Empirical Cumulative Distribution Research Articles

Statistical inference for innovation distribution in ARMA and multi-step-ahead prediction via empirical process

The kernel distribution estimator (KDE) is proposed based on residuals of the innovation distribution in the autoregressive moving-average (ARMA) time series. The deviation between KDE and the innovation distribution function is shown to converge to the Brownian bridge, leading to the construction of a Kolmogorov–Smirnov smooth simultaneous confidence band for the innovation distribution function. Additionally, an empirical cumulative distribution function (CDF) based on prediction residuals is introduced for the multi-step-ahead prediction error distribution function. This empirical process weakly converges to a Gaussian process with a specific covariance function. Furthermore, a quantile estimator is derived from the empirical CDF of prediction residuals, and multi-step-ahead prediction intervals (PIs) for future observations are established using these estimated quantiles. The PIs achieve the nominal prediction level asymptotically for the finite variance ARMA model. Simulation studies and analysis of crude oil price data confirm the validity of the asymptotic theory.

The Distance Between: An Algorithmic Approach to Comparing Stochastic Models to Time-Series Data

While mean-field models of cellular operations have identified dominant processes at the macroscopic scale, stochastic models may provide further insight into mechanisms at the molecular scale. In order to identify plausible stochastic models, quantitative comparisons between the models and the experimental data are required. The data for these systems have small sample sizes and time-evolving distributions. The aim of this study is to identify appropriate distance metrics for the quantitative comparison of stochastic model outputs and time-evolving stochastic measurements of a system. We identify distance metrics with features suitable for driving parameter inference, model comparison, and model validation, constrained by data from multiple experimental protocols. In this study, stochastic model outputs are compared to synthetic data across three scales: that of the data at the points the system is sampled during the time course of each type of experiment; a combined distance across the time course of each experiment; and a combined distance across all the experiments. Two broad categories of comparators at each point were considered, based on the empirical cumulative distribution function (ECDF) of the data and of the model outputs: discrete based measures such as the Kolmogorov–Smirnov distance, and integrated measures such as the Wasserstein-1 distance between the ECDFs. It was found that the discrete based measures were highly sensitive to parameter changes near the synthetic data parameters, but were largely insensitive otherwise, whereas the integrated distances had smoother transitions as the parameters approached the true values. The integrated measures were also found to be robust to noise added to the synthetic data, replicating experimental error. The characteristics of the identified distances provides the basis for the design of an algorithm suitable for fitting stochastic models to real world stochastic data.

Defining a clinically meaningful within-patient change threshold for the Cohen-Mansfield Agitation Inventory in Alzheimer’s dementia

IntroductionThe Cohen-Mansfield Agitation Inventory (CMAI) quantifies the frequency of agitation behaviors in elderly persons. This post hoc analysis of data from the brexpiprazole clinical program aimed to determine a meaningful within-patient change (MWPC) threshold for CMAI Total score among patients with agitation associated with dementia due to Alzheimer’s disease.MethodsData were included from three 12-week, multicenter, randomized, double-blind, placebo-controlled, parallel-arm trials of brexpiprazole for the treatment of agitation associated with dementia due to Alzheimer’s disease (ClinicalTrials.gov identifiers: NCT01862640, NCT01922258, NCT03548584). Change in CMAI Total score (range 29–203; higher scores indicate higher frequency of agitation behaviors) from baseline to Week 12 was the primary endpoint in each trial. MWPC thresholds were estimated from anchor-based mean change analyses and receiver operating characteristic (ROC) curves. The Clinical Global Impression–Severity of illness (CGI-S) and Clinical Global Impression–Improvement (CGI-I) scales, both as related to agitation, were used as anchors. Empirical cumulative distribution functions (eCDFs) and probability density functions (PDFs) were plotted as supportive evidence. Distribution-based methods were also employed.ResultsData from 898 patients were analyzed (mean age, 73.7 years; mean baseline CMAI Total score, 73.8). The mean CMAI Total score change corresponding to a difference of small improvement vs. stable (CGI-S one-point decrease vs. no change), or minimally improved vs. no change (CGI-I rating of 3 vs. 4), ranged from −10.6 to −13.5 points. The mean CMAI Total score change corresponding to a difference of moderate improvement vs. stable (CGI-S two-point decrease vs. no change), or much improved vs. no change (CGI-I rating of 2 vs. 4), ranged from −20.2 to −25.7 points. ROC curve analyses generally produced smaller estimates of meaningful change. eCDFs and PDFs showed good distribution and separation of CMAI Total score change between CGI-S/CGI-I categories. In distribution-based analyses, the minimal detectable change for CMAI Total score (10.5–11.8 points) was generally lower than anchor-suggested thresholds.ConclusionTriangulation of evidence from anchor- and distribution-based analyses supports an MWPC threshold for CMAI Total score of −20 points, with a threshold range of −15 to −25 points, in patients with agitation associated with dementia due to Alzheimer’s disease.

AoUPRS: A Cost-Effective and Versatile PRS Calculator for the All of Us Program.

The All of Us (AoU) Research Program provides a comprehensive genomic dataset to accelerate health research and medical breakthroughs. Despite its potential, researchers face significant challenges, including high costs and inefficiencies associated with data extraction and analysis. AoUPRS addresses these challenges by offering a versatile and cost-effective tool for calculating polygenic risk scores (PRS), enabling both experienced and novice researchers to leverage the AoU dataset for significant genomic discoveries. AoUPRS is implemented in Python and utilizes the Hail framework for genomic data analysis. It offers two distinct approaches for PRS calculation: the Hail MatrixTable (MT) and the Hail Variant Dataset (VDS). The MT approach provides a dense representation of genotype data, while the VDS approach offers a sparse representation, significantly reducing computational costs. In performance evaluations, the VDS approach demonstrated a cost reduction of up to 99.51% for smaller scores and 85% for larger scores compared to the MT approach. Both approaches yielded similar predictive power, as shown by logistic regression analyses of PRS for coronary artery disease, atrial fibrillation, and type 2 diabetes. The empirical cumulative distribution functions (ECDFs) for PRS values further confirmed the consistency between the two methods. AoUPRS is a versatile and cost-effective tool that addresses the high costs and inefficiencies associated with PRS calculations using the AoU dataset. By offering both dense and sparse data processing approaches, AoUPRS allows researchers to choose the approach best suited to their needs, facilitating genomic discoveries. The tool's open-source availability on GitHub, coupled with detailed documentation and tutorials, ensures accessibility and ease of use for the scientific community.

IGF1R and FLT1 in female endothelial cells and CHD2 in male microglia play important roles in Alzheimer's disease based on gender difference analysis

ObjectiveThis study investigated sex-specific pathogenesis mechanisms in Alzheimer's disease (AD) using single-nucleus RNA sequencing (snRNA-seq) data. MethodsData from the Gene Expression Omnibus (GEO) were searched using terms “Alzheimer's Disease”, “single cell”, and “Homo sapiens”. Studies excluding APOE E4 and including comprehensive gender information with 10× sequencing methods were selected, resulting in GSE157827 and GSE174367 datasets from human prefrontal cortex samples. Sex-stratified analyses were conducted on these datasets, and the outcomes of the analysis for GSE157827 were compared with those of GSE174367. The findings were validated using expression profiling from the mouse dataset GSE85162. Furthermore, real-time PCR experiments in mice further confirmed these findings. The Seurat R package was used to identify cell types, and batch effects were mitigated using the Harmony R package. Cell proportions by sex were compared using the Mann-Whitney-Wilcoxon test, and gene expression variability was displayed with an empirical cumulative distribution plot. Differentially expressed genes were identified using the FindMarkers function with the MAST test. Transcription factors were analyzed using the RcisTarget R package. ResultsSeven cell types were identified: astrocytes, endothelial cells, excitatory neurons, inhibitory neurons, microglia, oligodendrocytes, and oligodendrocyte progenitor cells. Additionally, five distinct subpopulations of both endothelial and microglial cells were also identified, respectively. Key findings included: (1) In endothelial cells, genes involved in synapse organization, such as Insulin Like Growth Factor 1 Receptor (IGF1R) and Fms Related Receptor Tyrosine Kinase 1(FLT1), showed higher expression in females with AD. (2) In microglial cells, genes in the ribosome pathway exhibited higher expression in males without AD compared to females (with or without AD) and males with AD. (3) Chromodomain Helicase DNA Binding Protein 2 (CHD2) negatively regulated gene expression in the ribosome pathway in male microglia, suppressing AD, this finding was further validated in mice. (4) Differences between Asians and Caucasians were observed based on sex and disease status stratification. ConclusionsIGF1R and FLT1 in endothelial cells contribute to AD in females, while CHD2 negatively regulates ribosome pathway gene expression in male microglia, suppressing AD in humans and mice.

Image Feature Extraction Using Symbolic Data of Cumulative Distribution Functions

Symbolic data analysis is an emerging field in statistics with great potential to become a standard inferential technique. This research introduces a new approach to image feature extraction using the empirical cumulative distribution function (ECDF) and distribution function of distribution values (DFDV) as symbolic data. The main objective is to reduce the dimension of huge pixel data by organizing them into more coherent pixel-intensity distributions. We propose a partitioning method with different breakpoints to capture pixel intensity variations effectively. This results in an ECDF representing the proportion of pixel intensities and a DFDV representing the probability distribution at specific points. The novelty of this approach lies in using ECDF and DFDV as symbolic features, thus summarizing the data and providing a more informative representation of the pixel value distribution, facilitating image classification analysis based on intensity distribution. The experimental results underscore the potential of this method in distinguishing image characteristics among existing image classes. Image features extracted using this approach promise image classification analysis with more informative image representations. In addition, theoretical insights into the properties of DFDV distribution functions are gained.

Association between GLIM-diagnosed malnutrition and quality of life in older patients with cancer

BackgroundOlder patients with cancer have a higher risk for malnutrition and impaired quality of life (QoL). The present study aimed to investigate the relationship between malnutrition diagnosed according to the Global Leadership Initiative Malnutrition (GLIM) criteria and QoL across various tumor types, and to evaluate the combined prognostic value of malnutrition and QoL in predicting survival among older patients with cancer. MethodsThis multicenter, observational cohort study included 5310 older patients with cancer and 2184 with malnutrition (moderate stage, n = 1023; severe stage, n = 1161). An empirical cumulative distribution curve was performed to illustrate the correlation between malnutrition and QoL. The primary objective was to investigate the association between malnutrition and QoL using logistic regression analysis. Survival analyses were performed to assess the combined prognostic value of malnutrition and QoL. ResultsThe median age of the patients (66.9% male, 33.1% female) was 70 years (interquartile range [IQR] 67–74 years) years. The median QoL score was highest in patients without malnutrition (91.88 [IQR 84.44–97.44]), followed by those with moderate (86.15 [IQR 76.18–93.85) and severe (82.31 [IQR 69.87–91.11]) malnutrition. Logistics regression revealed that the risk for developing impaired QoL increased 1.98 (95% confidence interval [CI] 1.64–2.38; P < 0.001) and 2.33 (95% CI 1.93–2.81; P < 0.001) times in patients with moderate and severe malnutrition, respectively. Kaplan–Meier curves showed that QoL in combination with GLIM criteria demonstrated a significant discriminative performance for survival and served as an independent prognostic factor among older patients with cancer, especially for lung and gastric cancers. ConclusionsMalnutrition diagnosed according to the GLIM criteria was a predictor of impaired QoL. Additionally, the combination of QoL and malnutrition demonstrated utility for predicting survival outcomes in older patients with cancer.

Exploring cumulative probability functions for streamflow drought magnitude: Global scale analysis and parametric vs. non-parametric comparisons

Streamflow droughts pose significant challenges to water resource management and environmental sustainability. The accurate characterization of streamflow drought magnitude is essential for effective mitigation, assessment and adaptation strategies. In this study, we explore the implications of choosing different cumulative probability distribution functions (cdfs) on the determination of streamflow drought magnitude, as assessed by the z-score values of the standardized streamflow index (SSI) and return periods. Our investigation encompasses a comprehensive global-scale analysis, with the aim of identifying the most suitable cdfs for characterizing streamflow droughts. To accomplish this objective, we incorporate global simulated streamflow values from the model WaterGAP 2.2d and observed streamflow values from 280 Global Runoff Data Centre (GRDC) stations for the period 1981 – 2010. We evaluate the performance of 118 parametric cdfs for each of the 12 calendar monthly streamflow values at each model grid cell and GRDC station to determine the best fitting parametric cdf. Moreover, we go beyond the conventional scope of such studies by further assessing the best-fitting cdfs alongside non-parametric cdfs such as the Empirical cumulative distribution function (ecdf) and the cumulative distribution function derived from the Kernel density estimation function (kcdf). Among our findings, we establish a subset of 23 parametric cdfs that exhibit the best fit for the global streamflow values concerning all 12 calendar monthly streamflow values at individual GRDC stations or grid cells within the specified period. Furthermore, we observe that the accuracy of streamflow simulation and the length of the reference period directly influence the selection of the most suitable parametric cdf. Our comparative analysis reaffirms the existing understanding that opting for the best-fitting parametric cdf, rather than a non-parametric alternative, mitigates the risk of overestimating drought magnitudes. However, we emphasize the crucial importance of considering the intended purpose, approach-specific sensitivities, and uncertainties when choosing the most suitable parametric cdf for any calendar monthly streamflow values.

Statistical downscaling of precipitation in northwestern Iran using a hybrid model of discrete wavelet transform, artificial neural networks, and quantile mapping

AbstractDownscaling of daily precipitation from Global Circulation Models (GCMs)-predictors at a station level, especially in arid and semi-arid regions, has remained a formidable challenge yet. The current study aims at proposing a coupled model of Discrete Wavelet Transform (DWT), Artificial Neural Networks (ANNs), and Quantile Mapping (QM) for statistical downscaling of daily precipitation. Given the historic (1978–2005) and future (2006–2100) predictors of eight-selected GCMs under Representative Concentration Pathways (RCPs) 2.6, 4.5, and 8.5, a viable DWT-ANN model was developed for each station. Subsequently, we linked QM to DWT-ANN for bias correction and drizzle effect postprocessing of the DWT-ANN-historic/future projected precipitation. The skill of DWT-ANN-QM was demonstrated using various evaluation metrics, including Taylor diagram, Quantile–Quantile plot, Empirical Cumulative Distribution Function, and wet/dry spell analysis. We appraise the efficacy of the coupled model at 12 weather stations over the Gharehsoo River Basin (GRB) in northwestern Iran. Compared to the observed wet/dry spells, the dry-spells were better simulated via DWT-ANN-QM rather than the wet-spells wherein length and exceedance probability of the spells were overestimated. Results indicated that the future precipitation across the GRB will rise, on average, from 10 to 17% depending on weather station. Seasonal spatial distribution of the middle future (2041–2070) precipitation illustrated that an increase for fall and winter, especially, is expected, whereas the amount of the future spring and summer precipitation is projected to be declined. Having been developed and tested in a semi-arid basin, the efficacy of the coupled model should be further assessed in more humid climates.

Calibrated Empirical Neutrosophic Cumulative Distribution Function Estimation for Both Symmetric and Asymmetric Data

The traditional stratification weight is widely used in survey sampling for estimation under stratified random sampling (StRS). A neutrosophic calibration approach is proposed under neutrosophic statistics for the first time with the aim of improving conventional stratification weight. This addresses the challenge of estimating the empirical cumulative distribution function (CDF) of a finite population using the neutrosophic technique. The neutrosophic technique extends traditional statistics, dealing with indeterminate, vague, and uncertain values. Thus, using additional information, we are able to obtain an effective estimate of the neutrosophic CDF. The suggested estimator yields an interval range in which the population empirical CDF is likely to exist rather than a single numerical value. The proposed family of neutrosophic estimators will be defined under suitable calibration constraints. A simulation study is also computed in order to assess the effectiveness of the suggested and adapted neutrosophic estimators using real-life symmetric and asymmetric datasets.

A Novel Application of Fractional Order Derivative Moth Flame Optimization Algorithm for Solving the Problem of Optimal Coordination of Directional Overcurrent Relays

The proper coordination of directional overcurrent relays (DOCRs) is crucial in electrical power systems. The coordination of DOCRs in a multi-loop power system is expressed as an optimization problem. The aim of this study focuses on improving the protection system’s performance by minimizing the total operating time of DOCRs via effective coordination with main and backup DOCRs while keeping the coordination constraints within allowable limits. The coordination problem of DOCRs is solved by developing a new application strategy called Fractional Order Derivative Moth Flame Optimizer (FODMFO). This approach involves incorporating the ideas of fractional calculus (FC) into the mathematical model of the conventional moth flame algorithm to improve the characteristics of the optimizer. The FODMFO approach is then tested on the coordination problem of DOCRs in standard power systems, specifically the IEEE 3, 8, and 15 bus systems as well as in 11 benchmark functions including uni- and multimodal functions. The results obtained from the proposed method, as well as its comparison with other recently developed algorithms, demonstrate that the combination of FOD and MFO improves the overall efficiency of the optimizer by utilizing the individual strengths of these tools and identifying the globally optimal solution and minimize the total operating time of DOCRs up to an optimal value. The reliability, strength, and dependability of FODMFO are supported by a thorough statistics study using the box-plot, histograms, empirical cumulative distribution function demonstrations, and the minimal fitness evolution seen in each distinct simulation. Based on these data, it is evident that FODMFO outperforms other modern nature-inspired and conventional algorithms.

Estimating the Distribution of True Rates of Visual Field Progression in Glaucoma.

The purpose of this study was to estimate the distribution of the true rates of progression (RoP) of visual field (VF) loss. We analyzed the progression of mean deviation over time in series of ≥ 10 tests from 3352 eyes (one per patient) from 5 glaucoma clinics, using a novel Bayesian hierarchical Linear Mixed Model (LMM); this modeled the random-effect distribution of RoPs as the sum of 2 independent processes following, respectively, a negative exponential distribution (the "true" distribution of RoPs) and a Gaussian distribution (the "noise"), resulting in a skewed exGaussian distribution. The exGaussian-LMM was compared to a standard Gaussian-LMM using the Watanabe-Akaike Information Criterion (WAIC). The random-effect distributions were compared to the empirical cumulative distribution function (eCDF) of linear regression RoPs using a Kolmogorov-Smirnov test. The WAIC indicated a better fit with the exGaussian-LMM (estimate [standard error]: 192174.4 [721.2]) than with the Gaussian-LMM (192595 [697.4], with a difference of 157.2 [22.6]). There was a significant difference between the eCDF and the Gaussian-LMM distribution (P < 0.0001), but not with the exGaussian-LMM distribution (P = 0.108). The estimated mean (95% credible intervals, CIs) "true" RoP (-0.377, 95% CI = -0.396 to -0.359 dB/year) was more negative than the observed mean RoP (-0.283, 95% CI = -0.299 to -0.268 dB/year), indicating a bias likely due to learning in standard LMMs. The distribution of "true" RoPs can be estimated with an exGaussian-LMM, improving model accuracy. We used these results to develop a fast and accurate analytical approximation for sample-size calculations in clinical trials using standard LMMs, which was integrated in a freely available web application.

Prolonged lung-to-finger circulation time indicates an increased risk of intermittent hypoxaemia in sleep apnoea patients.

Intermittent hypoxaemia is closely associated with cardiovascular dysfunction and may be a more accurate indicator of obstructive sleep apnoea (OSA) severity than conventional metrics. Another key factor is the lung-to-finger circulation time (LFCt), defined as the duration from the cessation of a respiratory event to the lowest point of oxygen desaturation. LFCt serves as a surrogate marker for circulatory delay and is linked with cardiovascular function. Yet, the specific associations between respiratory and hypoxaemia characteristics and LFCt in patients with OSA remain unclear. This study aims to investigate these associations, ultimately contributing to a more nuanced understanding of OSA severity. The study comprised 878 in-lab polysomnographies of patients with suspected OSA. The conventional OSA metrics were computed along with nine hypoxaemia metrics and then divided into quartiles (Q1-Q4) based on respiratory event duration. In addition, these were further divided into subquartiles based on LFCt. The empirical cumulative distribution functions (CDFs) and linear regression models were used to investigate the association between desaturation metrics and LFCt. The results showed that prolonged LFCt was associated with increased hypoxic severity. Based on CDFs, the hypoxic severity significantly increased with longer LFCt despite the duration of respiratory events. Furthermore, fall duration was elevated in patients with longer LFCt (Q1- desaturation fall duration (FallDur): 14.6 s; Q4-FallDur: 29.8 s; p<0.0001). The regression models also showed significant association between hypoxic severity and LFCt (Q1-desaturation fall slope (FallSlope): β=-3.224; Q4-FallSlope: β=-6.178; p<0.0001). Considering LFCt along with desaturation metrics might be useful in estimating the association between the severity of OSA, physiological consequences of respiratory events and cardiac health.

Regional climate models and bias correction methods for rainfall-runoff modeling in Katar watershed, Ethiopia

Systematic errors in regional climate models (RCMs) hinder their implementation and lead to uncertainties in regional hydrological climate change studies. As a result, checking the accuracy of climate model simulations and applying bias correction are preliminary methods for achieving consistent findings. Therefore, identifying suitable RCM models for bias correction is important for providing reliable inputs for evaluating climate change impacts. The impacts of bias correction methods on streamflow were assessed on the Katar catchment within the Lake Ziway subbasin using coordinated regional climate downscaling experiments with a spatial resolution of 50 km (CORDEX-44) RCMs through the Integrated Hydrological Modelling System (IHMS) version 6.3. This study evaluated fourteen RCM models under five precipitation and three temperature bias correction methods for the Katar catchment. Statistical approaches, such as bias (PBIAS), the root mean square error (RMSE), the mean absolute error (MAE), the coefficient of variation (CV), the coefficient of determination (R2), and the relative volume error (RVE), are used for performance analysis. GERICS-MPI, RAC4-NOAA-2G, and CCLM4-NCCR-AFR-22 have better performances for both rainfall and temprature. The empirical cumulative distribution function (ECDF) method performed best in removing bias from the frequency-based statistics of rainfall and streamflow, followed by the power transformation (PT), distribution mapping (DM), local intensity scaling (LOCI), and linear scaling (LS) methods. Specifically, for temperature, the VARI and DM methods perform better in frequency-based statistics than the LS method. The performance of hydrological modeling is strongly affected by the selection of rainfall bias correction methods. In addition, the effect of the temperature bias correction method was not significant. The adequacy of the BCM depends on the RCM models and regional context. Therefore, the BCM implementation procedure can be adapted from region to region. This study revealed that the performance of the RCM models differed and that the errors in the RCM model outputs were reduced by the use of bias correction methods.

Accelerating Adversarially Robust Model Selection for Deep Neural Networks via Racing

Recent research has introduced several approaches to formally verify the robustness of neural network models against perturbations in their inputs, such as the ones that occur in adversarial attacks. At the same time, this particular verification task is known to be computationally challenging. More specifically, assessing the robustness of a neural network against input perturbations can easily take several hours of compute time per input vector, even when using state-of-the-art verification approaches. In light of this, it becomes challenging to select from a given set of neural network models the one that is best in terms of robust accuracy, i.e., the fraction of instances for which the model is known to be robust against adversarial perturbations, especially when given limited computing resources. To tackle this problem, we propose a racing method specifically adapted to the domain of robustness verification. This racing method utilises Delta-values, which can be seen as an efficiently computable proxy for the distance of a given input to a neural network model to the decision boundary. We present statistical evidence indicating significant differences in the empirical cumulative distribution between robust and non-robust inputs as a function of Delta-values. Using this information, we show that it is possible to reliably expose vulnerabilities in the model with relatively few input iterations. Overall, when applied to selecting the most robust network from sets of 31 MNIST and 27 CIFAR-10 networks, our proposed method achieves speedups of a factor of 108 and 42, respectively, in terms of cumulative running time compared to standard local robustness verification on the complete testing sets.

Meaningful within-patient change for clinical outcome assessments: model-based approach versus cumulative distribution functions

ABSTRACT Objectives The FDA recommends the use of anchor-based methods and empirical cumulative distribution function (eCDF) curves to establish a meaningful within-patient change (MWPC) for a clinical outcome assessment (COA). In practice, the estimates obtained from model-based methods and eCDF curves may not closely align, although an anchor is used with both. To help interpret their results, we investigated and compared these approaches. Methods Both repeated measures model (RMM) and eCDF approaches were used to estimate an MWPC on a target COA. We used both real-life (ClinicalTrials.gov: NCT02697773) and simulated data sets that included 688 patients with up to six visits per patient, target COA (range 0 to 10), and an anchor measure on patient global assessment of osteoarthritis from 1 (very good) to 5 (very poor). Ninety-five percent confidence intervals for the MWPC were calculated by the bootstrap method. Results The distribution of the COA score changes affected the degree of concordance between RMM and eCDF estimates. The COA score changes from simulated normally distributed data led to greater concordance between the two approaches than did COA score changes from the actual clinical data. The confidence intervals of MWPC estimate based on eCDF methods were much wider than that by RMM methods, and the point estimate of eCDF methods varied noticeably across visits. Conclusions Our data explored the differences of model-based methods over eCDF approaches, finding that the former integrates more information across a diverse range of COA and anchor scores and provides more precise estimates for the MWPC.

Feasibility of using real-world free thyroxine data from the US and Europe to enable fast and efficient transfer of reference intervals from one population to another

ObjectivesThe direct approach for determining reference intervals (RIs) is not always practical. This study aimed to generate evidence that a real-world data (RWD) approach could be applied to transfer free thyroxine RIs determined in one population to a second population, presenting an alternative to performing multiple RI determinations. Design and methodsTwo datasets (US, n = 10,000; Europe, n = 10,000) were created from existing RWD. Descriptive statistics, density plots and cumulative distributions were produced for each data set and comparisons made. Cumulative probabilities at the lower and upper limits of the RIs were identified using an empirical cumulative distribution function. According to these probabilities, estimated percentiles for each dataset and estimated differences between the two sets of percentiles were obtained by case resampling bootstrapping. The estimated differences were then evaluated against a pre-determined acceptance criterion of ≤7.8% (inter-individual biological variability). The direct approach was used to validate the RWD approach. ResultsThe RWD approach provided similar descriptive statistics for both populations (mean: US = 16.1 pmol/L, Europe = 16.4 pmol/L; median: US = 15.4 pmol/L, Europe = 15.8 pmol/L). Differences between the estimated percentiles at the upper and lower limits of the RIs fulfilled the pre-determined acceptance criterion and the density plots and cumulative distributions demonstrated population homogeneity. Similar RI distributions were observed using the direct approach. ConclusionsThis study provides evidence that a RWD approach can be used to transfer RIs determined in one population to another.

Parallel multi-objective optimization for expensive and inexpensive objectives and constraints

Expensive objectives and constraints are key characteristics of real-world multi-objective optimization problems. In practice, they often occur jointly with inexpensive objectives and constraints. This paper presents the Inexpensive Objectives and Constraints Self-Adapting Multi-Objective Constraint Optimization algorithm that uses Radial Basis function Approximations (IOC-SAMO-COBRA) for such problems. This is motivated by the recently proposed Inexpensive Constraint Surrogate-Assisted Non-dominated Sorting Genetic Algorithm II (IC-SA-NSGA-II). These algorithms and their counterparts that do not explicitly differentiate between expensive and inexpensive objectives and constraints are compared on 22 widely used test functions. The IOC-SAMO-COBRA algorithm finds significantly better (identical/worse) Pareto fronts in at least 78% (6%/16%) of all test problems compared to IC-SA-NSGA-II measured with both the hypervolume and Inverted Generational Distance+ performance metric. The empirical cumulative distribution functions confirm this advantage for both algorithm variants that exploit the inexpensive constraints. In addition, the proposed method is compared against state-of-the-art practices on a real-world cargo vessel design problem. On this 17-dimensional two-objective practical problem, the proposed IOC-SAMO-COBRA outperforms SA-NSGA-II as well. From an algorithmic perspective, the comparison identifies specific strengths of both approaches and indicates how they should be hybridized to combine their best components.

Distinguishing Geogenic Load and Anthropogenic Contribution to Soil Contamination in Mineralised Mountain Landscape of Ore Mountains (Czech Republic) Using Cumulative Distribution Functions

In ore regions impacted by mining and metal smelting emissions, distinguishing between geogenic anomalies and anthropogenic contamination poses a significant challenge. In a study from two areas with different mining histories in the Ore Mountains, Czech Republic, we demonstrate that sampling of topsoils and subsoils respecting local geology and correct soil data treatment respecting soil textural variability effects are indispensable to the correct construction and interpretation of geochemical maps and identification of anthropogenic contamination by As, Cu, Pb, and Zn. The list of analysed elements must include both potentially toxic and lithogenic elements, otherwise natural controls of soil composition cannot be deciphered. By using empirical cumulative distribution functions, we found that local backgrounds for As/Fe and Pb/Ti are naturally elevated (5.7 to 9.8 times and 2.1 to 2.7 times higher, respectively) compared to the global averages. We constructed geochemical maps with topsoil minus subsoil concentrations to show the main directions of spreading anthropogenic contamination. The anthropogenic diffuse contamination contribution was calculated and expressed as an enrichment relative to the local background (16% and 12% for As/Fe and 17% and 14% for Pb/Ti, respectively). This corresponds to topsoil enrichment by ca. 15 and 14 mg kg−1 for As and ca. 35 and 42 mg kg−1 for Pb in the two study areas. The obtained estimates were comparable to the results from the local peat archives. The approach we used is efficient in deciphering natural and anthropogenic controls of PTEs in geochemically complicated areas.

542 - Validation of the skin pain numerical rating scale of the Pruritus and Symptoms Assessment for Atopic Dermatitis for adults and adolescents with moderate-to-severe atopic dermatitis

Abstract Background Skin pain is a common and burdensome symptom of atopic dermatitis (AD), and its severity increases with disease progression. The Pruritus and Symptoms Assessment for Atopic Dermatitis (PSAAD) is a validated 11-item patient-reported instrument developed in accordance with regulatory agency guidance for assessment of the daily symptoms of patients with AD, including skin pain. Objective To establish content validity and evaluate the psychometric properties of the skin pain numerical rating scale (NRS) item of the PSAAD. Methods The skin pain NRS is a single-item measure from the PSAAD and is used to assess skin pain severity over the past 24 hours with the question “How painful was your skin over the past 24 hours?” on a 10-point scale from 0 (not painful) to 10 (extremely painful). A qualitative validation analysis consisting of concept elicitation (CE) interviews; electronic completion of the PSAAD measure, including the skin pain NRS; and cognitive debriefing (CD) interviews was conducted for adults and adolescents with mild-to-severe AD. Evaluation of psychometric properties of the skin pain NRS—including test-retest reliability, estimation of meaningful within-patient change (MWPC), known-group validity, ability to detect change, construct validity, quality of completion, and ceiling and floor effects—was conducted based on a post hoc qualitative and quantitative analysis of pooled data, with skin pain NRS as part of the PSAAD in the abrocitinib monotherapy phase 3 trials JADE MONO-1 (NCT03349060) and JADE MONO-2 (NCT03575871). Data from patients (≥12 years of age) with moderate-to-severe AD were pooled across all treatment arms. Results Among 30 CE interviews (adolescents [12-17 years], n=15; adults [≥18 years], n=15) conducted over 2 rounds of testing, 20 of 30 (67%) patients reported skin pain. During CD interviews (n=30), 100% of patients interpreted the skin pain NRS item as intended, and 73% reported it as relevant. The psychometric validation analysis included 736 patients (JADE MONO-1, N=347; JADE MONO-2, N=389). The test-retest reliability of the skin pain NRS was evidenced by large intraclass correlation coefficients (ICC; 0.76 and 0.72 in JADE MONO-1 and MONO-2, respectively) for a single daily skin pain score, which increased to 0.93 and 0.91 for a measurement averaging at least 4 scores per week. Convergent validity was demonstrated by correlations between skin pain and other clinician- and patient-­reported AD measures (median correlation &amp;gt;0.4 starting at week 4). The skin pain NRS distinguished between “clear” and “severe” disease severity groups, assessed using the Patient Global Assessment (PtGA) and Investigator’s Global Assessment (IGA) as continuous and categorical anchors (P&amp;lt;0.0001); differences were also significant among other disease severity groups using the PtGA and IGA as continuous anchors (P&amp;lt;0.0001). Based on the PtGA and IGA anchor analysis, the estimated MWPC was 1.9 and ranged from 2.7 to 3.9 points using the empirical cumulative distribution function analysis. Ability to detect change was demonstrated by linear relationships between disease severity measures and skin pain scores (correlation of ≥0.5 between the skin pain NRS and the PtGA). More than 90% of patients provided at least 4 daily skin pain scores each week. No floor or ceiling effects were observed. Conclusions The qualitative and quantitative data from initial PSAAD development and psychometric evaluation of the skin pain NRS from the PSAAD support its content validity, reliability, construct validity, and ability to detect change. These findings corroborate the 4-point improvement in skin pain as the adequate and meaningful cut-off to define a skin pain responder in JADE MONO-1 and MONO-2.