Permutation Tests for Assessing Potential Non-Linear Associations between Treatment Use and Multivariate Clinical Outcomes.

In many psychometric applications, the relationship between the mean of an outcome and a quantitative covariate is too complex to be described by simple parametric functions; instead, flexible nonlinear relationships can be incorporated using penalized splines. Penalized splines can be conveniently represented as a linear mixed effects model (LMM), where the coefficients of the spline basis functions are random effects. The LMM representation of penalized splines makes the extension to multivariate outcomes relatively straightforward. In the LMM, no effect of the quantitative covariate on the outcome corresponds to the null hypothesis that a fixed effect and a variance component are both zero. Under the null, the usual asymptotic chi-square distribution of the likelihood ratio test for the variance component does not hold. Therefore, we propose three permutation tests for the likelihood ratio test statistic: one based on permuting the quantitative covariate, the other two based on permuting residuals. We compare via simulation the Type I error rate and power of the three permutation tests obtained from joint models for multiple outcomes, as well as a commonly used parametric test. The tests are illustrated using data from a stimulant use disorder psychosocial clinical trial.

Blind Additive Gaussian White Noise Level Estimation from a Single Image by Employing Chi-Square Distribution.

The additive Gaussian white noise (AGWN) level in real-life images is usually unknown, for which the empirical setting will make the denoising methods over-smooth fine structures or remove noise incompletely. The previous noise level estimation methods are easily lost in accurately estimating them from images with complicated structures. To cope with this issue, we propose a novel noise level estimation scheme based on Chi-square distribution, including the following key points: First, a degraded image is divided into many image patches through a sliding window. Then, flat patches are selected by using a patch selection strategy on the gradient maps of those image patches. Next, the initial noise level is calculated by employing Chi-square distribution on the selected flat patches. Finally, the stable noise level is optimized by an iterative strategy. Quantitative, with association, to qualitative results of experiments on synthetic real-life images validate that the proposed noise level estimation method is effective and even superior to the state-of-the-art methods. Extensive experiments on noise removal using BM3D further illustrate that the proposed noise level estimation method is more beneficial for achieving favorable denoising performance with detail preservation.

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.

Estimation of genetic variance contributed by a quantitative trait locus: correcting the bias associated with significance tests.

The Beavis effect in quantitative trait locus (QTL) mapping describes a phenomenon that the estimated effect size of a statistically significant QTL (measured by the QTL variance) is greater than the true effect size of the QTL if the sample size is not sufficiently large. This is a typical example of the Winners' curse applied to molecular quantitative genetics. Theoretical evaluation and correction for the Winners' curse have been studied for interval mapping. However, similar technologies have not been available for current models of QTL mapping and genome-wide association studies where a polygene is often included in the linear mixed models to control the genetic background effect. In this study, we developed the theory of the Beavis effect in a linear mixed model using a truncated noncentral Chi-square distribution. We equated the observed Wald test statistic of a significant QTL to the expectation of a truncated noncentral Chi-square distribution to obtain a bias-corrected estimate of the QTL variance. The results are validated from replicated Monte Carlo simulation experiments. We applied the new method to the grain width (GW) trait of a rice population consisting of 524 homozygous varieties with over 300 k single nucleotide polymorphism markers. Two loci were identified and the estimated QTL heritability were corrected for the Beavis effect. Bias correction for the larger QTL on chromosome 5 (GW5) with an estimated heritability of 12% did not change the QTL heritability due to the extremely large test score and estimated QTL effect. The smaller QTL on chromosome 9 (GW9) had an estimated QTL heritability of 9% reduced to 6% after the bias-correction.

Improved One-Class Modeling of High-Dimensional Metabolomics Data via Eigenvalue-Shrinkage.

One-class modelling is a useful approach in metabolomics for the untargeted detection of abnormal metabolite profiles, when information from a set of reference observations is available to model "normal" or baseline metabolite profiles. Such outlying profiles are typically identified by comparing the distance between an observation and the reference class to a critical limit. Often, multivariate distance measures such as the Mahalanobis distance (MD) or principal component-based measures are used. These approaches, however, are either not applicable to untargeted metabolomics data, or their results are unreliable. In this paper, five distance measures for one-class modeling in untargeted metabolites are proposed. They are based on a combination of the MD and five so-called eigenvalue-shrinkage estimators of the covariance matrix of the reference class. A simple cross-validation procedure is proposed to set the critical limit for outlier detection. Simulation studies are used to identify which distance measure provides the best performance for one-class modeling, in terms of type I error and power to identify abnormal metabolite profiles. Empirical evidence demonstrates that this method has better type I error (false positive rate) and improved outlier detection power than the standard (principal component-based) one-class models. The method is illustrated by its application to liquid chromatography coupled to mass spectrometry (LC-MS) and nuclear magnetic response spectroscopy (NMR) untargeted metabolomics data from two studies on food safety assessment and diagnosis of rare diseases, respectively.

A comparative study of computation approaches of the generalized F-test.

The Generalized F-test is derived based on the Generalized P-value Method to test the equality of normally distributed group means under unequal variances. There are two approaches to compute the p-value of the GF test, based on beta and chi-squared random numbers. From prior art in the literature, it appears that the two computation approaches of the Generalized tests are equivalent. In this study, the equivalence of these approaches is investigated in an extensive Monte-Carlo simulation study in terms of Type I error probability and penalized power. It is found that the equivalence of the computation approaches is not quite correct and that there is a difference between their conclusion, and researchers should decide which one is powerful than the others according to the structure of data, such as sample size, and the number of groups. Also, real data examples are given to show the opposite decisions of the computation approaches.

Expected Logarithm and Negative Integer Moments of a Noncentral χ2-Distributed Random Variable.

Closed-form expressions for the expected logarithm and for arbitrary negative integer moments of a noncentral χ2-distributed random variable are presented in the cases of both even and odd degrees of freedom. Moreover, some basic properties of these expectations are derived and tight upper and lower bounds on them are proposed.

What Causes the Mean Bias of the Likelihood Ratio Statistic with Many Variables?

Survey data often contain many variables. Structural equation modeling (SEM) is commonly used in analyzing such data. However, conventional SEM methods are not crafted to handle data with a large number of variables (p). A large p can cause Tml, the most widely used likelihood ratio statistic, to depart drastically from the assumed chi-square distribution even with normally distributed data and a relatively large sample size N. A key element affecting this behavior of Tml is its mean bias. The focus of this article is to determine the cause of the bias. To this end, empirical means of Tml via Monte Carlo simulation are used to obtain the empirical bias. The most effective predictors of the mean bias are subsequently identified and their predictive utility examined. The results are further used to predict type I errors of Tml. The article also illustrates how to use the obtained results to determine the required sample size for Tml to behave reasonably well. A real data example is presented to show the effect of the mean bias on model inference as well as how to correct the bias in practice.

Bounds on Identification of Genome Evolution Pacemakers.

Several studies have pointed out that the tight correlation between genes' evolutionary rate is better explained by a model denoted as the Universal PaceMaker (UPM) rather than by a simple rate constancy as manifested by the classical hypothesis of molecular clock (MC). Under UPM, each gene is associated with a single pacemaker (PM) and varies its evolutionary rate according to this PM ticks. Hence, the relative rates of all genes associated with the same PM remain nearly constant, whereas the absolute rates can change arbitrarily according to the PM ticks. A consequent question to that mentioned is finding the gene-PM association only from the gene sequence data. This, however, turns to be a nontrivial task and is affected by the number of variables, their random noise, and the amount of available information. To this end, a clustering heuristic was devised by exploiting the correlation between corresponding edge lengths across thousands of gene trees. Nevertheless, no theoretical study linking the relationship between the affecting parameters was done. We here study this question by providing theoretical bounds, expressed by the system parameters, on probabilities for positive and negative results. We corroborate these results by a simulation study that reveals the critical role of the variances.

Novel Scoring System for Prediction of Cardiac Syndrome X in Women with Typical Angina and a Positive Exercise Tolerance Test.

A major diagnostic challenge for cardiologists is to distinguish cardiac syndrome X (CSX) from obstructive coronary artery disease in women with typical angina and a positive exercise tolerance test (ETT). We performed this study to develop a scoring system that more accurately predicts CSX in this patient population. Data on 976 women with typical angina and a positive ETT who underwent coronary angiography at our center were randomly divided into derivation and validation datasets. We developed a backward stepwise logistic regression model that predicted the presence of CSX, and a scoring system was derived from it. The derivation dataset (809 patients) was calibrated by uing a Hosmer-Lemeshow goodness-of-fit test (8 degrees of freedom; χ2=12.9; P=0.115), and the area under the curve was 0.758. The validation dataset (167 patients) was calibrated in the same way (8 degrees of freedom; χ2=9.0; P=0.339), and the area under the curve was 0.782. Independent predictors of CSX were age <55 years; negative histories of smoking, diabetes mellitus, hyperlipidemia, hypertension, or familial premature coronary artery disease; and highly positive ETTs. A total score >9.5 was the optimal cutoff point for differentiating CSX from obstructive coronary artery disease. Our proposed scoring system is a simple, objective, and accurate system for distinguishing CSX from obstructive coronary artery disease in women with typical angina and positive ETTs. It may help determine which of these patients need invasive coronary angiograms or noninvasive tests like computed tomographic coronary angiography.

Identifying a motor proficiency barrier for meeting physical activity guidelines in children.

OBJECTIVES: This study examined the existence of a threshold level (proficiency barrier) of actual motor competence (MC) below which a child is not likely to attain 60min of moderate-to-vigorous physical activity (MVPA) per day. DESIGN: A cross-sectional study. METHODS: Actual MC was assessed in 326 children (48.5% boys; age=9.50±1.24years) using the Test of Gross Motor Development-2; MVPA was measured with ActiGraph GT3X+accelerometers. Perceived MC, included as a potential mediating variable, was assessed with the Self-Perception Profile for Children. Binary logistic (mediation) regression analyses controlling for sex and a chi-squared test were used to gain insight into the relationship between (the levels of) actual MC and the percentage of children meeting the MVPA guideline. RESULTS: Actual MC significantly predicted the percentage of children meeting the guideline (B=.03, SE=.01, p<.001), even when controlling for sex. Perceived MC did not mediate this relationship. Children with high actual MC (65-100 percentile) were 2.46 (p=.003) times more likely to meet the guideline than children with low actual MC (0-27 percentile). CONCLUSIONS: The present study demonstrates the potential impact of low MC on children's MVPA levels and suggests evidence for the existence of a proficiency barrier for meeting MVPA guidelines. Almost 90% of the children whose actual MC is below the 'average' threshold do not meet the MVPA guideline. As more children with higher levels of actual MC meet the guideline than their less competent peers, it is crucial to provide opportunities to sufficiently develop children's actual MC.

Modified Distribution-Free Goodness-of-Fit Test Statistic.

Covariance structure analysis and its structural equation modeling extensions have become one of the most widely used methodologies in social sciences such as psychology, education, and economics. An important issue in such analysis is to assess the goodness of fit of a model under analysis. One of the most popular test statistics used in covariance structure analysis is the asymptotically distribution-free (ADF) test statistic introduced by Browne (Br J Math Stat Psychol 37:62-83, 1984). The ADF statistic can be used to test models without any specific distribution assumption (e.g., multivariate normal distribution) of the observed data. Despite its advantage, it has been shown in various empirical studies that unless sample sizes are extremely large, this ADF statistic could perform very poorly in practice. In this paper, we provide a theoretical explanation for this phenomenon and further propose a modified test statistic that improves the performance in samples of realistic size. The proposed statistic deals with the possible ill-conditioning of the involved large-scale covariance matrices.

Analysing the risky factors of central lymph node metastasis in papillary thyroid microcarcinoma / 国际外科学杂志

Objective To evaluate the relationship between clinicopathological features and central lymph nodes metastasis in patients with papillary thyroid microcarcinoma (PTMC),and aim to provide an appropriate operation in clinic.Methods The clinical data of 536 patients undergoing surgical treatment in Department of Thyroid Surgery,the First Affiliated Hospital of Zhengzhou University from January 2015 to December 2017,who had pathologically confirmed popillary thyroid microcarcinoma (PTMC) were retrospectively analyzed.Thyroidectomy and isthmectomy with central compartment neck dissection were performed in all patients.The patients were divided into two groups according to whether there existed central lymph node metastasis,and compared the differences of gender,age,number of cancer lesions,tumor breakthrough envelope,BRAFV600E gene mutation,and tumor maximum diameter in the central lymph node metastasis,respectively,by t-test x2-test.Univariate logistic regression analysis and multivariate binary logistic regression analysis were conducted to find risky factors.Results There existed difference between two groups by completing the gender,age,the BRAFV600E gene mutation and maximal tumor diameter(P ＜ 0.05).Univariate logistic regression analysis indicated that gender (P =0.046),age (P ＜ 0.01),maximal tumor diameter(P ＜0.01) and the BRAFV600E gene mutation(P =0.016) were significant predictors for central lymph nodes metastasis.And multivariate binary logistic regression analysis revealed that the rate of lymph node metastasis significantly increased in cases of larger tumor diameter(P ＜0.01),BRAFV600E gene mutation(P =0.035) and ageing below 45 years old (P ＜ 0.01).Conclusions The treatment for central lymph node metastasis of PTMC should be different considering elements including BRAF600E gene mutation prophylactic,ageing below 45 years old and larger tumor diameter.Therefore central lymphadenectomy should be performed when the primary lesion was resected.

A Powerful Variant-Set Association Test Based on Chi-Square Distribution.

Detecting the association between a set of variants and a given phenotype has attracted a large amount of attention in the scientific community, although it is a difficult task. Recently, several related statistical approaches have been proposed in the literature; powerful statistical tests are still highly desired and yet to be developed in this area. In this paper, we propose a powerful test that combines information from each individual single nucleotide polymorphism (SNP) based on principal component analysis without relying on the eigenvalues associated with the principal components. We compare the proposed approach with some popular tests through a simulation study and real data applications. Our results show that, in general, the new test is more powerful than its competitors considered in this study; the gain in detecting power can be substantial in many situations.

Relationship between BRAFV600E gene and TERT promoter mutations with cervical lymph node metastasis in papillary thyroid carcinoma / 国际外科学杂志

Objective To clarify the role of BRAFV600E and TERT promoter mutations in cervical lymph node metastasis in papillary thyroid carcinoma.Methods The data of 432 patients with thyroid papillary carcinoma who underwent surgery from February 2017 to September 2017 at the First Affiliated Hospital of Zhengzhou University were analyzed retrospectively.The mutation of BRAFV600E and TERT promoter was detected by Sanger sequencing.The effect of BRAFV600E and TERT on cervical lymph node metastasis in patients with papillary thyroid carcinoma was analyzed by Chi-square test.Results The mutation rates of BRAFV600E and TERT promoter were 77.8％ (336/ 432) and 5.3％ (23/432) respectively in 432 papillary thyroid carcinoma patients.The probability of cervical lymph node metastasis in patients with BRAFV600E mutation was significantly higher than that in non-mutation patients (P ＜ 0.05).The probability of cervical lymph node metastasis in patients with TERT promoter mutation was significantly higher than that in non-mutated patients (P ＜ 0.05).Patients with both BRAFV600E and TERT promotermutation had a significantly higher incidence of cervical lymph node metastases than patients with the BRAFV600E mutation alone (P ＜ 0.05).Conclusions The mutations of BRAFV600E and TERT promoter are closely relevant to the occurrence of cervical lymph node metastasis in papillary thyroid carcinoma.Preoperative fine-needle aspiration cytology and postoperative routine pathological molecular diagnosis can help clinicians to develop a more rational treatment strategy,and a more accurate assessment of the risk of relapse.

Clinical analysis of risk factors for central compartment lymph node metastasis in stage cNO papillary thyroid microcarcinoma and preventive dissection / 国际外科学杂志

Objective To discuss the clinical characteristics for central compartment lymph node metastasis in stage cNO papillary thyroid microcarcinoma and significance and feasibility of preventive dissection,aimed to provide reference for clinical treatment.Methods Reviewed the clinical data of 277 patients with stage cNO papillary thyroid microcarcinoma from Jul.2011 to Dec.2015 underwent surgery in the Department of General Surgery of Lianyungang East Hospital.Evaluated the necessity of prophylactic central lymph node dissection.Adopted chi square test and Logistic regression to analyze its relationship with patients' gender,age,tumor number,tumor size,enveloped infiltration,single and bilateral tumor.All 277 patients underwent primary radical resection with ipsilateral central lymph node dissection.The specimen of resection was analyzed by routine pathology.Results The positive rate of thyroid papillary microcarcinoma lymph node metastasis was 36.8 ％ (102/277).The elements of male patients (P =0.023),age ＜ 45 years (P ＜ 0.001) and tumor diameter ＞ 0.5 cm (P =0.019)had high positive rate.The multivariable analysis showed that male patients (OR =2.63,P ＜ 0.001),age ＜ 45 years (OR =2.25,P =0.016),tumor diameter ＞ 0.5 c m (OR =2.13,P =O.009) were independent risk factors for CLN metastasis.Forty-three (15.5％) cases had transient parathyroid function.No Permanent recurrent nerve paralysis and hyperparathyroidism occurred in this group.Conclusions Prophylactic central lymph node dissection is helpful for accurate staging of tumor classification and risk assessment,has important significance,on the follow-up of patients after treatment of choice.For male patients,age ＜ 45,tumor diameter ＞ 0.5 cm,enveloped infiltration,the central compartment lymph node dissection may be necessary.

Research of preoperative D-dimer value in patients with gastric cancer in judging gastric cancer metastasis and assessing prognosis / 国际外科学杂志

Objective To explore the value of preoperative D-dimer in patients with gastric cancer in judging gastric cancer metastasis and assessing prognosis.Methods Clinicopathological data of 132 patients with gastric cancer in the First Affiliated Hospital of Anhui Medical University between Jan.2010 and Jan.2011 was analyzed retrospectively in this study.All patients were divided into two groups according to the cutoff value (1.465 mg/L)of D-dimer and the relationships between D-dimer and clinicopathological data were determined by chi-square test.Moreover,the association of preoperative D-dimer and the prognosis was analyzed by Kaplan-Meier analysis and Log-rank test.Univariate and multivaritate Cox model were used to analyze the factors which might affect the survival of the patients and significant independent factors.Results A total of 132 patients were enrolled in this study in accordance with the inclusion criteria.D-dimer was positively correlated with the depth of invasion (x2 =4.996,P ＜ 0.05),age (x2 =4.311,P ＜ 0.05) and distant metastasis of gastric cancer (x2 =16.641,P ＜0.01),but not with thc gcndcr,lymph node metastasis,tumor size,the degree of differentiation and TNM stage (P ＞ 0.05).The mean D-dimer level was (1.39 ± 0.7) mg/L in distant metastasis patients and (0.97 ±0.83) mg/L in non distant metastasis patients (P =0.023),the mean plasma D-dimer level in patients alive at the 5 years after the surgery was (0.78 ± 0.58) mg/L,which was significantly lower than the amounts determined for the deceased patients (0.75 ± 0.58) mg/L (P ＜ 0.01).The Kaplan-Meier curves showed that the patients with gastric cancer had a longer time in the low D-dimer group than in the high D-dimer group,showing a significant difference between the two groups (P ＜ 0.01).Univariate analysis showed that the overall survival rate was significantly correlated with the gender,D-dimer,tumor size,the depth of invasion,lymph node metastasis and TNM stage (P all ＜ 0.05).The D-dimer was proved to be independent risk factor for the prognosis of gastric cancer by multivariate analysis(P ＜ 0.05).Conclusion According to the analysis,D-dimer may be valuable biomarker for metastasis patients,besides,D-dimer was an independent prognostic factor for patients with gastric cancer.

Significance and expression of metdherin in gastric adenocarcinoma and its regulating mechanism of invasion and migration / 国际外科学杂志

Objective This study aimed at observing expression and clinical significance of metadherin in gastric adenocarcinoma and exploring the potentially regulating mechanism of metadherin in invation and migration of gastric cancer.Methods Expressions of metadherin and E-cadherin in primay lesion of gastric cancer were detected by immunohistochemistry and their correlation to clinicopathologic characteristics and prognosis were analyzed by Chi-square tests.Transwell assay and wound healing assay were applied for the ability of invasion and metastasis in gastric cancer cells.Then,the down-regulatied metadherin expression in MKN45 cells by RNA interference (siRNA) was carried out and furthermore,the regulation role of metadherin in epithelial-mesenchymal transition was analyzed also in invasion and migration of gastric cancer cells.Results The positive expression of metadherin was correlated to invading depth (P =0.029),lymph node metastasis (P =0.001),TNM stage (P =0.014) and inhibiting E-cadherin expression (P =0.001).The patients with positive metabherin shared poorer prognosis.Furthermore,the down-regulated metabherin in MKN45 cells would result in the increasing expression of E-cadherin,as well as decreasing expression of N-eadherin,Slug and Snail.At the same time,the abilities of invasion (P =0.027) and migration (P =0.008) of MKN45 cells was decreased.Conclusion metabherin induces EMT in metastasis of gastric adenocarcinoma via activating either Slug or Snail but not twist,which would result in the poorer prognosis.

Comparison of efficacy of Oxaliplatin combined with Tegafur Gimeracil Oteracil Potassium Capsule and mFOLFOX6 method in the treatment of gastric cancer with liver metastasis / 国际外科学杂志

Objective To compare the efficacy and influence on the immune function of oxaliplatin combined with tegafur gimeracil oteracil potassium capsule and mFOLFOX6 method in the treatment of gastric cancer with liver metastasis.Methods One hundred and thirty-four gastric cancer with liver metastasis patients who underwent treatment from Jan.2014 to Jan.2016 in Yulin First Hospital were selected as the participants and randomly divided observation group (67 cases) and control group (67 cases).The control group was treated by mFOLFOX6 method,while the observation group was treated by oxaliplatin combined with tegafur gimeracil oteracil potassium capsule.After treatment,the curative effects were evaluated.The life quality in each group as performed by KPS method before the treatment and in every period of treatment.Before and after the treatment,the levels of CD3 +,CD4 +,CD8 + and CD19 + were detected in two groups and the toxicity was compared.The SPSS 22.0 software was used to analyze relevant data,the measurement data was described by (x ± s) and using t-test,the enumeration data was described by percentage,using the Chi-square test.Results The total effective rate was 52.2％ in the observation group,higher than the 38.8％ in the control group (P ＜ 0.05).After the third and fourth course of treatment,the karnofsky perfomance status score were (81.3 ± 9.7) and (83.2 ± 9.9),were significantly higher in the observation group than which in the control group (P ＜ 0.05).After the treatment,the levels of CD3 +,CD4+,CD8+ andCD19+ were (54.21 ±6.38)％,(24.11 ±2.41) ％,(21.33±3.16) ％ and (7.18 ±1.13) ％ in the observation group,and higher than the control group (P ＜ 0.05).During the treatment,there were no serious toxicity occurs in the patients and the rates of toxicity were significantly lower in the observation group than which in the control group (P ＜ 0.05).Conclusion Oxaliplatin combined with tegafur gimeracil oteracil potassium capsule has a better effect and safety for therapy in the treatment of gastric cancer with liver metastasis than mFOLFOX6.