Distributional Assumptions Research Articles

Multidimensional scaling improves distance-based clustering for microbiome data.

Clustering patients into subgroups based on their microbial compositions can greatly enhance our understanding of the role of microbes in human health and disease etiology. Distance-based clustering methods, such as partitioning around medoids (PAM), are popular due to their computational efficiency and absence of distributional assumptions. However, the performance of these methods can be suboptimal when true cluster memberships are driven by differences in the abundance of only a few microbes, a situation known as the sparse signal scenario. We demonstrate that classical multidimensional scaling (MDS), a widely used dimensionality reduction technique, effectively denoises microbiome data and enhances the clustering performance of distance-based methods. We propose a two-step procedure that first applies MDS to project high-dimensional microbiome data into a low-dimensional space, followed by distance-based clustering using the low-dimensional data. Our extensive simulations demonstrate that our procedure offers superior performance compared to directly conducting distance-based clustering under the sparse signal scenario. The advantage of our procedure is further showcased in several real data applications. The R package MDSMClust is available at https://github.com/wxy929/MDS-project. gchen25@wisc.edu. Supplementary data are available at Bioinformatics online.

Adaptive transformer modelling of density function for nonparametric survival analysis

Survival analysis holds a crucial role across diverse disciplines, such as economics, engineering and healthcare. It empowers researchers to analyze both time-invariant and time-varying data, encompassing phenomena like customer churn, material degradation and various medical outcomes. Given the complexity and heterogeneity of such data, recent endeavors have demonstrated successful integration of deep learning methodologies to address limitations in conventional statistical approaches. However, current methods typically involve cluttered probability distribution function (PDF), have lower sensitivity in censoring prediction, only model static datasets, or only rely on recurrent neural networks for dynamic modelling. In this paper, we propose a novel survival regression method capable of producing high-quality unimodal PDFs without any prior distribution assumption, by optimizing novel Margin-Mean-Variance loss and leveraging the flexibility of Transformer to handle both temporal and non-temporal data, coined UniSurv. Extensive experiments on several datasets demonstrate that UniSurv places a significantly higher emphasis on censoring compared to other methods.

Assessment of Reliability Allocation Methods for Electronic Systems: A Systematic and Bibliometric Analysis

Reliability allocation is the process of assigning reliability targets to sub-systems within a system to meet the overall reliability requirements. However, many traditional reliability allocation methods rely on assumptions that are often unrealistic, leading to misleading, unachievable, and costly outcomes. This paper provides a historical review of reliability allocation methods, focusing on the Weighing Factor Method (WFM), with a detailed analysis of its main findings, assumptions, and limitations. Additionally, the review covers methods for reliability optimization, redundancy optimization, and multi-state system optimization, highlighting their strengths and shortcomings. A case study is presented to demonstrate how the assumption of an exponential distribution impacts the reliability allocation process, showing the limitations it imposes on practical implementations. Furthermore, a bibliometric analysis is conducted to assess publication trends in the field of reliability allocation. Through examples, particularly in the context of electronic systems using commercial off-the-shelf (COTS) components, the challenges are discussed, and recommendations for alternative approaches to improve the reliability allocation process are provided.

Causal Discovery and Reasoning for Continuous Variables with an Improved Bayesian Network Constructed by Locality Sensitive Hashing and Kernel Density Estimation

The structure learning of a Bayesian network (BN) is a crucial process that aims to unravel the complex dependencies relationships among variables using a given dataset. This paper proposes a new BN structure learning method for data with continuous attribute values. As a non-parametric distribution-free method, kernel density estimation (KDE) is applied in the conditional independence (CI) test. The skeleton of the BN is constructed utilizing the test based on mutual information and conditional mutual information, delineating potential relational connections between parents and children without imposing any distributional assumptions. In the searching stage of BN structure learning, the causal relationships between variables are achieved by using the conditional entropy scoring function and hill-climbing strategy. To further enhance the computational efficiency of our method, we incorporate a locality sensitive hashing (LSH) function into the KDE process. The method speeds up the calculations of KDE while maintaining the precision of the estimates, leading to a notable decrease in the time required for computing mutual information, conditional mutual information, and conditional entropy. A BN classifier (BNC) is established by using the computationally efficient BN learning method. Our experiments demonstrated that KDE using LSH has greatly improved the speed compared to traditional KDE without losing fitting accuracy. This achievement underscores the effectiveness of our method in balancing speed and accuracy. By giving the benchmark networks, the network structure learning accuracy with the proposed method is superior to other traditional structure learning methods. The BNC also demonstrates better accuracy with stronger interpretability compared to conventional classifiers on public datasets.

Exhalation of Rn-219 by patients treated with Radium-223

BackgroundTreatment with Ra-223 dichloride is approved for the therapy of castration resistant prostate cancer (CRPC) with symptomatic bone metastases and no known visceral metastases in Europe since 2013, and Ra-223 is under discussion for labelling other molecules and nanoparticles. The direct progeny of Ra-223 is Rn-219, also known as actinon, a radioactive noble gas with a half-life of 3.98 s. This Rn-219 can be exhaled by patients while Ra-223 is present in the blood. Hence, direct measurements for assessing the exhalation of Rn-219 were performed for the first time in the context of the non-interventional multicenter study “RAPSODY”, a substudy to the international early access program, which aimed at assessing the radiation exposure of relatives of patients suffering from castration resistant prostate cancer with bone metastases and treated with Ra-223 dichloride in an outpatient setting, in order to investigate if this kind of method is functional and tolerated by the patients.MethodsRn-219 was measured directly in patients’ exhalations using Alphaguard radon monitors (Saphymo, formerly Genitron, Frankfurt, Germany), originally intended for the measurement of Rn-222, and custom-made breath-test kits. Measurements were performed 20–30 min p. i. and 3–4 h p. i. In total, datasets from 21 administrations in 14 patients were obtained.ResultsAlthough 75% of the measurement data 20–30 min p. i. and 35% of the measurement data 3–4 h p. i., respectively, were censored due to exceedance of the upper limit of the Alphaguards’ measurement range in the applied measurement setup, statistical data were derived based on the assumption of lognormal distributions. For measurements 3–4 h p. i., mean activity concentrations of Rn-219 in exhaled breath of approx. 4.4 kBq/l were obtained. In measurements 20–30 min p. i., the expectation value of the activity concentration of approx. 6 kBq/l, derived by statistical methods, was higher.ConclusionsDirect measurements using Alphaguard instruments are suitable for assessing the exhalation of Rn-219 by patients treated with Ra-223. The measurement method is well tolerated by the patients. Rn-219 is present in patients’ exhalations. Our results are in accordance with published data obtained using other, indirect measurement methods.

Semi‐Parametric Least‐Area Linear‐Circular Regression Through Möbius Transformation

ABSTRACTThis paper introduces a novel regression model designed for angular response variables with linear predictors, utilizing a generalized Möbius transformation to define the regression curve. By mapping the real axis to the circle, the model effectively captures the relationship between linear and angular components. A key innovation is the introduction of an area‐based loss function, inspired by the geometry of a curved torus, for efficient parameter estimation. The semi‐parametric nature of the model eliminates the need for specific distributional assumptions about the angular error, enhancing its versatility. Extensive simulation studies, incorporating von Mises and wrapped Cauchy distributions, highlight the robustness of the framework. The model's practical utility is demonstrated through real‐world data analysis of Bitcoin and Ethereum, showcasing its ability to derive meaningful insights from complex data structures.

Bayesian p-curve mixture models as a tool to dissociate effect size and effect prevalence

Much research in the behavioral sciences aims to characterize the “typical” person. A statistically significant group-averaged effect size is often interpreted as evidence that the typical person shows an effect, but that is only true under certain distributional assumptions for which explicit evidence is rarely presented. Mean effect size varies with both within-participant effect size and population prevalence (proportion of population showing effect). Few studies consider how prevalence affects mean effect size estimates and existing estimators of prevalence are, conversely, confounded by uncertainty about effect size. We introduce a widely applicable Bayesian method, the p-curve mixture model, that jointly estimates prevalence and effect size by probabilistically clustering participant-level data based on their likelihood under a null distribution. Our approach, for which we provide a software tool, outperforms existing prevalence estimation methods when effect size is uncertain and is sensitive to differences in prevalence or effect size across groups or conditions.

Tooth design and verification of face spline transmission in hub bearing

The hub bearing with face spline transmission is a new type of hub bearing. The design method and standards are lack. In this work, the geometric relationship of the tooth profile parameters and the meshing situation are derived for the hub bearing face spline. The outer diameter D, number of teeth Z, and face tooth profile angle φ are key design parameters. The verification conditions for preload, extrusion stress, tooth root bending stress, and shear stress are established based on strength theory and assumption of uniform load distribution. To validate the design, a case study is conducted on the hub bearing face spline in a certain vehicle model, with theoretical calculation and simulation of stress by using Finite Element Method. The present FEM results compare well with those of the literature data. Finally, through the incorporation the torque strength and durability tests of the face spline, the reliability of the design theory in this work is confirmed. The results indicates that, the tooth tip fillet r1 has a significant impact on the meshing area, the maximum principal stress near the tooth root is highest at the arc of the tooth root, proving that the selection of the dangerous section is appropriate. The work has value in promoting the development of automotive wheel hub bearings.

Joint modelling location and scale with the LTS estimation method

The joint modelling of location and scale presents significant challenges in regression, particularly in handling outliers and variance heterogeneity. Robust estimation methods are crucial in this context to ensure reliable analyses. This paper introduces a novel joint location and scale model (JLSM-LTS) based on the least trimmed squares (LTS) estimation method, specifically designed to address these issues. We present a detailed estimation procedure for accurately determining JLSMLTS parameters. To evaluate its effectiveness, we perform extensive simulations and apply the model to a real dataset. For comparison, we include alternative models: the joint location and scale model with normal distribution assumptions (JLSMN) and the M-regression-based models (JLSM-M) using Huber and Tukey functions. The results demonstrate the robustness of JLSM-LTS in managing outliers and heteroscedasticity, highlighting its advantages in joint modelling scenarios and its potential to enhance regression analysis under challenging conditions.

A Bayesian joint bent-cable model for longitudinal measurements and survival time with heterogeneous random-effects distributions

ABSTRACT Biomarkers are measured repeatedly in clinical studies until a pre-defined endpoint, such as death from certain causes, is reached. Such repeated measurements may present a dynamic process for understanding when to expect the study’s endpoint. Joint modelling is often employed to handle such a model. Typically, shared random effects are assumed to be common to both the longitudinal component and the study’s endpoint. These shared random effects usually assume homogeneous and follow a normal distribution. However, identifying homogeneous subgroups is important when the underlying population is heterogeneous. This issue has received little attention in the literature, particularly for multi-phase longitudinal responses. In this paper, we propose a joint modelling approach for longitudinal and survival models using a bent-cable mixed model for longitudinal measurements and a Weibull distribution for the survival component. We also incorporate a finite mixture of normal distribution assumptions to account for the unobserved heterogeneity in the shared random effects model. A Bayesian MCMC is developed for parameter estimation and inferences. The proposed method is evaluated using simulation studies and the Tehran Lipid and Glucose Study dataset.

Missing data in the eligibility criteria of synthetic controls from real-world data

ABSTRACT Randomized clinical trials (RCTs) can benefit from using Real-World Data (RWD) as a supplementary data source to enhance their analysis. An Augmented RCT combines randomized treatment and control groups with synthetic controls derived from RWD. This way, the trial can achieve less prospective enrollment, higher statistical power, and lower costs. However, to ensure scientific validity, the synthetic controls must satisfy the same eligibility criteria as the trial participants. A major challenge is that RWD often have missing data that hinder the eligibility assessment. This problem has been overlooked in the literature and this paper offers statistical solutions to address it. We use multiple imputations to handle missing data in the variables involved in the eligibility criteria. We also propose a generalized propensity score weighting procedure to adjust for the life expectancy requirement, a common eligibility criterion in oncology clinical trials but usually unavailable in RWD. Since the life expectancy is an unmeasured confounder, we discuss the statistical assumptions required to correct its bias. We validate the proposed solutions through simulation studies and the analysis of an Augmented RCT in oncology.

Bidirectional f-Divergence-Based Deep Generative Method for Imputing Missing Values in Time-Series Data

Imputing missing values in high-dimensional time-series data remains a significant challenge in statistics and machine learning. Although various methods have been proposed in recent years, many struggle with limitations and reduced accuracy, particularly when the missing rate is high. In this work, we present a novel f-divergence-based bidirectional generative adversarial imputation network, tf-BiGAIN, designed to address these challenges in time-series data imputation. Unlike traditional imputation methods, tf-BiGAIN employs a generative model to synthesize missing values without relying on distributional assumptions. The imputation process is achieved by training two neural networks, implemented using bidirectional modified gated recurrent units, with f-divergence serving as the objective function to guide optimization. Compared to existing deep learning-based methods, tf-BiGAIN introduces two key innovations. First, the use of f-divergence provides a flexible and adaptable framework for optimizing the model across diverse imputation tasks, enhancing its versatility. Second, the use of bidirectional gated recurrent units allows the model to leverage both forward and backward temporal information. This bidirectional approach enables the model to effectively capture dependencies from both past and future observations, enhancing its imputation accuracy and robustness. We applied tf-BiGAIN to analyze two real-world time-series datasets, demonstrating its superior performance in imputing missing values and outperforming existing methods in terms of accuracy and robustness.

Application of Statistical Methods for the Characterization of Radon Distribution in Indoor Environments: A Case Study in Lima, Peru

This study evaluates the effectiveness of advanced statistical and geospatial methods for analyzing radon concentration distributions in indoor environments, using the district of San Martín de Porres, Lima, Peru, as a case study. Radon levels were monitored using LR-115 nuclear track detectors over three distinct measurement periods between 2015 and 2016, with 86 households participating. Detectors were randomly placed in various rooms within each household. Normality tests (Shapiro–Wilk, Anderson–Darling, and Kolmogorov–Smirnov) were applied to assess the fit of radon concentrations to a log-normal distribution. Additionally, analysis of variance (ANOVA) was used to evaluate the influence of environmental and structural factors on radon variability. Non-normally distributed data were normalized using a Box–Cox transformation to improve statistical assumptions, enabling subsequent geostatistical analyses. Geospatial interpolation methods, specifically Inverse Distance Weighting (IDW) and Kriging, were employed to map radon concentrations. The results revealed significant temporal variability in radon concentrations, with geometric means of 146.4 Bq·m−3, 162.3 Bq·m−3, and 150.8 Bq·m−3, respectively, across the three periods. Up to 9.5% of the monitored households recorded radon levels exceeding the safety threshold of 200 Bq·m−3. Among the interpolation methods, Kriging provided a more accurate spatial representation of radon concentration variability compared to IDW, allowing for the precise identification of high-risk areas. This study provides a framework for using advanced statistical and geospatial techniques in environmental risk assessment.

Ordered correlation forest

. Empirical studies in various social sciences often involve categorical outcomes with inherent ordering, such as self-evaluations of subjective well-being and self-assessments in health domains. While ordered choice models, such as the ordered logit and ordered probit, are popular tools for analyzing these outcomes, they may impose restrictive parametric and distributional assumptions. This article introduces a novel estimator, the ordered correlation forest, that can naturally handle non linearities in the data and does not assume a specific error term distribution. The proposed estimator modifies a standard random forest splitting criterion to build a collection of forests, each estimating the conditional probability of a single class. Under an “honesty” condition, predictions are consistent and asymptotically normal. The weights induced by each forest are used to obtain standard errors for the predicted probabilities and the covariates’ marginal effects. Evidence from synthetic data shows that the proposed estimator features a superior prediction performance than alternative forest-based estimators and demonstrates its ability to construct valid confidence intervals for the covariates’ marginal effects. Comparisons using various real-world data sets further highlight the advantages of forest-based estimators over parametric models in larger samples while showing that the ordered correlation forest remains competitive in smaller samples.

HOLT-WINTER METHOD FOR FORECASTING LIQUID ALUMINUM SULFATE USAGE FOR PROBABILISTIC INVENTORY MODELING Q WITH ERLANG DISTRIBUTION

Water is a natural resource important for life and daily activities. Water distributed by the Regional Drinking Water Company (PDAM) should include a coagulation process using liquid aluminum sulfate as a coagulant before it can be consumed. Therefore, this research aims to predict the need for liquid aluminum sulfate in PDAM from 2023 to 2024 using Holt-Winter's method. It also aims to evaluate the optimum liquid aluminum sulfate chemical inventory policy using Q probabilistic inventory model with Normal and erlang probabilistic distributions in PDAM. The data was obtained from Tirta Musi PDAM in Palembang City, Indonesia. The results of forecasting liquid aluminum sulfate demand level data with the Holt-Winter multiplicative method provide the smallest MAPE value. The erlang probability distribution assumption has been met through the Kolmogorov Smirnov test method. The erlang probabilistic inventory model provides a more optimal policy solution than the normal probabilistic inventory model, with minimum total cost and higher service level.

Review of Impact of Risk Reduction Sessions on Sexual Behaviors in HIV Prevention Trials: Insights from Africa.

Over the past two decades, numerous HIV prevention trials have targeted thousands of young African women, aiming not only to reduce transmissions through biomedical interventions but also to promote safe sexual practices through intensive risk reduction sessions. The primary objective of this study was to review the impact of risk reduction sessions in HIV prevention trials conducted in Africa. We assessed changes in sexual behaviors among women enrolled in various biomedical intervention trials across the African region using both visual and quantitative evaluations. Meta-analysis techniques were used to estimate overall odds ratios. In a sub-group analysis, we also used semiparametric regression models to capture important features of the associations between sexual behaviors across the study visits with minimal statistical assumptions. Key time points were identified using the "zero-crossing" technique. Overall summary odds ratio (OR) for condom use in last sex was estimated as 2.21 (95% CI 2.06, 2.36). In our sub-group analysis, women who reported multiple sexual partners declined (adjusted odds ratios (aORs) range: 0.61-0.67) while condom use in last sex improved over time (aORs ranged from 2.22-to-2.60); 347(57%) women HIV seroconverted within the first 6-months which was the most crucial time point with substantial reductions in risky behaviors. This review highlights that the gradual cumulative effect of risk reduction sessions, rather than an immediate substantial impact, may have significant implications in clinical research settings. Effective and sustainable risk reduction programs should include biological components such as pre-exposure prophylaxis (PrEP) to reduce HIV transmission.

Classical and Bayesian estimates of traffic intensity for M/M/1 queue with state-dependent service

This paper presents the estimates of the parameters of a Markovian queuing model that considers a Poisson arrival rate and a state-dependent service rate based on the system’s condition. State-dependent service implies that the server’s performance varies according to the number of customers waiting for service. If there’s a lengthy queue, the server operates more efficiently, whereas if there are fewer customers, the server works at a slower pace. The primary goal of this paper is to compute estimates for the traffic intensity ( ρ ), using two prominent statistical approaches: maximum likelihood (ML) and Bayesian estimation. The central premise of our study revolves around these estimation techniques under the assumption of various prior distributions, including the beta prior of first and second kind, gamma, truncated gamma, and uniform prior. To achieve our objectives, we employ the powerful method of Markov Chain Monte Carlo (MCMC) simulations. Here MCMC simulations serve as a crucial tool in generating estimates for traffic intensity, encompassing both ML and Bayesian perspectives. Moreover, we go beyond point estimates and obtained confidence intervals and credible intervals for the parameters. Also, we calculate the posterior risk which takes into consideration not only the estimates themselves but also the associated uncertainties.

Leveraging haplotype information in heritability estimation and polygenic prediction

Polygenic prediction has yet to make a major clinical breakthrough in precision medicine and psychiatry, where the application of polygenic risk scores is expected to improve clinical decision-making. Most widely used approaches for estimating polygenic risk scores are based on summary statistics from external large-scale genome-wide association studies, which rely on assumptions of matching data distributions. This may hinder the impact of polygenic risk scores in modern diverse populations due to small differences in genetic architectures. Reference-free estimators of polygenic scores are instead based on genomic best linear unbiased predictions and model the population of interest directly. We introduce a framework, named hapla, with a novel algorithm for clustering haplotypes in phased genotype data to estimate heritability and perform reference-free polygenic prediction in complex traits. We utilize inferred haplotype clusters to compute accurate heritability estimates and polygenic scores in a simulation study and the iPSYCH2012 case-cohort for depression disorders and schizophrenia. We demonstrate that our haplotype-based approach robustly outperforms standard genotype-based approaches, which can help pave the way for polygenic risk scores in the future of precision medicine and psychiatry.

Estimating percentiles of time-to-failure distribution obtained from a Weibull accelerated degradation model

We propose a nonparametric kernel estimation method to estimate the percentiles of the time-to-failure distribution under the usual use condition obtained from a Weibull accelerated degradation model. We discuss some of the well-known parametric method that used to estimate the time-to-failure distribution and its percentile under the usual use condition including ordinary least square method and maximum likelihood method. The different exiting methods were compared with the kernel method through simulation by using the mean square error and the bootstrap confidence interval length. In general, when the distributional assumption is available, the maximum likelihood estimator performs better than the other two estimators, while the kernel estimator performs better than the other two estimators when the distributional assumption is not available. Application to real data set was disscuced.

The Effectiveness of Emotion-Focused Therapy on Emotion Dysregulation and Resilience in Patients with Chronic Pain and Depressive Symptoms

The present study aimed to examine the effectiveness of emotion-focused therapy (EFT) on emotion dysregulation and resilience in patients with chronic pain and depressive symptoms. The present study was a quasi-experimental design with a pretest-posttest control group. The statistical population included all patients with chronic pain and depressive symptoms who visited counseling and psychology clinics in Yazd in 2024. A total of 30 individuals were selected through convenience sampling based on the inclusion and exclusion criteria. The research instruments included the Emotion Dysregulation Scale by Gratz and Roemer and the Connor-Davidson Resilience Scale. Participants in the experimental group received 12 one-hour sessions of emotion-focused therapy. Data analysis was conducted using SPSS-26 software and covariance analysis, considering statistical assumptions. The results of the covariance analysis indicated a significant difference between the experimental and control groups in the variables of emotion dysregulation and resilience (P < 0.05). Based on the study findings, emotion-focused therapy can be considered an appropriate intervention to support patients with chronic pain and depressive symptoms.