Statistical Model Research Articles

Relation of volatile organic compounds to renal function in American adolescents: three statistical models

ABSTRACT This study was conducted to evaluate the relationship between 17 urinary metabolites of volatile organic compounds (mVOCs) in adolescents and renal function parameters (estimated glomerular filtration rate (eGFR), albumin-to-creatinine ratio (ACR), urinary albumin, serum uric acid (SUA), and blood urea nitrogen (BUN)). In adjusted generalised linear models (GLM), mVOCs were positively correlated with eGFR, urinary albumin, and BUN, and mVOCs were negatively correlated with ACR and SUA. Weighted Quartile Sum (WQS) index correlated with eGFR [β(95%CI): 0.040 (0.028, 0.052)], urine albumin [β(95%CI): 0.275 (0.203, 0.622)], SUA [β(95%CI): 0.040 (0.025, 0.055)] and BUN [β(95%CI): 0.102 (0.082, 0.122)]. In Bayesian Kernel Machine Regression (BKMR) model, total compound effect was positively correlated with eGFR, positive associations were observed in high concentration of the mixture with urine albumin and ACR. Findings suggest that single and mixed exposures to mVOCs may affect renal parameters in adolescents.

Morphological changes to peripheral joints supporting thumb trapezial metacarpal osteoarthritis.

The present study aims to determine if morphological differences of the scaphoid, trapezoid, and second metacarpal are associated with thumb osteoarthritis by comparing three-dimensional bone models of healthy controls and osteoarthritis patients. Fifty-eight patients with moderate to severe thumb osteoarthritis (modified Eaton≥II) and 35 healthy controls from a larger completed investigation were examined. To quantify morphological variations, a statistical shape model was created that classified binary with respect to the Eaton grading system: non-osteoarthritis or moderate/severe osteoarthritis (II-IV). Three-dimensional surface models based on computed tomography images from the scaphoid, trapezoid, and second metacarpal were used to "train" the statistical shape model and yielded features that best explain variation within the three bones: the principal components These principal components were tested for significant differences between patient and control group. Additionally, a statistical shape model entailing all three bones was created. For the second metacarpal, only a single principal component was significantly associated with osteoarthritis (p=0.035). The combined model utilizing all three bones, however, showed that with using one principal component of each of the bones, we could classify a sample as moderate/severe trapeziometacarpal osteoarthritis with an accuracy of 0.77. No individual shape components of the scaphoid or trapezoid significantly correlated to osteoarthritis. This study affirms that basilar thumb osteoarthritis is not limited to the trapeziometacarpal joint. Future studies investigating surrounding bones and joints as contributors to disease occurrence or progression will provide a more holistic insight into the prevention, diagnostic, and treatment of thumb osteoarthritis.

Comprehensive analysis of compost maturity differences across stages and materials with statistical models.

Aerobic composting is an environmentally friendly and effective approach to treating organic solid waste. The variability in material composition introduces complex interactions between environmental factors and materials, which in turn affects compost maturity. This study uses multiple statistical analyses to systematically compare key indicators across composting processes for kitchen waste, livestock manure, and sludge. The results show that material type and composting stage have a significant impact on compost maturity (p<0.001). High-precision modeling (R2>0.90) was achieved using a Stacking model on the composting dataset, with interpretability analysis highlighting the important roles of temperature, moisture content, and nitrogen content across different composting materials. The combined effects of environmental and material changes jointly influence the composting progression. In kitchen waste composting, strong interactions between multiple indicators were observed, while moisture shifts in livestock manure and sludge composting primarily influenced compost maturity by promoting decomposition and enhancing nitrogen retention, respectively. Partial dependence analysis quantified the relationships between key indicators and compost maturity scores. These findings offer a scientific basis for identifying key factors and optimization paths in various composting processes, supporting the development of more effective composting strategies.

Shared chemoresistance genes in ESCC and cervical Cancer: Insights from pharmacogenomics and Mendelian randomization.

Neoadjuvant chemotherapy, particularly the use of platinum-based compounds and taxanes, is pivotal in the treatment of epithelial-derived tumors, such as cervical cancer and esophageal squamous cell carcinoma (ESCC); however, resistance remains a significant challenge. Utilizing Mendelian randomization (MR) with pharmacogenomics offers a novel approach to understanding the genetic underpinnings of drug responses, thereby aiding in personalized treatment. Single-cell RNA sequencing (scRNA-seq) analysis revealed a shared cellular subpopulation of CD8+T effector memory (CD8+TEM) cells that are pivotal in mediating chemotherapy resistance in ESCC and cervical cancer. A two-sample approach was employed for MR using data from genome-wide association studies, focusing on single nucleotide polymorphisms (SNPs) linked to CD8+TEM cell expression. The SNPs were carefully selected, and statistical models, including the Wald ratio and inverse variance weighted methods, were used for robust causal effect estimation. These were supplemented by MR-Egger and weighted median analyses to address pleiotropy and variant heterogeneity. 3-(4,5-Dimethylthiazol-2-yl)-2,5 diphenyl tetrazolium bromide (MTT) and immunohistochemistry assays were used to verify the relationship between the gene and drug sensitivity. Increased proportion of CD8+TEM cells were observed in resistant samples. MR identified IL32, SPOCK1, and TRBC2 as key genes associated with resistance to cisplatin, carboplatin, and paclitaxel, respectively. These findings were validated across various cohorts and underscored the role of CD8+TEM cells in drug responsiveness. The results of the MTT and immunohistochemistry assays confirmed the MR findings. Our study highlights the significant role of CD8+TEM cells in the chemoresistance of ESCC and cervical cancer and identified three genetic markers crucial for resistance to common chemotherapeutic agents. These findings suggest potential pathways for developing personalized treatment strategies, offering clinically relevant insights that could enhance therapeutic efficacy and help overcome drug resistance in patients with ESCC or cervical cancer.

Statistical optimization of hyaluronidase production by Ochrobactrum intermedium MEFS strain along with in vivo application in the treatment of aesthetic filler complications.

This study aims to optimize the production of microbial hyaluronidase (hyase) from Ochrobactrum intermedium MEFS strain using a statistical model and assess its effectiveness in degrading dermal filler in hairless mice. Plackett-Burman design identified nicotinic acid and CaBr as the main factors affecting hyase activity, with optimal concentrations of 5.51 μg/mL for nicotinic acid and 99.76 mM for CaBr, resulting in hyase activity of 320 U/mL, as determined by a central compound design. The purified hyase was applied to hairless mice to reverse dermal filler complications. Complete degradation occurred after 48 h with 60 U/mL and 72 h with 30 U/mL treatments. Histological analysis showed a strong inflammatory response (neutrophiles accumulation) 24 h post-injection, which shifted to moderate inflammation (mononuclear cells) after 14 days. Hyase treatment reduced inflammation in a dose-dependent manner, with 30 U/mL resulting in mild inflammation and 60 U/mL promoting tissue repair. Histological analysis also revealed that the HA filler was completely eliminated when hyase was used at a dosage of 60 U/mL. This approach has proven more effective in completely eliminating the filler and supporting tissue regeneration. This is the first report of using microbial hyase in filler injections, offering potential for treating aesthetic filler complications.

Evaluation of antibiotic purchase data for ceftiofur and enrofloxacin and minimum inhibitory concentrations among Escherichia coli isolates from swine farms in the Midwestern United States using multiple statistical models.

Antimicrobial resistance is considered a global One Health threat. Controlling selection pressure by reducing antibiotic use in livestock is a significant component of the response to this threat. The science concerning use and resistance is complicated and affected by time from antibiotic exposure, changing bacterial fitness, and varies by drug and pathogen. From May 2020 through October 2023, we collected intestinal (substandard and sick pigs) and fecal swab (healthy pig) samples at breed-to-wean (BTW) and wean-to-market (WTM) swine production sites and isolated E. coli bacteria. Antibiotic susceptibility testing was performed on these isolates to determine minimum inhibitory concentrations (MIC) for ceftiofur and enrofloxacin. Monthly antibiotic purchase data were used to calculate the active milligrams of drug purchased and these were divided by the kilograms of pigs produced from a farm site to provide a mass-adjusted proxy metric for farm-level antibiotic use. The relationship between use and MIC was then evaluated using a variety of multivariable statistical models. Across multiple modeling approaches, both farm type (i.e., BTW versus WTM) and farm-level antibiotic use maintained statistically significant relationships relative to E. coli MIC values for each respective drug. Use of ceftiofur and enrofloxacin can lead to increased MIC values among E. coli over time. The reasons for antibiotic purchases were not tracked as part of this project. Future work should evaluate the age of the individual pig and the time from last treatment when sampling these animals to separate out the group from individual-level effects of antibiotic use.

On the cluster of the families of hybrid polynomial kernels in kernel density estimation

This study introduces a novel cluster of hybrid polynomial kernel families, designed to achieve significantly lower asymptotic mean integrated squared error compared to traditional kernels. These hybrid kernels are developed by heuristically combining classical polynomial kernels using probability axioms. An in-depth analysis of error propagation within these kernels is conducted, utilizing both simulation experiments and real-life datasets, including the Life Span of Batteries and COVID-19 datasets. The findings consistently demonstrate that the proposed hybrid kernels outperform their classical counterparts in various density estimation tasks across different distribution types and sample sizes. This research highlights the potential of hybrid polynomial kernels to enhance accuracy in density estimation, advocating for their adoption in statistical modelling and analysis.

Robust trajectory optimization under arbitrary uncertainty using ensemble weather forecasting and statistical aircraft performance model

Robust trajectory optimization under arbitrary uncertainty using ensemble weather forecasting and statistical aircraft performance model

Efficacy of biochar as a catalyst for a Fenton-like reaction: Experimental, statistical and mathematical modeling analysis

Efficacy of biochar as a catalyst for a Fenton-like reaction: Experimental, statistical and mathematical modeling analysis

Physics-based numerical implementation framework towardsmuti-scale contact problem

This paper establishes a general computational framework to solve the muti-scale contact problem by integrating the statistical contact model with the finite element format. Compared to existing models, the proposed method is applicable to most geometric configurations and can effectively evaluate the pressure distribution. In this work, a modified Karush-Kuhn-Tucker (KKT) condition is proposed by the assumption that asperity height obeys the Gaussian distribution. Therefore, in the variational formula, the contact contribution is decomposed into body contribution and asperity contribution, corresponding to the nominal smooth surface and roughness, respectively. Then the linearization and constraint enforcement of these two components are derived, followed by a nonlinear Newton-Raphson-based iterative algorithm. The contact patch test and Hertz contact test are conducted, and the predicted results are consistent with the theoretical and experimental values, confirming the effectiveness and accuracy of the proposed approach. It is worth noting that in the Hertz contact test, the contact pressure distribution varies progressively with the roughness level and external force, tending to the Hertz limit or Gaussian limit. This means that the proposed method can be applied to any roughness and load. Finally, the contact behaviors of the transmission interface of a piezoelectric actuator, i.e., a typical multi-scale contact problem, are studied as an engineering application case.

New insights of the adsorption and photodegradation of reactive black 5 dye using water-soluble semi-conductor nanocrystals: Mechanism interpretation and statistical physics modeling

New insights of the adsorption and photodegradation of reactive black 5 dye using water-soluble semi-conductor nanocrystals: Mechanism interpretation and statistical physics modeling

Dyadic adjustment of persons with albinism and their significant other: A Bayesian mediation model of the Actor-Partner Interdependence (APIMeM).

Limited standardized empirical research exists in France on the psychosocial implications of albinism, prompting an investigation into how affected persons adapt to their disabilities. Recent advancements in health psychology have led researchers to adopt a systemic approach, considering disabilities and involving close relatives in the adaptation process. The aim of this study was to explore the mediating role of dyadic coping within family dyads, where one is a person with albinism (PWA) and the other is a close relative. The study included 38 family dyads with each member responding individually to an online standardized protocol. Participants were recruited through convenience sampling, facilitated by a patient association (Genespoir) and professionals from medical referral centers involved in the project. Dyads with a PWA born, raised, or residing in Africa during the study were excluded. Three statistical models based on Actor-Partner Interdependence Mediation Model (APIMeM) were Bayesian-tested using weakly informative priors. Models 2 and 3 emerged as the most effective at explaining the data. Model 2 showed the mediating role of common dyadic coping between the quality of the relationship and anxiety level and suggested that PWAs tend to feel more anxious when they report high levels of shared adaptation with their close relative. Model 3 highlighted the role of albinism-related emotional impact in mediating the relationship between stigma consciousness and overall quality of life, but this was observed only among PWAs. Greater consciousness of stigma among PWAs was associated with increased emotional impact, resulting in a more impaired quality of life. Social implications of albinism seem to be crucial in dyadic adjustment to albinism. Personal perceptions and the associated stigma (i.e., ableism) linked to albinism may influence the ambivalent manner in which individuals adapt to their condition. Future studies should further investigate these intricate mechanisms, as outlined by our proposed conceptual model.

Pamrevlumab plus nab-paclitaxel/gemcitabine (Pam + GA) as first- and second-line therapy in metastatic pancreatic cancer (mPDAC): Results from Precision Promise (PrP) Bayesian platform trial.

673 Background: Pamrevlumab (Pam) is a fully human recombinant monoclonal antibody against connective tissue growth factor. Early clinical data with Pam plus chemotherapy showed a favorable safety profile and potential efficacy in PDAC. In PrP, Pam + GA was tested as first line (Line 1) and second line (Line 2) therapy for mPDAC vs GA. PrP is a phase 2/3, innovative Bayesian adaptive platform trial sponsored by the Pancreatic Cancer Action Network testing multiple experimental arms efficiently against common controls (1). Methods: Randomization is 70% (adaptive amongst experimental arms in stage 1) and 15%:15% amongst two control arms (GA, mFOLFIRINOX). Pam + GA graduates from stage 1 to 2 if the Bayesian predictive power (PP) of eventual success is ≥ 35% for one of the arm’s signatures [Line 1, Line 2 or Line 1 &amp; 2 (All)]. All participants (pts) are followed for 12 months (mos) after last pt randomized and treated in Pam + GA. Stages 1 and 2 are combined for final analysis. Efficacy is defined by overall survival (OS) hazard ratio (HR, experimental vs control), by a Bayesian statistical model. Superiority (HR &lt; 1) is claimed at final analysis if the Bayesian probability of superiority is ≥ 98%. Results: Pam + GA entered PrP in Jun 2021. Between 6/2021 - 1/2023, at 23 US sites, 317 pts were treated and are included in the mITT analysis. 213 pts were treated in the Pam + GA arm (102 Line 1; 111 Line 2), 45 in the GA arm (23 Line 1; 22 Line 2), 31 in the mFOLFIRINOX arm and 28 in other experimental arms. All treated pts before and during Pam + GA enrollment were in the Bayesian model, with outcomes adjusted via a time machine to increase the trial’s statistical power. Baseline characteristics were balanced across the arms. Pam + GA met criteria to graduate to stage 2 in Sep 2022 in the All signature (Line 1 &amp; 2). At final analysis, Pam + GA did not meet the OS primary endpoint [model estimated HR: 1.18 (95% credible interval, 0.88, 1.56), posterior Pr(HR &lt; 1) = 0.14, below specified ≥ 0.98]. No benefit was seen in PFS nor ORR (Table). No new safety signals were seen. Conclusions: PrP, the first Bayesian platform trial in mPDAC, performed as designed; Pam + GA did not improve OS versus GA in Line 1 and Line 2 mPDAC. The novel Bayesian design warrants further study in mPDAC to enhance efficiency of drug development. Future designs should explore different strategies to allocate patients to control arm(s) vs experimental arms and accommodate novel agents intended to benefit subsets of mPDAC. 1. Picozzi, ASCO TPS 4188, 2022. Clinical trial information: NCT04229004 . Line 1 Line 2 GA Pam + GA Hazard Ratio GA Pam + GA Hazard Ratio Model Estimated mOS (mos) 11.3 9.7 1.18(95% CI* 0.88, 1.56) 7.8 6.6 1.18(95% CI* 0.88, 1.56) mPFS (mos) 5.3 5.9 0.64(95% CI^ 0.36, 1.14) 7.0 3.9 1.35(95% CI^ 0.78, 2.33) ORR (%) 26.1 35.3 4.5 9.0 *Credible Interval. ^Confidence Interval.

EWMA control chart framework for efficient Maxwell quality characteristic monitoring: An application to the aerospace industry

The Maxwell distribution is extensively employed in statistical modeling to analyze data, notably in the fields of chemistry, astrophysics, demography, actuarial sciences, economics, industry, and engineering. Recently, the application of the Maxwell data generating process (DGP) has focused extensively on the domain of statistical control charts. The V chart and VSQ chart are often used to identify unexpected changes in the distributional shift of the Maxwell process. The VSQ chart offers considerably better performance than the V chart for detecting moderate to large shifts in the scale parameter. However, the VSQ chart adopts the fundamental structure of the Shewhart monitoring scheme and is insensitive to small alterations in the target parameter. We propose a new control chart, namely, the Maxwell exponentially weighted moving average (MXEWMA) chart, for improved monitoring of quality attributes that are assumed to conform to Maxwell data generation. The factors used to design the parameters of the proposed chart are computed at different false alarm probabilities and across various sample sizes. The effectiveness of the suggested scheme is considered in terms of the different features of the run length (RL) distribution, including the average, median and standard deviation. A comparative study of the MXEWMA chart with the existing VSQ chart was performed across various sample sizes. The comparative analysis showed that the MXEWMA chart is an effective alternative and performs well in detecting reasonably small shifts in the parameter. Simulated data are employed to describe the computational procedure of the MXEWMA scheme. The simulation analysis demonstrated that the MXEWMA chart outperforms the existing method in identifying slight changes in the studied parameters. A real dataset is also considered to support the theoretical part of the work.

Investigating a Domain Adaptation Approach for Integrating Different Measurement Instruments in a Longitudinal Clinical Registry.

In a longitudinal clinical registry, different measurement instruments might have been used for assessing individuals at different time points. To combine them, we investigate deep learning techniques for obtaining a joint latent representation, to which the items of different measurement instruments are mapped. This corresponds to domain adaptation, an established concept in computer science for image data. Using the proposed approach as an example, we evaluate the potential of domain adaptation in a longitudinal cohort setting with a rather small number of time points, motivated by an application with different motor function measurement instruments in a registry of spinal muscular atrophy (SMA) patients. There, we model trajectories in the latent representation by ordinary differential equations(ODEs), where person-specific ODE parameters are inferred from baseline characteristics. The goodness of fit and complexity of the ODE solutions then allow to judge the measurement instrument mappings. We subsequently explore how alignment can be improved by incorporating corresponding penalty terms into model fitting. To systematically investigate the effect of differences between measurement instruments, we consider several scenarios based on modified SMA data, including scenarios where a mapping should be feasible in principle and scenarios where no perfect mapping is available. While misalignment increases in more complex scenarios, some structure is still recovered, even if the availability of measurement instruments depends on patient state. A reasonable mapping is feasible also in the more complex real SMA data set. These results indicate that domain adaptation might be more generally useful in statistical modeling for longitudinal registrydata.

Application of Machine Learning Predicting Injuries in Traffic Accidents through the Application of Random Forest

Background: The objective of this work is to analyze and predict the harmfulness in traffic accidents. Method: Several Random Forest statistical models are created, in which the predictable variable (response/ output variable) is the harmfulness of the accident, while the input variables are the various characteristics of the accident. In addition, these generated models will allow estimating the influence or importance of each of the factors studied (input variables) concerning the harmfulness of road accidents so that it is possible to know in which aspects it is more profitable to work with the objective of reducing mortality from traffic accidents [1]. Results: In this regard, the predictive algorithm has an out-of-bag error of 26.55% and an overall accuracy of 74.1%. Meanwhile, the local accuracy of the mildly wounded class is 66.1% compared to 81.4% of the dead and severely wounded class, which, as mentioned, has higher prediction reliability. Conclusion: Finally, it is worth noting the enormous usefulness of the Random Forest machine learning technique, which provides very useful information for possible research or studies that may be carried out. In the specific case of this work, through the use of the R programming language, which in turn presents a wide range of freely accessible utilities and functions with which it may be interesting working, it has generated results of great value for this area of activity, important to society as road safety.

Toxicology and clinical protocol development of DUO-207: An ultrasmall nanomedicine co-delivering gemcitabine and paclitaxel for the treatment of metastatic pancreatic cancer.

749 Background: The long-term survival rates for metastatic pancreatic cancer have remained stubbornly low for decades. Most pancreatic cancers have dense, fibrous stroma tissue surrounding their tumors, which contributes to tumor growth and acts as a barrier to many therapies. Nanomedicines have been developed for use in oncology to reduce toxicity and improve efficacy, but a majority are too large (&gt; 100nm) to effectively penetrate dense stroma. DUO-207 is a novel ultrasmall nanomedicine (~ 20nm) composed of copolymer-conjugated gemcitabine that encapsulates paclitaxel. Numerous preclinical efficacy models have demonstrated DUO-207’s ability to penetrate and accumulate in tumor tissue. Here we describe results from toxicology studies performed in canines that assisted in the design of a phase 1b clinical trial using the continual reassessment method (CRM). Methods: A single cycle, bridging toxicology study of DUO-207 with a recovery period was performed in canines. Animal equivalent doses of nano-albumin-bound paclitaxel (nAb-PTX) and gemcitabine were administered as the standard of care (SoC) comparator. Blood was analyzed for hematological toxicity, biomarkers of major organ toxicity, and drug toxicokinetics. Toxicology results from DUO-207 were then used in a statistical model to explore plausible scenarios for clinical dose escalation. Results: DUO-207 treated canines demonstrated improved clinical observations compared to SoC. As expected, hematologic toxicities occurred in a dose dependent fashion in the DUO-207 group but no hepato- or nephrotoxicity was noted. Based on these data, a phase 1b CRM design has been developed with 90% power to detect the maximum tolerated dose in key scenarios with an average sample size of 11 patients per group. Conclusions: In summary, DUO-207 is a novel, ultrasmall nanomedicine that can co-deliver paclitaxel and gemcitabine in a single intravenous infusion to treat stroma-rich cancers. DUO-207 demonstrated dose dependent hematological toxicities but improved clinical observations compared to SoC and lacked signals of renal and hepatoxicity. Toxicokinetic data from canines was used in a statistical model to determine patient numbers for phase 1b dosing using the CRM. Duo Oncology will conduct its clinical trial in 2025.

Investigating the Effectiveness of Coal-Fired Power Plant Operations: Management, Technical and Air Pollution Aspects

Coal-fired energy has been a major part of Malaysia's power supply, causing environmental pollution and slowing sustainable growth. To address these issues, we evaluated a coal-fired power plant's efficiency using a questionnaire completed by industry experts. This study seeks to find factors affecting coal-fired power generation efficiency and create a statistical model. The questionnaire covered five areas: best management practices, technology efficiency, cost efficiency, fuel efficiency, air pollution control, and the best available technique. Principal Component Analysis (PCA) was used to simplify large data sets. The results showed that 15 principal components were valid, with a KMO value of 0.836 (greater than 0.50) and a Bartlett Test value below 0.05. The results show a strong correlation between the best available technique and various indicators: best management practice (r=0.614, p&lt;0.01), technology efficiency (r=0.719, p&lt;0.01), cost efficiency (r=0.529, p&lt;0.05), fuel efficiency (r=0.662, p&lt;0.01), and air pollution control efficiency (r=-0.752, p&lt;0.01). The model indicates that verifying the standard operating procedure (SOP) is crucial for improving power generation efficiency and reducing human error (R²=0.914). This study pinpoints issues reducing power plant efficiency, particularly regarding emissions, and shows that the regression model is strong (R² = 0.916–0.647). It will assist policymakers and researchers in creating sustainable environmental management plans. Doi: 10.28991/ESJ-2025-09-01-06 Full Text: PDF

Does intestine length explain digesta retention times in birds and mammals?

Previous studies have indicated that across birds and mammals, body mass is a comparatively poor predictor of the time digesta is retained in the digestive tract (mean retention time, MRT). Rather, MRT might be determined by gastrointestinal anatomy, which can differ considerably within and between trophic guilds. Here, we used two recent literature compilations on the intestine length and the MRT in birds (n=33 species) and mammals (n=149) and applied comparative statistical approaches to assess whether intestine length is more closely correlated with MRT than body mass. Regardless of the statistical model used, whether small species (< 120g and any larger bats) were included or not, or whether birds and mammals were assessed together or separately, intestinal length generally yielded a better model fit to MRT than body mass, supporting the general concept. Nevertheless, data scatter was substantial, indicating that intestine length, though better than body mass, is still a limited explanatory factor for MRT. The intestine length-MRT relationship is an example of the direct statistical assessment of a generally presumed form-function relationship that is typically represented as a narrative. In the comparative literature, such assessments are rare.

Exploring the potential of regional cloud vertical structure climatology statistical model in estimating surface downwelling longwave radiation

Exploring the potential of regional cloud vertical structure climatology statistical model in estimating surface downwelling longwave radiation