An exact projection pursuit-based algorithm for multivariate two-sample nonparametric testing applicable to retrospective and group sequential studies.

Nonparametric tests for equality of multivariate distributions are frequently desired in research. It is commonly required that test-procedures based on relatively small samples of vectors accurately control the corresponding Type I Error (TIE) rates. Often, in the multivariate testing, extensions of null-distribution-free univariate methods, e.g., Kolmogorov-Smirnov and Cramér-von Mises type schemes, are not exact, since their null distributions depend on underlying data distributions. The present paper extends the density-based empirical likelihood technique in order to nonparametrically approximate the most powerful test for the multivariate two-sample (MTS) problem, yielding an exact finite-sample test statistic. We rigorously apply one-to-one-mapping between the equality of vectors' distributions and the equality of distributions of relevant univariate linear projections. We establish a general algorithm that simplifies the use of projection pursuit, employing only a few of the infinitely many linear combinations of observed vectors' components. The displayed distribution-free strategy is employed in retrospective and group sequential manners. A novel MTS nonparametric procedure in the group sequential manner is proposed. The asymptotic consistency of the proposed technique is shown. Monte Carlo studies demonstrate that the proposed procedures exhibit extremely high and stable power characteristics across a variety of settings. Supplementary materials for this article are available online.

Feasibility Analysis of ECG-Based pH Estimation for Asphyxia Detection in Neonates.

Birth asphyxia is a potential cause of death that is also associated with acute and chronic morbidities. The traditional and immediate approach for monitoring birth asphyxia (i.e., arterial blood gas analysis) is highly invasive and intermittent. Additionally, alternative noninvasive approaches such as pulse oximeters can be problematic, due to the possibility of false and erroneous measurements. Therefore, further research is needed to explore alternative noninvasive and accurate monitoring methods for asphyxiated neonates. This study aims to investigate the prominent ECG features based on pH estimation that could potentially be used to explore the noninvasive, accurate, and continuous monitoring of asphyxiated neonates. The dataset used contained 274 segments of ECG and pH values recorded simultaneously. After preprocessing the data, principal component analysis and the Pan-Tompkins algorithm were used for each segment to determine the most significant ECG cycle and to compute the ECG features. Descriptive statistics were performed to describe the main properties of the processed dataset. A Kruskal-Wallis nonparametric test was then used to analyze differences between the asphyxiated and non-asphyxiated groups. Finally, a Dunn-Sidák post hoc test was used for individual comparison among the mean ranks of all groups. The findings of this study showed that ECG features (T/QRS, T Amplitude, Tslope, Tslope/T, Tslope/|T|, HR, QT, and QTc) based on pH estimation differed significantly (p < 0.05) in asphyxiated neonates. All these key ECG features were also found to be significantly different between the two groups.

A Characterization of Most(More) Powerful Test Statistics with Simple Nonparametric Applications.

Data-driven most powerful tests are statistical hypothesis decision-making tools that deliver the greatest power against a fixed null hypothesis among all corresponding data-based tests of a given size. When the underlying data distributions are known, the likelihood ratio principle can be applied to conduct most powerful tests. Reversing this notion, we consider the following questions. (a) Assuming a test statistic, say T, is given, how can we transform T to improve the power of the test? (b) Can T be used to generate the most powerful test? (c) How does one compare test statistics with respect to an attribute of the desired most powerful decision-making procedure? To examine these questions, we propose one-to-one mapping of the term "most powerful" to the distribution properties of a given test statistic via matching characterization. This form of characterization has practical applicability and aligns well with the general principle of sufficiency. Findings indicate that to improve a given test, we can employ relevant ancillary statistics that do not have changes in their distributions with respect to tested hypotheses. As an example, the present method is illustrated by modifying the usual t-test under nonparametric settings. Numerical studies based on generated data and a real-data set confirm that the proposed approach can be useful in practice.

Nonparametric Test for Volatility in Clustered Multiple Time Series.

Contagion arising from clustering of multiple time series like those in the stock market indicators can further complicate the nature of volatility, rendering a parametric test (relying on asymptotic distribution) to suffer from issues on size and power. We propose a test on volatility based on the bootstrap method for multiple time series, intended to account for possible presence of contagion effect. While the test is fairly robust to distributional assumptions, it depends on the nature of volatility. The test is correctly sized even in cases where the time series are almost nonstationary (i.e., autocorrelation coefficient ≈1). The test is also powerful specially when the time series are stationary in mean and that volatility are contained only in fewer clusters. We illustrate the method in global stock prices data.

The construction efficiency study of China National Ecological Civilization Pilot Zone with network SBM model: a city-based analysis.

The Chinese government proposed the establishment of China National Ecological Civilization Pilot Zone in 2016 to further explore the coordinated development of economy and environment. Fujian, Jiangxi, and Guizhou provinces were selected as the first batch of pilot zones. After years of exploration, it is necessary to discuss and summarize the construction progress of the three pilot zones from the perspective of the city. In this study, first, the ecological civilization pilot zone construction system was decomposed into an economic construction subsystem (ECS) and an environmental optimization subsystem (EOS). Then, a two-stage network SBM model was adopted to calculate the efficiencies of the subsystems, and the Kruskal-Wallis test was used to measure the efficiency difference. Finally, a panel data regression model was applied to explore the influencing factors of both subsystems. The results show that the ECS efficiency is higher than that of the EOS, and the ECS efficiency in Fujian is significantly better than that in Jiangxi and Guizhou. However, there is no significant difference in EOS efficiency in the three provinces. Furthermore, industrial structure and population agglomeration have a significant effect on ECS efficiency, environmental regulation has a significant impact on EOS, and the technology level has a significant impact on both subsystems. Based on the results, policy implications for improving the efficiency of the two subsystems were given respectively.

Selection and application of statistical methods in medical research / 上海预防医学

Statistics plays an important role in medical research， and the selection of appropriate statistical methods is crucial for drawing reliable and valuable conclusions. This paper provides a brief introduction to commonly used statistical analysis methods for medical data， covering descriptive analysis， parametric test， nonparametric test， correlation analysis， regression analysis， and analysis of survival data. It focuses on discussing the assumptions of multiple linear regression， logistic regression and Cox proportional risk regression， as well as how to choose the appropriate statistical methods for analyzing and interpreting medical data based on different research objectives and data types.

Influence of center surgical aortic valve volume on outcomes of transcatheter aortic valve replacement.

Objective: The utilization of transcatheter aortic valve replacement (TAVR) technology has exceeded that of traditional surgical aortic valve replacement (SAVR). In addition, the role of minimum surgical volume requirements for TAVR centers has recently been disputed. The present work evaluated the association of annual institutional SAVR caseload on outcomes following TAVR. Methods: The 2012-2018 Nationwide Readmissions Database was queried for elective TAVR hospitalizations. The study cohort was split into early (Era 1: 2012-2015) and late (Era 2: 2016-2018) groups. Based on restricted cubic spline modeling of annual hospital SAVR caseload, institutions were dichotomized into low-volume and high-volume centers. Multivariable regressions were used to determine the influence of high-volume status on in-hospital mortality and perioperative complications following TAVR. Results: An estimated 181,740 patients underwent TAVR from 2012 to 2018. Nationwide TAVR volume increased from 5893 in 2012 to 49,983 in 2018. After adjustment for relevant patient and hospital factors, high-volume status did not alter odds of TAVR mortality in Era 1 (adjusted odds ratio, 0.94; P = .52) but was associated decreased likelihood of mortality in Era 2 (adjusted odds ratio, 0.83; P = .047). High-volume status did not influence the risk of perioperative complications during Era 1. However, during Era 2, patients at high-volume centers had significantly lower odds of infectious complications, relative to low-volume hospitals (adjusted odds ratio, 0.78; P = .002). Conclusions: SAVR experience is associated with improved TAVR outcomes in a modern cohort. Our findings suggest the need for continued collaboration between cardiologists and surgeons to maximize patient safety.

Assessment of Environmental Demands of Age-Friendly Communities from Perspectives of Different Residential Groups: A Case of Wuhan, China.

Age-friendly communities (AFCs) are an important measure for fostering active aging. The key to achieving an age-friendly living environment is to construct or renovate it according to the residents' demands. To date, very few studies have attempted to delve into the AFCs' environmental demand from different groups' perspectives. Based on the theory of place attachment, the aim of this paper is to explore the demand diversity of different groups for the AFC environment. This study employs the nonparametric test and the Ordinal Priority Approach (OPA) to investigate the demands from the residents' perspectives, and is enhanced by incorporating experts' opinions. The empirical analysis shows that residents have a high level of demand for the physical environment (indoor and outdoor) and social environment (community services and social participation). At the same time, experts advocate the importance of using digital technologies to support people aged 45-65 who have higher requirements for a community environment than older adults. The findings also show that other backgrounds, such as gender, living arrangements, and year of the community establishment, lead to different demands. However, the impact of residents' education level, occupation, income, and self-care ability on the environmental demands is low. Based on the research findings, the paper provides some practical suggestions for the future design and development of AFCs.

The Chi-Square Test of Distance Correlation.

Distance correlation has gained much recent attention in the data science community: the sample statistic is straightforward to compute and asymptotically equals zero if and only if independence, making it an ideal choice to discover any type of dependency structure given sufficient sample size. One major bottleneck is the testing process: because the null distribution of distance correlation depends on the underlying random variables and metric choice, it typically requires a permutation test to estimate the null and compute the p-value, which is very costly for large amount of data. To overcome the difficulty, in this paper we propose a chi-square test for distance correlation. Method-wise, the chi-square test is non-parametric, extremely fast, and applicable to bias-corrected distance correlation using any strong negative type metric or characteristic kernel. The test exhibits a similar testing power as the standard permutation test, and can be utilized for K-sample and partial testing. Theory-wise, we show that the underlying chi-square distribution well approximates and dominates the limiting null distribution in upper tail, prove the chi-square test can be valid and universally consistent for testing independence, and establish a testing power inequality with respect to the permutation test.

New multivariate tests for assessing covariate balance in matched observational studies.

We propose new tests for assessing whether covariates in a treatment group and matched control group are balanced in observational studies. The tests exhibit high power under a wide range of multivariate alternatives, some of which existing tests have little power for. The asymptotic permutation null distributions of the proposed tests are studied and the P-values calculated through the asymptotic results work well in simulation studies, facilitating the application of the test to large data sets. The tests are illustrated in a study of the effect of smoking on blood lead levels. The proposed tests are implemented in an R package BalanceCheck.

TWO-SAMPLE TESTS FOR MULTIVARIATE REPEATED MEASUREMENTS OF HISTOGRAM OBJECTS WITH APPLICATIONS TO WEARABLE DEVICE DATA.

Repeated observations have become increasingly common in biomedical research and longitudinal studies. For instance, wearable sensor devices are deployed to continuously track physiological and biological signals from each individual over multiple days. It remains of great interest to appropriately evaluate how the daily distribution of biosignals might differ across disease groups and demographics. Hence, these data could be formulated as multivariate complex object data, such as probability densities, histograms, and observations on a tree. Traditional statistical methods would often fail to apply, as they are sampled from an arbitrary non-Euclidean metric space. In this paper we propose novel, nonparametric, graph-based two-sample tests for object data with the same structure of repeated measures. We treat the repeatedly measured object data as multivariate object data, which requires the same number of repeated observations per individual but eliminates any assumptions on the errors of the repeated observations. A set of test statistics are proposed to capture various possible alternatives. We derive their asymptotic null distributions under the permutation null. These tests exhibit substantial power improvements over the existing methods while controlling the type I errors under finite samples as shown through simulation studies. The proposed tests are demonstrated to provide additional insights on the location, inter- and intra-individual variability of the daily physical activity distributions in a sample of studies for mood disorders.

Longitudinal Predictive Curves of Health Risk Factors for American Adolescent Girls.

PURPOSE: The aim of this study is to compare age-variant 18 health risk factors by constructing longitudinal predictive curves between African-American (AA) and Caucasian American (CA) adolescent girls. METHODS: A total of 2,379 girls (51% AA) from ages 9 to 10 were recruited in the National Heart, Lung, and Blood Institute Growth and Health Study. The various health indicators and dietary habits of these girls were assessed annually for 10 years. We model 2nd, 5th, 95th, and 98th percentile values of the health risk factors to compare trajectories between AA and CA adolescents by employing novel kernel smoothing regression and global tests of equality for regression curves. Health risk factors such as dietary fiber, intake of sodium, sugar, and total calories, systolic blood pressure, weight, body fat percentage, and high-density lipoprotein levels were compared. RESULTS: Trajectories of sugar, sodium, and total calories intake and systolic blood pressure, weight, body fat percentage, and high-density lipoprotein among AA girls were significantly higher than those of CA girls throughout their adolescence. CONCLUSIONS: AA girls exhibit several health risk factors that are significantly higher than those of CA adolescent girls at the 95th and 98th percentile. Interventions may be warranted for the purposes of ensuring access to health risk information as well as a greater ease of access to healthier food choices within the educational food system.

Establishment of the reference interval for high-sensitivity cardiac troponin T in healthy children of Chongqing Nan'an district.

OBJECTIVE: To detect the concentration of high-sensitivity cardiac troponin T (hs-cTnT) in healthy children aged 0-14 years by electrochemiluminescence immunoassay (ECLIA), so as to explore the differences in different ages and genders. The aim of this study is to establish the reference interval for hs-cTnT in healthy children aged 0-14 years. METHODS: After screening, 3463 healthy children, including 1924 boys and 1539 girls, were selected from 4617 children aged 0-14 years. They were divided into nine groups: one day (umbilical cord blood; 'UCB'), one day (venous blood; 'VB'), 2-28 days, 29 days-<3 months, 3-<6 months, 6 months-<1 year old, 1-< 3 years old, 3-< 6 years old and 6-14 years old. A nonparametric test was used to detect the hs-cTnT concentration. The upper limit of the reference interval is the mean of the 99th percentile after bootstrap sampling. RESULTS: Hs-cTnT levels conformed to a non-Gaussian distribution. There was no significant difference in the concentration of hs-cTnT between boys and girls in the general data, but there were differences between boys and girls in the 3-<6 years old and 6-14 years old age groups. Except for UCB and 2-28 days, the concentration of hs-cTnT was significantly different in other age groups. The level of hs-cTnT in neonatal serum (2-28 days) was the highest. In other groups, it decreased gradually with age and dropped to the reference range of adults (0-14ng/L) at one-year old. The upper limit of reference interval of hs-cTnT concentration in each group was, respectively, 60.8, 78.8, 96.6, 58.6, 34.2, 16.2, 11.4, 8.0 (7.8 female), and 7.9 (7.3 female) ng/L. CONCLUSIONS: Referring to WS/T 402-2012 establishment of reference intervals for clinical laboratory testing projects and CLSI (Clinical and Laboratory Standards Institute) C28-A3 documents and the joint expert consensus of ESC (European Society of Cardiology) and ACC (American College of Cardiology) in 2007, we established the reference interval of hs-cTnT concentration in children aged 0-14 years in Chongqing Nan'an district of China which can provide certain reference value for clinical diagnosis and treatment of myocarditis and myocardial (micro) injury in children.

Statistical Methods for Analysis of Protein Microarray Data Using R.

This chapter aims to provide statistical methods for analyzing protein microarray data. It uses a publicly available protein array dataset and emphasizes practical applications in statistics using R, a statistical software. A wide range of statistical methods will be demonstrated, including descriptive statistics, hypothesis testing, false discovery rate, receiver operating characteristic curve, correlation, visualization, and power analysis. The R code used to perform the statistical analyses will be provided.

Ecological hazard assessment via species sensitivity distributions: The non-exchangeability issue.

Probabilistic approaches to hazard assessment use species sensitivity distributions (SSDs) to characterize hazard for toxicants exposure for different species within a community. Many of the assumptions at the core of SSDs are unrealistic, among them the assumption that the tolerance levels of all species in a specific ecological community are a priori exchangeable for each new toxic substance. Here we propose the use of a particular test to detect situations where such an assumption is violated. Then, a new method based on non-nested random effects model is required to identify novel SSDs capable of taking into account species non-exchangeability. Credible intervals, representing SSD uncertainty, could be determined based on our procedure. This leads to new and reliable estimates of the environmental hazard. We present a Bayesian modeling approach to address model inference issues, using Markov chain Monte Carlo sampling.

Nonparametric analysis of nonhomogeneous multistate processes with clustered observations.

Frequently, clinical trials and observational studies involve complex event history data with multiple events. When the observations are independent, the analysis of such studies can be based on standard methods for multistate models. However, the independence assumption is often violated, such as in multicenter studies, which makes standard methods improper. This work addresses the issue of nonparametric estimation and two-sample testing for the population-averaged transition and state occupation probabilities under general multistate models with cluster-correlated, right-censored, and/or left-truncated observations. The proposed methods do not impose assumptions regarding the within-cluster dependence, allow for informative cluster size, and are applicable to both Markov and non-Markov processes. Using empirical process theory, the estimators are shown to be uniformly consistent and to converge weakly to tight Gaussian processes. Closed-form variance estimators are derived, rigorous methodology for the calculation of simultaneous confidence bands is proposed, and the asymptotic properties of the nonparametric tests are established. Furthermore, I provide theoretical arguments for the validity of the nonparametric cluster bootstrap, which can be readily implemented in practice regardless of how complex the underlying multistate model is. Simulation studies show that the performance of the proposed methods is good, and that methods that ignore the within-cluster dependence can lead to invalid inferences. Finally, the methods are illustrated using data from a multicenter randomized controlled trial.

Temporal variation of airborne fungi in university library rooms and its relation to environmental parameters and potential confounders.

Indoor airborne fungi have been associated with adverse human health effects. Therefore, it is important to understand the causes of underlying variation in airborne fungi in indoor environments. This study consequently aimed to investigate the association between indoor fungi with temporal variation, environmental parameters, and potential confounders over 10 months in four library rooms using Andersen samplers. Indoor fungal concentrations peaked in October and were lowest in March in both stack rooms, whereas the highest concentrations in both reading rooms were observed in September with lowest concentrations in July. Nonparametric analyses revealed higher fungal concentrations in the rooms that were significantly associated with relative humidity ≥ 60%, PM2.5 ≥ 35 µg/m3, number of people ≥ 16, open windows, working air conditioners, and room area < 400 m2. Multiple linear regression modeling for the library building considering only continuous variables revealed that relative humidity, PM2.5, and the number of people were significant predictors of fungal concentrations. Additionally, the model with continuous and categorical variables suggested that relative humidity, PM2.5, the number of people, ceiling fan condition, window state, and air conditioner operating status were significant predictor variables of concentrations. Outdoor fungal concentrations were a significant predictor for the two models of indoor fungal concentrations for each room. Ceiling fan or air conditioner operation was associated with altered fungal particle concentrations. These results provide a deeper understanding of indoor air fungal quality.

How to use χ2 test correctly——the likelihood ratio test and the six nonparametric tests of the survival data and the implementation of the SAS software / 四川精神卫生

The purpose of this article was to introduce the likelihood ratio test， six nonparametric tests， and the SAS implementation of the survival data. Based on the assumption that the survival data had the exponential distribution， the likelihood ratio test method was derived， the main difference between six nonparametric test methods was that they had different weight functions. Under the conditions of non-stratification and stratification， the seven survival data hypothesis testing methods mentioned above could be used， and their common point was that their test statistics all followed the χ2 distribution. Through two examples and by means of the SAS software， the article realized the various hypothesis tests for two or more groups of survival data， outputed and explained SAS calculation results， and made statistical and professional conclusions.

A Consistent Nonparametric Test for Granger Non-Causality Based on the Transfer Entropy.

To date, testing for Granger non-causality using kernel density-based nonparametric estimates of the transfer entropy has been hindered by the intractability of the asymptotic distribution of the estimators. We overcome this by shifting from the transfer entropy to its first-order Taylor expansion near the null hypothesis, which is also non-negative and zero if and only if Granger causality is absent. The estimated Taylor expansion can be expressed in terms of a U-statistic, demonstrating asymptotic normality. After studying its size and power properties numerically, the resulting test is illustrated empirically with applications to stock indices and exchange rates.

Spatiotemporal Patterns of Ecosystem Service Value Changes and Their Coordination with Economic Development: A Case Study of the Yellow River Basin, China.

By integrating multiple remote sensing data sources this study accurately assesses the spatiotemporal characteristics of changes in ecosystem service values (ESVs) in the Yellow River Basin from 2000 to 2015 through Theil-Sen median trend analysis and the Mann-Kendall test. The stability and continuity of the ESVs were comprehensively characterized using coefficients of variation and the Hurst exponent. The degree of coherence between ESVs and economic growth (represented by gross domestic product GDP) on the same temporal and spatial scales was analyzed using ecological-economic coordination (EEC) models. The results show that (1) from 2001 to 2015 the total ESV and the ESV per unit area in the Yellow River Basin generally showed a U-shaped pattern (decreasing slightly then increasing rapidly). (2) The areas with increasing ESVs made up approximately 55.6% of the total area of the river basin. The areas with a decreasing pattern were mainly in the west and north of the Yellow River Basin. (3) The stability and continuity of the ESVs showed a clustered, compact distribution. (4) The most common level of EEC was slightly uncoordinated followed by slightly coordinated and highly coordinated. The proportion of coordinated areas was relatively higher in cultivated land and the lowest in built-up land.