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Previous studies have reported that the significant association between serum calcium and mortality substantially in patients, especially among those with intensive care unit (ICU). And In diabetes mellitus, congestive heart failure (CHF) is a significant comorbidity. We aim to evaluate the association between serum calcium levels and in-hospital mortality among patients with diabetes and congestive heart failure. The participants in this study were extracted from the Medical Information Mart for Intensive Care IV (MIMIC-IV) database. To scrutinize potential associations between serum calcium levels and in-hospital mortality, a comprehensive analysis encompassing multivariate logistic regression, cubic spline function model, threshold effect analysis, and subgroup analysis was performed. This retrospective cohort study encompassed 7063 patients, among whom the in-hospital mortality stood at 12.2%. In the multivariate logistic regression, adjusted odds ratios (ORs) were contrasted with the reference category Q6 (8.8-9.1 mg/dL) for serum calcium levels and in-hospital mortality. The adjusted ORs for Q1 (≤ 7.7 mg/dL), Q2 (7.7-8 mg/dL), and Q7 (≥ 9.1 mg/dL) were 1.69 (95% CI 1.17-2.44, p = 0.005), 1.62 (95% CI 1.11-2.36, p = 0.013), and 1.57 (95% CI 1.1-2.24, p = 0.012) respectively. The dose-response analysis uncovered a U-shaped relationship between serum calcium levels and in-hospital mortality in diabetic patients with heart failure. Subgroup analyses confirmed result stability notwithstanding the influence of diverse factors. Our investigation revealed a U-shaped correlation between serum calcium levels and in-hospital mortality in diabetes patients with congestive heart failure, pinpointing a significant inflection point at 9.05 mg/dL.

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This study proposes a versatile and efficient optimisation method for discrete coils that induce a magnetic field by their steady currents. The prime target is gradient coils for MRI (Magnetic Resonance Imaging). The derivative (gradient) of the z-component the magnetic field, which is calculated by the Biot-Savart's law, with respect to the z-coordinate in the Cartesian xyz coordinate system is considered as the objective function. Then, the derivative of the objective function with respect to a change of coils in shape is formulated according to the concept of shape optimisation. The resulting shape derivative (as well as the Biot-Savart's law) is smoothly discretised with the closed B-spline curves. In this case, the control points (CPs) of the curves are naturally selected as the design variables. As a consequence, the shape derivative is discretised to the sensitivities of the objective function with respect to the CPs. Those sensitivities are available to solve the present shape-optimisation problem with a certain gradient-based nonlinear-programming solver. The numerical examples exhibit the mathematical reliability, computational efficiency, and engineering applicability of the proposed methodology based on the shape derivative/sensitivities and the closed B-spline curves.

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Various guidelines recommend the first follow-up cystoscopy at 3 months; however, no data exist on the optimal timing for initial follow-up cystoscopy. We tried to provide evidence on the timing of the first cystoscopy after the initial transurethral resection of bladder tumor (TUR-BT) for patients with non-muscle invasive bladder cancer (NMIBC) using big data. This was a retrospective National Health Insurance Service database analysis. The following outcomes were considered: recurrence, progression, cancer-specific mortality, and all-cause mortality. Exposure was the time-to-treatment initiation (TTI), a continuous variable representing the time to the first cystoscopy from the first TUR-BT within 1 year. Additionally, we categorized TTI (TTIc) into five levels: < 2, 2-4, 4-6, 6-8, and 8-12 months. A landmark time of 1 year after the initial TUR-BT was described to address immortal-time bias. We identified the optimal time for the first cystoscopy using Cox regression models with and without restricted cubic splines (RCS) for TTI and TTIc, respectively. Among 26,660 patients, 16,880 (63.3%) underwent cystoscopy within 2-4 months. A U-shaped trend of the lowest risks at TTI was observed in the 2-4 months group for progression, cancer-specific mortality, and all-cause mortality. TTI within 0-2 months had a higher risk of progression (aHR 1.36; 95% confidence intervals [CI] 1.15-1.60; p < 0.001) and cancer-specific mortality (aHR 1.29; 95% CI 1.05-1.58; p = 0.010). Similarly, TTI within 8-12 months had a higher risk of progression (aHR 2.09; 95% CI 1.67-2.63; p < 0.001) and cancer-specific mortality (aHR 1.96; 95% CI 1.48-2.60; p < 0.001). Based on the RCS models, the risks of progression, cancer-specific mortality, and all-cause mortality were lowest at TTI of 4 months. The timing of the first cystoscopy follow-up was associated with oncologic prognosis. In our model, undergoing cystoscopy at 4 months has shown the best outcomes in clinical course. Therefore, patients who do not receive cystoscopy at approximately 4 months for any reason need more careful follow-up to predict a poor clinical course.

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The soil's physical and mechanical (SPM) properties have significant impacts on soil processes, such as water flow, nutrient movement, aeration, microbial activity, erosion, and root growth. To digitally map some SPM properties at four global standard depths, three machine learning algorithms (MLA), namely, random forest, Cubist, and k-nearest neighbor, were employed. A total of 200-point observation was designed with the aim of a field survey across the Marvdasht Plain in Fars Province, Iran. After sampling from topsoil (0 to 30 cm) and subsoil depths (30 to 60 cm), the samples were transferred to the laboratory to determine the mean weight diameter (MWD) and geometric mean diameter (GMD) of aggregates in the laboratory. In addition, shear strength (SS) and penetration resistance (PR) were measured directly during the field survey. In parallel, 79 environmental factors were prepared from topographic and remote sensing data. Four soil variables were also included in the modeling process, as they were co-located with SPM properties based on expert opinion. For selecting the most influential covariates, the variance inflation factor (VIF) and Boruta methods were employed. Two covariate dataset scenarios were used to assess the impact of soil and environmental factors on the modeling of SPM properties including SPM and environmental covariates (scenario 1) and SPM, environmental covariates, and soil variables (scenario 2). From all covariates, nine soil and environmental factors were selected for modeling the SPM properties, of which four of them were the soil variables, three were related to remote sensing, and two factors had topographic sources. The results indicated that scenario 2 outperformed in all standard depths. The findings suggested that clay and SOM are key factors in predicting SPM, highlighting the importance of considering soil variables in addition to environmental covariates for enhancing the accuracy of machine learning prediction. The k-nearest neighbor algorithm was found to be highly effective in predicting SPM, while the random forest algorithm yielded the highest R2 value (0.92) for penetration resistance properties at 15-30 depth. Overall, the approach used in this research has the potential to be extended beyond the Marvdasht Plain of Fars Province, Iran, as well as to other regions worldwide with comparable soil-forming factors. Moreover, this study provides a valuable framework for the digital mapping of SPM properties, serving as a guide for future studies seeking to predict SPM properties. Globally, the output of this research has important significance for soil management and conservation efforts and can facilitate the development of sustainable agricultural practices.

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Vascular access for hemodialysis is of paramount importance. Although studies have found that central venous catheter (CVC) is often associated with poor outcomes and switching to arteriovenous fistula (AVF) and arteriovenous grafts (AVG) is beneficial, it has not been fully elucidated how the effect of switching of access on outcomes changes over time and whether the effect depends on switching time. In this paper we propose to relate the observed survival time for patients without access change and the counterfactual time for patients with access change using an AFT model with time-varying effects. The flexibility of AFT model allows us to account for baseline effect and the prognostic effect from covariates at access change while estimating the effect of access change. The effect of access change overtime is modeled nonparametrically using a cubic spline function. Simulation studies show excellent performance. Our methods are applied to investigate the effect of vascular access change over time in dialysis patients. It is concluded that the benefit of switching from CVC to AVG depends on the time of switching, the sooner the better.

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The aim of this study was to estimate genetic and environmental parameters, across bull's age, for semen quality traits including pre- and postcryopreservation semen concentration, sperm motility, and sperm viability as well as ejaculate volume and number of doses per ejaculate. A data set on 96,595 ejaculates from 2,831 Nordic Holstein bulls collected between 2006 and 2019 was used. Genetic and environmental parameters were estimated using a random regression model and applying the average-information REML approach. Spline functions were chosen to fit the additive genetic and permanent environmental effects across bull's age, and the optimal number of knots was chosen using cross validation. Residual variance heterogeneity was assumed in different bull age classes. The estimated repeatabilities of semen quality traits ranged from 0.16 to 0.85 across different ages of bulls. The estimated heritabilities of semen quality traits ranged from 0.02 to 0.56 across different ages of bulls. The results indicate possibilities for genetic improvement of semen quality traits through selective breeding.

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Most human traits are influenced by the interplay between genetic and environmental factors. Many statistical methods have been proposed to screen for gene-environment interaction (GxE) in the post genome-wide association study era. However, most of the existing methods assume a linear interaction between genetic and environmental factors toward phenotypic variations, which diminishes statistical power in the case of nonlinear GxE. In this paper, we present a flexible statistical procedure to detect GxE regardless of whether the underlying relationship is linear or not. By modeling the joint genetic and GxE effects as a varying-coefficient function of the environmental factor, the proposed model is able to capture dynamic trajectories of GxE. We employ a likelihood ratio test with a fast Monte Carlo algorithm for hypothesis testing. Simulations were conducted to evaluate validity and power of the proposed model in various settings. Real data analysis was performed to illustrate its power, in particular, in the case of nonlinear GxE.

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BACKGROUND AND AIM: Metabolic dysfunction associated fatty liver disease (MAFLD) is the most common liver disease and dyslipidemia is commonly considered a prominent risk factor for MAFLD. This study was to investigate the association between the apolipoprotein B/A1 (apo B/A1) ratio and the risk of MAFLD based on new diagnostic criteria. METHODS: We conducted a cross-sectional study on 3341 participants. Restricted cubic spline (RCS) analyses, logistic regression, Synergistic effects analyses and stratified analyses were used to evaluate the association between the apo B/A1 ratio and the risk of MAFLD. RESULTS: The apo B/A1 ratio was nonlinearly related to the increased risk of MAFLD and the OR and 95% CI for the apo B/A1 95th percentile was 1.700 (1.004-2.879) compared with the 50th percentile. Each 1 SD increase in apo B/A1 ratio would increase the 1.313-fold risk of the risk of MAFLD in all participants and 1.46-fold risk in normolipidemic participants. Synergistic effects indicated elevated Apo B/A1 ratio and dyslipidemia collectively contributed to an increased risk of MAFLD [OR (95 %CI): 2.496(1.869-3.334)]. CONCLUSIONS: The apo B/A 1 ratio was a risk factor of the presence of MAFLD. Dyslipidemia and elevated the Apo B/A1 ratio can synergistically contributed to the risk of MAFLD.

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A vast majority of the countries are under economic and health crises due to the current epidemic of coronavirus disease 2019 (COVID-19). The present study analyzes the COVID-19 using time series, an essential gizmo for knowing the enlargement of infection and its changing behavior, especially the trending model. We consider an autoregressive model with a non-linear time trend component that approximately converts into the linear trend using the spline function. The spline function splits the series of COVID-19 into different piecewise segments between respective knots in the form of various growth stages and fits the linear time trend. First, we obtain the number of knots with their locations in the COVID-19 series to identify the transmission stages of COVID-19 infection. Then, the estimation of the model parameters is obtained under the Bayesian setup for the best-fitted model. The results advocate that the proposed model appropriately determines the location of knots based on different transmission stages and know the current transmission situation of the COVID-19 pandemic in a country.

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BACKGROUND: High Blood Urea Nitrogen (BUN) and high Serum Creatinine (SCr) levels are risk factors for Coronary Artery Disease (CAD). However, the relationship between the Blood Urea Nitrogen to Creatinine (BUN/SCr) ratio (UCR) and the risk of CAD in patients living with new-onset diabetes is unclear. This study aimed to examine the relationship between blood UCR and the risk of CAD in patients living with new-onset type 2 diabetes mellitus (T2DM). METHODS: We analyzed the data from the cohort of 12,299 patients living with type 2 diabetes mellitus. Primary endpoints were the events of CAD. The ANOVA test (continuous indicators) and χ2 test (categorical indicators) were used to assess the differences of baseline characteristics across the groups of UCR. In order to understand the correlation between variables, we performed correlation analysis on variables that have significant differences between CAD group and non-CAD group. Multivariate-adjusted Cox proportional hazard regression models were applied to estimate the association of the blood UCR with the risk of CAD in patients living with T2DM. The Kaplan-Meier survival function plotting and the log-rank test were used to evaluate the event-free survival according to the groups of UCR. The restricted cubic spline model was used to show the adjusted association between blood UCR and risk of CAD in patients living with T2DM. RESULTS: During a median follow-up of 2.66 years, 1173 CAD were recorded with an event rate of 28.49 events per 1000 person-years. In multivariate-adjusted Cox regression models, elevated blood urea nitrogen to creatinine ratio (UCR) was associated with higher risk of CAD in patients living with T2DM [hazard ratio (HR), 1.782; 95% confidence interval (CI), 1.237-2.567]. The Kaplan-Meier survival curves indicated that the high group of UCR tended to have a lower event-free survival than the low group and medium group. There was a nonlinear trend toward increasing risk of CAD across the groups of UCR. And cubic spline function graph suggested that the influence of UCR level on HR for CAD increased significantly at UCR levels above 6.67. CONCLUSIONS: An elevated UCR was significantly associated with an increased risk for CAD in patients living with T2DM.

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OBJECTIVES: Efforts have been made to mathematically reconstruct the brain morphology from human fossil crania to clarify the evolutionary changes in the brain that are associated with the emergence of human cognitive ability. However, because conventional reconstruction methods are based solely on the endocranial shape, deep brain structures cannot be estimated with sufficient accuracy. Our study aims to investigate the possible morphological correspondence between the cranial and deep brain morphologies based on humans and African great apes, with the goal of a more precise reconstruction of fossil brains. MATERIALS AND METHODS: Midsagittal endocranial and deep brain landmarks were obtained from magnetic resonance images of humans and three species of African great apes. The average midsagittal endocranial profile of all four species was calculated after Procrustes registration. The spatial deformation function from each of the endocranial profiles to the average endocranial profile was defined, and the brain landmarks enclosed in the endocranium were transformed using the deformation function to evaluate the interspecific variabilities of the positions of the brain landmarks on the average endocranial profile. RESULTS: The interspecific differences in the shape-normalized positions of the corpus callosum, anterior commissure, thalamus center, and brainstem were approximately within the range of 2% of the human cranial length, indicating that the interspecific variabilities of the positions of these deep brain structures were relatively small among the four species. DISCUSSION: Such an invariant relationship of the deep brain structure and the endocranium that encloses the brain can potentially be utilized to reconstruct the brains of fossil hominins.

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PURPOSE: Obesity has been associated with an increased risk of the depression in the general population, but it is unknown whether this relationship applies equally to immigrants as well as non-immigrants. Furthermore, the nature of the relationship is uncertain, is it direct or curvilinear? The aim of this study is to examine the relationship between body mass index and major depressive episode among immigrants and non-immigrants. METHODS: To provide more statistically robust data, a series of cross-sectional health surveys of the Canadian population for the 5 years 2010-2014 were pooled to increase the number of immigrants in the study. Restricted cubic splines analysis was used to examine the nature of the association. RESULTS: Immigrants had lower 12-month depression and obesity prevalence rates than non-immigrants. In addition, it was found that non-immigrants were more likely to develop depression than immigrants, OR = 1.40 (95% CI, 1.16-1.67). Obese respondents were more likely to develop depression than normal weight respondents in both immigrant (OR = 1.55; 95% CI, 1.03-2.32) and non-immigrant groups (OR = 1.23; 95% CI, 1.15-1.32). A significant nonlinear elongated J-shaped association between obesity and depression was found for both immigrants and non-immigrants with increased risk of depression in obese individuals. CONCLUSION: Culture-specific, clinical-based interventions should be developed to improve the early identification, treatment and recovery of individuals with a high BMI particularly among those with BMIs in the obese range.

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Cow mature weight (MWT) has increased in the past 30 yr. Larger cows cost more to maintain, but their efficiency-and thus profitability-depends on the production environment. Incorporating MWT effectively into selection and mating decisions requires understanding of growth to maturity. The objective of this study was to describe growth to maturity in crossbred beef cattle using Brody, spline, and quadratic functions. Parameter estimates utilized data on crossbred cows from cycle VII and continuous sampling phases of the Germplasm Evaluation Program at the U.S. Meat Animal Research Center. The MWT were estimated at 6 yr from the fitted parameters obtained from the Brody (BMWT), spline (SMWT), and quadratic (QMWT) functions. These were defined as BMWT, SMWT, and QMWT for the Brody, spline, and quadratic functions, respectively. Key parameters from the Brody function were BMWT and maturing constant. The spline was fitted as piecewise linear where the two linear functions joined at a knot. Key parameters were knot position and SMWT. For the quadratic model, the main parameter considered was QMWT. Data were scaled for fitting such that 180 d was the y-intercept with the average weight at 180 d (214.3 kg) subtracted from all weights. Weights were re-expressed by adding 214.3 kg after analysis. Once data were edited, with outliers removed, there were parameter estimates for 5,156, 5,041, and 4,905 cows for the Brody, spline, and quadratic functions, respectively. The average maturing constant (SD) was 0.0023 d-1 (0.0008 d-1). The mean MWT estimates (SD) from the Brody, spline, and quadratic functions were 650.0 kg (64.0 kg), 707.3 kg (79.8 kg), and 597.8 kg (116.7 kg), respectively. The spline function had the highest average R2 value when fit to individual cows' data. However, the Brody function produced more consistent MWT estimates regardless of the timeframe of data available and produced the fewest extreme MWT. For the spline and quadratic functions, weights through 4 and 5 yr of age, respectively, were needed before consistent estimates of MWT were obtained. Of the three functions fitted, the Brody was best suited for estimating MWT at a later age in crossbred beef cattle.

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This work was motivated by observational studies in pregnancy with spontaneous abortion (SAB) as outcome. Clearly some women experience the SAB event but the rest do not. In addition, the data are left truncated due to the way pregnant women are recruited into these studies. For those women who do experience SAB, their exact event times are sometimes unknown. Finally, a small percentage of the women are lost to follow-up during their pregnancy. All these give rise to data that are left truncated, partly interval and right-censored, and with a clearly defined cured portion. We consider the non-mixture Cox regression cure rate model and adopt the semiparametric spline-based sieve maximum likelihood approach to analyze such data. Using modern empirical process theory we show that both the parametric and the nonparametric parts of the sieve estimator are consistent, and we establish the asymptotic normality for both parts. Simulation studies are conducted to establish the finite sample performance. Finally, we apply our method to a database of observational studies on spontaneous abortion.

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This paper concerns the problem of wood cellular structure image registration. Given the large variability of wood geometry and the important changes in the cellular organization due to moisture sorption, an affine-based image registration technique is not exhaustive to describe the overall hygro-mechanical behaviour of wood at micrometre scales. Additionally, free tools currently available for non-rigid image registration are not suitable for quantifying the structural deformations of complex hierarchical materials such as wood, leading to errors due to misalignment. In this paper, we adapt an existing non-rigid registration model based on B-spline functions to our case study. The so-modified algorithm combines the concept of feature recognition within specific regions locally distributed in the material with an optimization problem. Results show that the method is able to quantify local deformations induced by moisture changes in tomographic images of wood cell wall with high accuracy. The local deformations provide new important insights in characterizing the swelling behaviour of wood at the cell wall level.

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The use of non-linear regression models in the analysis of biological data has led to advances in poultry nutrition. Spline or broken-line nonlinear regression models are commonly used to estimate nutritional requirements. One particular application of broken-line models is estimating the maximum safe level (MSL) of feed ingredients beyond which the ingredients become toxic, resulting in reduced performance. The objectives of this study were to evaluate the effectiveness of broken-line models (broken-line linear or BLL; and broken-line quadratic or BLQ) in estimating the MSL; to identify the most efficient design of feeding trials by finding the optimal number of ingredient levels and replications; and to re-estimate the MSL of various test ingredients reported in the nutrition literature for comparison purposes. The Maximum Ingredient level Optimization Workbook (MIOW) was developed to simulate a series of experiments and estimate the MSL and the corresponding descriptive statistics (SD, SE, CI, and R2). The results showed that the broken-line models provided good estimates of the MSL (small SE and high R2) with the BLL model producing higher MSL values as compared to the BLQ model. Increasing the number of experimental replications or ingredient levels (independently of each other) reduced the SE of the MSL with diminishing returns. The SE of the MSL was reduced with increasing the size (total pens) of the simulated experiments by increasing either the number of replications or levels or both. The evaluation of MSLs reported in the existing literature revealed that the multiple range procedure used to determine the MSL in several reports can both overestimate and underestimate the MSL compared to the results obtained by the broken-line models. The results suggest that the broken-line linear models can be used in lieu of the multiple range test to estimate the MSL of feed ingredients along with the corresponding descriptive statistics, such as the SE of the MSL.

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OBJECTIVES: To examine the non-linear effects of meteorological factors on the incidence of influenza A H7N9 and to determine what meteorological measure, and on which day preceding symptom onset, has the most significant effect on H7N9 infection. METHODS: We applied a zero truncated Poisson regression model incorporating smoothed spline functions to assess the non-linear effect of temperature (maximum, minimum, and daily difference) and relative humidity on H7N9 human case numbers occurring in China from February 19, 2013 to February 18, 2014, adjusting for the effects of age and gender. RESULTS: Both daily minimum and daily maximum temperature contributed significantly to human infection with the influenza A H7N9 virus. Models incorporating the non-linear effect of minimum or maximum temperature on day 13 prior to disease onset were found to have the best predictive ability. For minimum temperature, high risk was found to range from approximately 5 to 9°C and moderate risk from -10 to 0°C; temperatures of >9°C represented a low risk. For maximum temperature, high risk was found to range from approximately 13 to 18°C and moderate risk from 0 to 4°C; temperatures of >18°C represented a low risk. Relative humidity was not significantly associated with the incidence of infection. The incidence of H7N9 was higher for males compared to females (p<0.01) and it peaked at around 60-70 years of age. CONCLUSIONS: We provide direct evidence to support the role of climate conditions in the spread of H7N9 and thereby address a critical question fundamental to our understanding of the epidemiology and evolution of H7N9. These findings could be used to inform targeted surveillance and control efforts aimed at reducing the future spread of H7N9.

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Meta-analyses have been widely used to combine information from survival data using estimated parameters in, for example, a Cox model. A number of approaches dealing with study level random effects have been developed. However, there are far fewer meta-analysis approaches for estimating survival or hazard functions. Typical approaches are based on the cumulative survival function using the generalized estimating equation. We propose an alternative approach following Efron's discrete logistic regression (Efron, 1988), but using generalized linear mixed models. We show that spline functions can be used in fitting the models to obtain smoothed estimates for hazard functions. The models also allow a semi-parametric structure to include factors such as random study effects and treatment groups. This approach models the hazard function based on which the survival function can be estimated too. We also propose a Bayesian bootstrap approach for statistical inference for both hazard and survival functions. This approach was applied to two meta-analysis data sets as examples to illustrate its use. Copyright © 2012 John Wiley & Sons, Ltd.

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OBJECTIVE: Evaluation of individual growth is important in orthodontics. The aim of this study was to develop a convenient software that can evaluate current growth status and predict further growth. METHODS: Stature data of 2 to 20 year-old Koreans (4893 boys and 4987 girls) were extracted from a nationwide data. Age-sex-specific continuous functions describing percentile growth curves were constructed using natural cubic spline function (NCSF). Then, final stature prediction algorithm was developed and its validity was tested using longitudinal series of stature measurements on randomly selected 200 samples. Various accuracy measurements and analyses of errors between observed and predicted stature using NCSF growth curves were performed. RESULTS: NCSF growth curves were shown to be excellent models in describing reference percentile stature growth curve over age. The prediction accuracy compared favorably with previous prediction models, even more accurate. The current prediction models gave more accurate results in girls than boys. Although the prediction accuracy was high, the error pattern of the validation data showed that in most cases, there were a lot of residuals with the same sign, suggestive of autocorrelation among them. CONCLUSION: More sophisticated growth prediction algorithm is warranted to enhance a more appropriate goodness of model fit for individual growth.

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