Distribution Of Observed Data Research Articles

CHI-SQUARE TESTS: A QUICK GUIDE FOR HEALTH RESEARCHERS

Pearsons chi-square (Χ²) tests are essential nonparametric statistical tools for analyzing associations among categorical data, making them crucial for research involving non-numeric variables. These tests are widely utilized in various research fields due to their independence from normal distribution assumptions. Chi-square tests are utilized to assess whether there is a significant association between groups, populations, or criteria, and to examine how closely observed data distributions align with expected ones. The three primary types of chi-square tests are: the Goodness-of-Fit test, which checks if the distribution of categorical data in a sample conforms to a predefined distribution the Test of Independence, which investigates whether there is a relationship between categorical variables within a single sample and the Test of Homogeneity, which compares the frequency counts of a categorical variable across multiple populations to see if their distributions are similar.For valid and reliable results, it is crucial to consider factors such as random sampling, adequate cell counts, sufficient sample size, and mutually exclusive variables. In healthcare research, chi-square tests are essential for analyzing risk factors, evaluating AYUSH treatments, assessing nursing interventions, and studying health behavior trends. This review underscores their importance in statistical analysis and evidence-based decision-making.

Improving prediction of groundwater quality in situations of limited monitoring data based on virtual sample generation and Gaussian process regression

The increasing pollution of aquifers by human activities over recent decades poses a threat to drinking water safety. While Gaussian Process Regression (GPR) is a robust tool for predicting and monitoring water quality, its effectiveness is hindered limitations of available data on model training and validation, known as the “small sample problem”. Various attempts to resolve this problem include virtual sample generation (VSG). This study aimed to increase the accuracy of GPR for predicting water quality in situations of limited datasets. Three VSG methods, namely Multi Distribution Mega-Trend Diffusion (MD-MTD), Generative Adversarial Network (GAN), and t-distributed stochastic nearest neighbor embedding (t-SNE) were compared for enhancing the accuracy of GPR model prediction of Strontium (Sr2+). The models were used to predict Sr2+ in the shallow aquifer system in Songyuan, Jilin Province. The results showed that t-SNE provided the most significant improvement to the accuracy of the GPR, with R2 increasing from 0.86 to 0.99 (12.98 %), followed by MD-MTD (R2 of 0.95, 9.39 %), with the least improvement obtained by GAN (R2 of 0.92, 5.98 %). Boxplots show that MD-MTD-GPR predictions do not fully capture observed data distributions. GANs accurately replicate the data distribution, while t-SNE-GPR achieves the highest prediction accuracy and handles data fluctuations. GPR accuracy improves with an increasing number of virtual samples but tends to decrease when the number exceeds 258 in this study. This study can guide the improvement of the accuracy of GPR for situations of limited datasets. The results of this study can help improve water quality management and drinking water safety in regions with sparse monitoring data.

Reconstruction of significant wave height distribution from sparse buoy data by using deep learning

Significant wave height plays a crucial role in influencing marine ecosystems, ocean shipping, and other maritime activities. The distribution of buoy observation data tends to be sparse. Gridded wave data obtained through numerical simulation typically offer broader applicability, albeit with higher computational demands. In this paper, a deep learning model based on Full Connected and Convolutional Neural Networks is proposed, utilizing sparse buoy observation data as input to reconstruct the distribution of significant wave height in the sea area. The model reconstruction results are validated using ERA5 data, demonstrating excellent performance. Additionally, we explore the influence of the model's spatial boundaries and the number of input buoys on reconstruction accuracy, as well as the adaptability of the model to different sea areas. This study provides a novel method and approach for the rapid and cost-effective retrieval of regional significant wave height.

Use of the instrumental inequalities in simulated mendelian randomization analyses with coarsened exposures.

Mendelian randomization (MR) requires strong unverifiable assumptions to estimate causal effects. However, for categorical exposures, the MR assumptions can be falsified using a method known as the instrumental inequalities. To apply the instrumental inequalities to a continuous exposure, investigators must coarsen the exposure, a process which can itself violate the MR conditions. Violations of the instrumental inequalities for an MR model with a coarsened exposure might therefore reflect the effect of coarsening rather than other sources of bias. We aim to evaluate how exposure coarsening affects the ability of the instrumental inequalities to detect bias in MR models with multiple proposed instruments under various causal structures. To do so,we simulated data mirroring existing studies of the effect of alcohol consumption on cardiovascular disease under a variety of exposure-outcome effects in which the MR assumptions were met for a continuous exposure. We categorized the exposure based on subject matter knowledge or the observed data distribution and applied the instrumental inequalities to MR models for the effects of the coarsened exposure. In simulations of multiple binary instruments, the instrumental inequalities did not detect bias under any magnitude of exposure outcome effect when the exposure was coarsened into more than 2 categories. However, in simulations of both single and multiple proposed instruments, the instrumental inequalities were violated in some scenarios when the exposure was dichotomized. The results of these simulations suggest that the instrumental inequalities are largely insensitive to bias due to exposure coarsening with greater than 2 categories, and could be used with coarsened exposures to evaluate the required assumptions in applied MR studies, even when the underlying exposure is truly continuous.

Linear Deconfounded Score Method: Scoring DAGs With Dense Unobserved Confounding.

This article deals with the discovery of causal relations from a combination of observational data and qualitative assumptions about the nature of causality in the presence of unmeasured confounding. We focus on applications where unobserved variables are known to have a widespread effect on many of the observed ones, which makes the problem particularly difficult for constraint-based methods, because most pairs of variables are conditionally dependent given any other subset, rendering the causal effect unidentifiable. In this article, we show that under the principle of independent mechanisms, unobserved confounding in this setting leaves a statistical footprint in the observed data distribution that allows for disentangling spurious and causal effects. Using this insight, we demonstrate that a sparse linear Gaussian directed acyclic graph (DAG) among observed variables may be recovered approximately and propose a simple adjusted score-based causal discovery algorithm that may be implemented with general-purpose solvers and scales to high-dimensional problems. We find, in addition, that despite the conditions we pose to guarantee causal recovery, performance in practice is robust to large deviations in model assumptions, and extensions to nonlinear structural models are possible.

Multiply robust estimators in longitudinal studies with missing data under control-based imputation.

Longitudinal studies are often subject to missing data. The recent guidance from regulatory agencies, such as the ICH E9(R1) addendum addresses the importance of defining a treatment effect estimand with the consideration of intercurrent events. Jump-to-reference (J2R) is one classical control-based scenario for the treatment effect evaluation, where the participants in the treatment group after intercurrent events are assumed to have the same disease progress as those with identical covariates in the control group. We establish new estimators to assess the average treatment effect based on a proposed potential outcomes framework under J2R. Various identification formulas are constructed, motivating estimators that rely on different parts of the observed data distribution. Moreover, we obtain a novel estimator inspired by the efficient influence function, with multiple robustness in the sense that it achieves n1/2-consistency if any pairs of multiple nuisance functions are correctly specified, or if the nuisance functions converge at a rate not slower than n-1/4 when using flexible modeling approaches. The finite-sample performance of the proposed estimators is validated in simulation studies and an antidepressant clinical trial.

Bounding the probabilities of benefit and harm through sensitivity parameters and proxies

Abstract We present two methods for bounding the probabilities of benefit (a.k.a. the probability of necessity and sufficiency, i.e., the desired effect occurs if and only if exposed) and harm (i.e., the undesired effect occurs if and only if exposed) under unmeasured confounding. The first method computes the upper or lower bound of either probability as a function of the observed data distribution and two intuitive sensitivity parameters, which can then be presented to the analyst as a 2-D plot to assist in decision-making. The second method assumes the existence of a measured nondifferential proxy for the unmeasured confounder. Using this proxy, tighter bounds than the existing ones can be derived from just the observed data distribution.

Deep Direct Discriminative Decoders for High-dimensional Time-series Data Analysis

The state-space models (SSMs) are widely utilized in the analysis of time-series data. SSMs rely on an explicit definition of the state and observation processes. Characterizing these processes is not always easy and becomes a modeling challenge when the dimension of observed data grows or the observed data distribution deviates from the normal distribution. Here, we propose a new formulation of SSM for high-dimensional observation processes with a heavy-tailed distribution. We call this solution the deep direct discriminative process (D4). The D4 brings deep neural networks’ expressiveness and scalability to the SSM formulation letting us build a novel solution that efficiently estimates the underlying state processes through high-dimensional observation signal.We demonstrate the D4 solutions in simulated and real data such as Lorenz attractors, Langevin dynamics, random walk dynamics, and rat hippocampus spiking neural data and show that the D4’s performance precedes traditional SSMs and RNNs. The D4 can be applied to a broader class of time-series data where the connection between high-dimensional observation and the underlying latent process is hard to characterize.

Mapping the milky way’s stellar halo with 2D data

ABSTRACT We propose a new method for measuring the spatial density distribution of the stellar halo of the Milky Way. Our method is based on a pairwise statistic of the distribution of stars in the sky, the angular two-point correlation function (ATPCF). The ATPCF utilizes two-dimensional data of stars only and is therefore immune to the large uncertainties in the determination of distances to stars. We test our method using mock stellar data coming from various models including the single power-law (SPL) and the broken power-law (BPL) density profiles. We also test the influence of axisymmetric flattening factors using both constant and varying values. We find that the ATPCF is a powerful tool for recovering the spatial distributions of the stellar haloes in our models. We apply our method to observational data from the type ab RR Lyrae catalogue in the Catalina Survey Data Release 1. In the 3-parameter BPL model, we find that $s_{1}=2.46_{-0.20}^{+0.18}, s_{2}=3.99_{-1.33}^{+0.75}$, and $r_{0}=31.11_{-5.88}^{+7.61}$, which are in good agreement with previous results. We also find that introducing an extra parameter, the radially varying flattening factor, greatly improves our ability to model accurately the observed data distribution. This implies perhaps that the stellar halo of the Milky Way should be regarded as oblate.

Medical prediction from missing data with max-minus negative regularized dropout.

Missing data is a naturally common problem faced in medical research. Imputation is a widely used technique to alleviate this problem. Unfortunately, the inherent uncertainty of imputation would make the model overfit the observed data distribution, which has a negative impact on the model generalization performance. R-Drop is a powerful technique to regularize the training of deep neural networks. However, it fails to differentiate the positive and negative samples, which prevents the model from learning robust representations. To handle this problem, we propose a novel negative regularization enhanced R-Drop scheme to boost performance and generalization ability, particularly in the context of missing data. The negative regularization enhanced R-Drop additionally forces the output distributions of positive and negative samples to be inconsistent with each other. Especially, we design a new max-minus negative sampling technique that uses the maximum in-batch values to minus the mini-batch to yield the negative samples to provide sufficient diversity for the model. We test the resulting max-minus negative regularized dropout method on three real-world medical prediction datasets, including both missing and complete cases, to show the effectiveness of the proposed method.

Dirichlet process mixture models for the analysis of repeated attempt designs.

In longitudinal studies, it is not uncommon to make multiple attempts to collect a measurement after baseline. Recording whether these attempts are successful provides useful information for the purposes of assessing missing data assumptions. This is because measurements from subjects who provide the data after numerous failed attempts may differ from those who provide the measurement after fewer attempts. Previous models for these designs were parametric and/or did not allow sensitivity analysis. For the former, there are always concerns about model misspecification and for the latter, sensitivity analysis is essential when conducting inference in the presence of missing data. Here, we propose a new approach which minimizes issues with model misspecification by using Bayesian nonparametrics for the observed data distribution. We also introduce a novel approach for identification and sensitivity analysis. We re-analyze the repeated attempts data from a clinical trial involving patients with severe mental illness and conduct simulations to better understand the properties of ourapproach.

Fault Diagnosis for Complex Equipment Based on Belief Rule Base with Adaptive Nonlinear Membership Function

Fault diagnosis of complex equipment has become a hot field in recent years. Due to excellent uncertainty processing capability and small sample problem modeling capability, belief rule base (BRB) has been widely used in the fault diagnosis. However, previous BRB models almost did not consider the diverse distributions of observation data which may reduce diagnostic accuracy. In this paper, a new fault diagnosis model based on BRB is proposed. Considering that the previous triangular membership function cannot address the diverse distribution of observation data, a new nonlinear membership function is proposed to transform the input information. Then, since the model parameters initially determined by experts are inaccurate, a new parameter optimization model with the parameters of the nonlinear membership function is proposed and driven by the gradient descent method to prevent the expert knowledge from being destroyed. A fault diagnosis case of laser gyro is used to verify the validity of the proposed model. In the case study, the diagnosis accuracy of the new BRB-based fault diagnosis model reached 95.56%, which shows better fault diagnosis performance than other methods.

Interplay of turbulence and proton-microinstability growth in space plasmas

Numerous prior studies have shown that as proton beta increases, a narrower range of proton temperature anisotropy values is observed. This effect has often been ascribed to the actions of kinetic microinstabilities because the distribution of observational data aligns with contours of constant instability growth rates in the beta-anisotropy plane. However, the linear Vlasov theory of instabilities assumes a uniform background in which perturbations grow. The established success of linear-microinstability theories suggests that the conditions in regions of extreme temperature anisotropy may remain uniform for a long enough time so that the instabilities have the chance to grow to sufficient amplitude. Turbulence, on the other hand, is intrinsically nonuniform and nonlinear. Thin current sheets and other coherent structures generated in a turbulent plasma may quickly destroy the uniformity. It is, therefore, not a-priori obvious whether the presence of intermittency and coherent structures favors or disfavors instabilities. To address this question, we examined the statistical distribution of growth rates associated with proton temperature-anisotropy driven microinstabilities and local nonlinear time scales in turbulent plasmas. Linear growth rates are, on average, substantially less than the local nonlinear rates. However, at the regions of extreme values of temperature anisotropy, near the “edges” of the populated part of the proton temperature anisotropy-parallel beta plane, the instability growth rates are comparable or faster than the turbulence time scales. These results provide a possible answer to the question as to why the linear theory appears to work in limiting plasma excursions in anisotropy and plasma beta.

Constraining the Hubble constant and its lower limit from the proper motion of extragalactic radio jets

ABSTRACT The Hubble constant (H0) is a measurement to describe the expansion rate of the Universe in the current era. However, there is a 4.4σ discrepancy between the measurements from the early Universe and the late Universe. In this research, we propose a model-free and distance-free method to constrain H0. Combining Friedman–Lemaître–Robertson–Walker cosmology with geometrical relation of the proper motion of extragalactic jets, the lower limit (H0,min) of H0 can be determined using only three cosmology-free observables: the redshifts of the host galaxies, and the approaching and receding angular velocities of radio jets. Using these, we propose to use the Kolmogorov–Smirnov test (K–S test) between cumulative distribution functions of H0,min to differentiate cosmology. We simulate 100, 200, and 500 extragalactic jets with three levels of accuracy of the proper motion (μa and μr), at 10, 5, and 1 per cent, corresponding to the accuracies of the current and future radio interferometers. We perform K–S tests between the simulated samples as theoretical distributions with different H0 and power-law index of velocity distribution of jets and mock observational data. Our result suggests increasing sample sizes leads to tighter constraints on both power-law index and the Hubble constant at moderate accuracy (i.e. $10$ and $5{{\ \rm per\ cent}}$), while at $1{{\ \rm per\ cent}}$ accuracy, increasing sample sizes leads to tighter constraints on power-law index more. Improving accuracy results in better constraints in the Hubble constant compared with the power-law index in all cases, but it alleviates the degeneracy.

Use of expert elicitation in the field of occupational hygiene: Comparison of expert and observed data distributions.

The concept of professional judgement underpins the way in which an occupational hygienist assesses an exposure problem. Despite the importance placed on professional judgement in the discipline, a method of assessment to characterise accuracy has not been available. In this paper, we assess the professional judgement of four occupational hygienists (‘experts’) when completing exposure assessments on a range of airborne contaminants across a number of job roles within a surface mining environment in the Pilbara region of Western Australia. The job roles assessed were project driller, mobile equipment operator, fixed plant maintainer, and drill and blast operator. The contaminants of interest were respirable crystalline silica, respirable dust, and inhalable dust. The novel approach of eliciting exposure estimates focusing on contaminant concentration and attribution of an exposure standard estimate was used. The majority of the elicited values were highly skewed; therefore, a scaled Beta distribution were fitted. These elicited fitted distributions were then compared to measured data distributions, the results of which had been collected as part of an occupational hygiene program assessing full-shift exposures to the same contaminants and job roles assessed by the experts. Our findings suggest that the participating experts within this study tended to overestimate exposures. In addition, the participating experts were more accurate at estimating percentage of an exposure standard than contaminant concentration. We demonstrate that this elicitation approach and the encoding methodology contained within can be applied to assess accuracy of exposure judgements which will impact on worker protection and occupational health outcomes.

Projection of Extreme Temperature Events over the Mediterranean and Sahara Using Bias-Corrected CMIP6 Models

Climate change continues to increase the intensity, frequency and impacts of weather and climate extremes. This work uses bias-adjusted Coupled Model Intercomparison Project Phase six (CMIP6) model datasets to investigate the future changes in temperature extremes over Mediterranean (MED) and Sahara (SAH) regions. The mid- (2041–2070) and far-future (2071–2100) are studied under two Shared Socioeconomic Pathways: SSP2-4.5 and SSP5-8.5 scenarios. Quantile mapping function greatly improved the performance of CMIP6 by reducing the notable biases to match the distribution of observation data, the Climate Prediction Center (CPC). Results show persistent significant warming throughout the 21st century, increasing with the increase in radiative forcing. The MED will record a higher increase in temperature extremes as compared to SAH. The warming is supported by the projected reduction in cold days (TX10p) and cold nights (TN10p), with the reduction in the number of cold nights exceeding cold days. Notably, warm spell duration index (WSDI) and summer days (SU) have a positive trend in both timelines over the entire study area. There is a need to simulate how climate sensitive sectors, such as water and agriculture, are likely to be affected by projected changes under different scenarios for informed decision making in the choice and implementation of adaptation and mitigation effective measures.

A spatially constrained skew Student’s-t mixture model for brain MR image segmentation and bias field correction

Accurate segmentation of brain magnetic resonance images is a key step in quantitative analysis of brain images. Finite mixture model is one of the most widely used methods in brain magnetic resonance image segmentation. However, due to the presence of intensity inhomogeneity artifact and noise, the image histogram distribution of brain MR images may follow a heavy tailed distribution or asymmetric distribution, which makes traditional finite mixture model, such as Gaussian mixture model, hard to achieve accurate segmentation results. To alleviate these problems, a novel spatially constrained finite skew student’s-t mixture model is proposed in this paper. Firstly, we propose anisotropic two-level spatial information, which combines the prior and posterior probabilities, to reduce the impact of noise. The proposed spatial information can preserve rich details, such as edges and corners. Secondly, we couple the anisotropic spatial information into the skew student’s-t distribution to fit the intensity distribution of observation data with heavy tail distribution or asymmetric distribution. Thirdly, we use a linear combination of a set of orthogonal basis functions to model the intensity inhomogeneities. Finally, the objective function integrates both tissue segmentation and the bias field estimation. In the implementation, we used an improved expectation maximization (EM) algorithm to estimate the model parameters. The experimental results of our model on synthetic data and brain magnetic resonance images are better than other state-of-the-art segmentation methods.

Immunohematological Parameters of Male and Female Blood Donors at Kenyatta National Hospital

Background: Immunohaematological reference intervals are critical in making accurate decisions in research, diagnosis and monitoring therapeutic outcomes. Consequently any gender – based disparities in the intervals need to be determined and so reflected when utilizing the ranges. This cross-section study to determine male and female immunohaematological reference intervals was conducted on suitable blood donors attended to at Kenyatta National Hospital blood donor Unit between 2018 and 2019.
 Objectives: To determine gender-based means, medians, 2.5 th and 97.5 th interquartile ranges of: CD4+ lymphocytes, red cell values, white cells absolute and differential counts and thrombocyte counts in suitable blood donors.
 Methods: A total of 108 (53.5%) female and 94 (46.5%) male volunteer blood donors aged between 18 and 60 years were recruited consecutively as they consented. Bootstrap methods were used to calculate means, medians and confidence intervals. The enrollees’ social demographic characteristics including: level of education, occupation, alcohol - drinking and smoking habits were captured using a questionnaire form. Immediately after blood donation five milliliters of blood samples for CD4+ analysis and haemogram were drawn from the pilot tube of the blood bag by injecting the cap of ethylene diamine tetra acetate (EDTA)-containing vacutaners with the donation needle. Analyses were done within 8 hours of sample collection using standard laboratory methods. The fit of the observed data distribution was determined using Shapiro – Wilk test with P > 0.05 indicating Gaussian distribution. Statistical analyses were done using SPSS version 21. Means, medians and 2.5 th and 97.5 th interquartiles were determined. Gender – based differences were compared using Mann Whitney U test with P < 0.05 being considered significant.
 Results: The male enrollees had a mean age of 31.91 years, while females’ mean age was 31.85 years. The majority of enrollees had tertially education with most males being in business and in formal employment; while most females were in business. Males demonstrated significantly higher mean values than females in: red blood cells (RBCs), haemoglobin (HB) and eosinophils (E). Significantly lower mean values in males than in females were demonstrated in: white blood cells (WBC), neutrophils (N), Lymphocytes (L), monocytes (M), CD4+ cells and Platelets (P).
 Conclusion: There exists significant gender-based differences in immunohaematological reference ranges that may lead to biased conclusions in laboratory diagnosis and research.

C-Reactive Protein Levels in Male and Female Blood Donors at Kenyatta National Hospital, Kenya

Background: C-reactive protein is an inflammatory marker and has found a wide clinical application in monitoring disease progress, effectiveness of treatment and post-operative complications. Determination of gender – based reference intervals of this protein would be of great value in eliminating any biases in results interpretation. It was in this endeavor that this cross-section study was conducted at Kenyatta National Hospital, blood donor unit, between 2018 and 2019. Objectives: To determine gender-based means, medians and 2.5 th and 97.5 th interquartile ranges of C-reactive protein (CRP) in suitable blood donors attended to at the blood donor unit of Kenyatta National Hospital, Kenya. Methods: A total of 108 (53.5%) female and 94 (46.5%) male volunteer blood donors aged between 18 and 60 years were recruited consecutively as they consented. Their social demographic characteristics were captured using a questionnaire form. Immediately after blood donation five milliliters of blood samples for CRP determination were drawn from the pilot tube of the blood bag by injecting the cap of an Ethylene dopamine tetra acetic acid (EDTA) vacutainer with the donation needle. Extracted plasma samples were stored frozen at -70 0 C till analysis. Analysis was done using standard laboratory methods. Statistical analyses were done using SPSS version 21. Bootstrap methods were used to calculate means, medians and confidence intervals. The fit of the observed data distribution was determined using Shapiro – Wilk tests with P > 0.05 indicating Gaussian distribution. Means, medians and 2.5 th and 97.5 th interquartiles were determined. Gender – based comparison of the medians were done using Wilcoxon rank-sum test with, p< 0.05, considered significant. Results: The male enrollees had a mean age of 31.91 years, while females’ mean age was 31.85 years. C-reactive protein demonstrated non-parametric distribution. Females’ medians were higher than males’ (11.7 mg/l vs. 4.4 mg/l, p< 0.01) Conclusion: The females have significantly higher CRP median values than males in health.

Assessment of professional judgement in the field of occupational hygiene: comparison of expert and observed data distributions

Assessment of professional judgement in the field of occupational hygiene: comparison of expert and observed data distributions