the risk of IFG. Subgroup analyses and sensitivity were also performed to ensure the robustness of the study findings. After adjusting for covariates, a positive association between the TyG index and the risk of IFG was found (HR = 1.43, 95% CI 1.27–1.60, P < 0.0001). The likelihood of IFG rose steadily as the TyG index quartiles (from Q1 to Q4) increased, with Q4 demonstrating a 62% elevated risk compared to Q1 (adjusted HR = 1.62, 95% CI 1.37–1.90). Additionally, we found the association between TyG index and risk of IFG was a linear. Sensitivity and subgroup analyses confirmed the stability of the results. Our study observed a linear association between the TyG index and the development of IFG in elderly Chinese individuals. Recognizing this association can help clinicians identify high-risk individuals and implement targeted interventions to reduce their risk of progressing to diabetes.

Comparison of Some Robust Methods of Difference Based Ridge Estimator in Semiparametric Regression Model

The semiparametric regression models have received a lot of attention from researchers recently because it combines parametric and nonparametric methods, it is one of the advanced topics in data analysis for various studies, which aims to find the best capabilities and a high level of efficiency. One of the most important semiparametric regression models is the partial linear regression model (PLM), which consists of a parametric component and a nonparametric component, for the purpose of estimating the parametric component, the difference method will be used to remove the nonparametric component. When the analysis hypotheses of the parametric component are not fulfilled, it will suffer from several problems, the most important of which is the problem of complete multicollinearity, besides the multicollinearity, there are also outliers in the data. In this research, the problems of multicollinearity and outliers of the semiparametric regression model were addressed, where simulation was used to generate data with different sample sizes and for different correlations and outlier ratios and for different methods such as [Difference Ridge based M robust with Nadaraya – Watson (DRMNW), Difference Ridge based S robust with Nadaraya – Watson (DRSNW), Difference Ridge based M robust with Smoothing spline (DRMSP), Difference Ridge based S robust with Smoothing spline (DRSSP)], the results showed that method Difference Ridge based M robust with Smoothing spline (DRMSP) is the best estimator.