This paper develops the large sample properties of the solutions of the general estimating equations which are unbiased or asymptotically unbiased or with nuisance parameters for correlated data.The authors do not mak...This paper develops the large sample properties of the solutions of the general estimating equations which are unbiased or asymptotically unbiased or with nuisance parameters for correlated data.The authors do not make the assumption that the estimating equations come from some objective function when we establish the large sample properties of the solutions.So these results extend the work of Newey and McFadden(1994) and are more widely applicable.Furthermore,we provide some examples to justify the importance of our work.展开更多
Missing covariate data arise frequently in biomedical studies.In this article,we propose a class of weighted estimating equations for the additive hazards regression model when some of the covariates are missing at ra...Missing covariate data arise frequently in biomedical studies.In this article,we propose a class of weighted estimating equations for the additive hazards regression model when some of the covariates are missing at random.Time-specific and subject-specific weights are incorporated into the formulation of weighted estimating equations.Unified results are established for estimating selection probabilities that cover both parametric and non-parametric modelling schemes.The resulting estimators have closed forms and are shown to be consistent and asymptotically normal.Simulation studies indicate that the proposed estimators perform well for practical settings.An application to a mouse leukemia study is illustrated.展开更多
This paper is devoted to the pointwise estimate of solutions for the initial value problem to the three-dimensional compressible magnetohydrodynamic equations, which models the dynamics of compressible quasi-neutrally...This paper is devoted to the pointwise estimate of solutions for the initial value problem to the three-dimensional compressible magnetohydrodynamic equations, which models the dynamics of compressible quasi-neutrally ionized fluids under the influence of electromagnetic fields. Based on the detailed analysis of the Green function of the linearized system, we obtain the pointwise estimates of smooth solutions when the initial data is sufficiently small with the algebraic decay to the constant equilibrium. As the by-product, we also show the corresponding pL-estimates of the smooth solutions.展开更多
In this paper, we consider a class of Monge-Ampere equations in relative differential geometry. Given these equations with zero boundary values in a smooth strictly convex bounded domain, we obtain second order deriva...In this paper, we consider a class of Monge-Ampere equations in relative differential geometry. Given these equations with zero boundary values in a smooth strictly convex bounded domain, we obtain second order derivative estimates of the convex solutions.展开更多
Objective:To explore the appropriate modeling method of the early warning model of ischemic stroke recurrence in TCM.Methods:This was a prospective,multi-center and registered study conducted in 7 clinical subcenters ...Objective:To explore the appropriate modeling method of the early warning model of ischemic stroke recurrence in TCM.Methods:This was a prospective,multi-center and registered study conducted in 7 clinical subcenters from 8 provinces and 10 cities in China between 3rd November 2016 and 27th April,2019.1,741 patients with first-ever ischemic stroke were recruited.Univariate analysis was carried out using distance correlation coefficient,mutual information entropy,and statistical correlation test.Multivariate analysis adopted multi-factor Cox regression model and combined with expert opinions in the field of stroke to determine modeling variables.The generalized estimating equation of longitudinal data and the Cox proportional hazard regression model of cross-sectional data were used to construct and compare in the early warning model of ischemic stroke recalls.The area under the ROC curve(AUC value)was used to evaluate the early warning capability of the model.Results:The follow-up time was 1-3 years,and the median follow-up time was 1.42 years(95%CI:1.37-1.47).Recurrence events occurred in 175 cases,and the cumulative recurrence rate was 10.05%(95%CI:8.64%-11.47%).The AUC values of the TCM syndrome and TCM constitution model were 0.71809 and 0.72668 based on the generalized estimating equation and the AUC values.Conclusion:The generalized estimating equation may be more suitable for the construction of early warning models of stroke recurrence with TCM characteristics,which provides a certain reference for the evaluation of secondary prevention of ischemic stroke.展开更多
In this article, we first propose the Riemann-Hilbert problem for uniformly elliptic complex equations of first order and its well-posed-ness in multiply connected domains.Then we give the integral representation of s...In this article, we first propose the Riemann-Hilbert problem for uniformly elliptic complex equations of first order and its well-posed-ness in multiply connected domains.Then we give the integral representation of solutions for modified Riemann-Hilbert problem of the complex equations. Moreover we shall obtain a priori estimates of solutions of the modified Riemann-Hilbert problem and verify its solvability. Finally the solvability results of the original boundary value problem can be obtained.展开更多
In longitudinal data analysis, our primary interest is in the estimation of regression parameters for the marginal expectations of the longitudinal responses, and the longitudinal correlation parameters are of seconda...In longitudinal data analysis, our primary interest is in the estimation of regression parameters for the marginal expectations of the longitudinal responses, and the longitudinal correlation parameters are of secondary interest. The joint likelihood function for longitudinal data is challenging, particularly due to correlated responses. Marginal models, such as generalized estimating equations (GEEs), have received much attention based on the assumption of the first two moments of the data and a working correlation structure. The confidence regions and hypothesis tests are constructed based on the asymptotic normality. This approach is sensitive to the misspecification of the variance function and the working correlation structure which may yield inefficient and inconsistent estimates leading to wrong conclusions. To overcome this problem, we propose an empirical likelihood (EL) procedure based on a set of estimating equations for the parameter of interest and discuss its <span style="font-family:Verdana;">characteristics and asymptotic properties. We also provide an algorithm base</span><span style="font-family:Verdana;">d on EL principles for the estimation of the regression parameters and the construction of its confidence region. We have applied the proposed method in two case examples.</span>展开更多
The purpose of this article is to investigate approaches for modeling individual patient count/rate data over time accounting for temporal correlation and non</span><span style="font-family:Verdana;"...The purpose of this article is to investigate approaches for modeling individual patient count/rate data over time accounting for temporal correlation and non</span><span style="font-family:Verdana;">-</span><span style="font-family:Verdana;">constant dispersions while requiring reasonable amounts of time to search over alternative models for those data. This research addresses formulations for two approaches for extending generalized estimating equations (GEE) modeling. These approaches use a likelihood-like function based on the multivariate normal density. The first approach augments standard GEE equations to include equations for estimation of dispersion parameters. The second approach is based on estimating equations determined by partial derivatives of the likelihood-like function with respect to all model parameters and so extends linear mixed modeling. Three correlation structures are considered including independent, exchangeable, and spatial autoregressive of order 1 correlations. The likelihood-like function is used to formulate a likelihood-like cross-validation (LCV) score for use in evaluating models. Example analyses are presented using these two modeling approaches applied to three data sets of counts/rates over time for individual cancer patients including pain flares per day, as needed pain medications taken per day, and around the clock pain medications taken per day per dose. Means and dispersions are modeled as possibly nonlinear functions of time using adaptive regression modeling methods to search through alternative models compared using LCV scores. The results of these analyses demonstrate that extended linear mixed modeling is preferable for modeling individual patient count/rate data over time</span><span style="font-family:Verdana;">,</span><span style="font-family:Verdana;"> because in example analyses</span><span style="font-family:Verdana;">,</span><span style="font-family:Verdana;"> it either generates better LCV scores or more parsimonious models and requires substantially less time.展开更多
AIM:To explore the value of fecal lactoferrin in predicting and monitoring the clinical severity of infectious diarrhea.METHODS:Patients with acute infectious diarrhea ranging from 3 mo to 10 years in age were enrolle...AIM:To explore the value of fecal lactoferrin in predicting and monitoring the clinical severity of infectious diarrhea.METHODS:Patients with acute infectious diarrhea ranging from 3 mo to 10 years in age were enrolled,and one to three stool samples from each subject were collected.Certain parameters,including white blood cells /differential count,C-reactive protein,fecal mucus,fecal pus cells,duration of fever,vomiting,diarrhea and severity(indicated by Clark and Vesikari scores),were recorded and analyzed.Fecal lactoferrin was determined by enzyme-linked immunosorbent assay and compared in different pathogen and disease activity.Generalized estimating equations(GEE) were also used for analysis.RESULTS:Data included 226 evaluations for 117 individuals across three different time points.Fecal lactoferrin was higher in patients with Salmonella(11.17 μg/g ± 2.73 μg/g) or Campylobacter(10.32 μg/g ± 2.94 μg/g) infections and lower in patients with rotavirus(2.82 μg/g ± 1.27 μg/g) or norovirus(3.16 μg/g ± 1.18 μg/g) infections.Concentrations of fecal lactoferrin were significantly elevated in patients with severe(11.32 μg/g ± 3.29 μg/g) or moderate(3.77 μg/g ± 2.08 μg/g) disease activity compared with subjects with mild(1.51 μg/g ± 1.36 μg/g) disease activity(P < 0.05).GEE analysis suggests that this marker could be used to monitor the severity and course of gastrointestinal infections and may provide information for disease management.CONCLUSION:Fecal lactoferrin increased during bacterial infection and with greater disease severity and may be a good marker for predicting and monitoring intestinal inflammation in children with infectious diarrhea.展开更多
In stratified survey sampling, sometimes we have complete auxiliary information. One of the fundamental questions is how to effectively use the complete auxiliary information at the estimation stage. In this paper, we...In stratified survey sampling, sometimes we have complete auxiliary information. One of the fundamental questions is how to effectively use the complete auxiliary information at the estimation stage. In this paper, we extend the model-calibration method to obtain estimators of the finite population mean by using complete auxiliary information from stratified sampling survey data. We show that the resulting estimators effectively use auxiliary information at the estimation stage and possess a number of attractive features such as asymptotically design-unbiased irrespective of the working model and approximately model-unbiased under the model. When a linear working-model is used, the resulting estimators reduce to the usual calibration estimator（or GREG）.展开更多
Objective This study explored the correlation of longitudinal changes in serum alanine aminotransferase （ALT） and aspartate aminotransferase （AST） levels with the incidence of metabolic syndrome （Mets） based on ...Objective This study explored the correlation of longitudinal changes in serum alanine aminotransferase （ALT） and aspartate aminotransferase （AST） levels with the incidence of metabolic syndrome （Mets） based on a dynamic health examination cohort. Methods A Mets-free dynamic cohort involving 4541 participants who underwent at least three health examinations from 2006 to 2011 was included in the study. Mets was defined according to the Chinese Medical Association Diabetes Branch definition that included hypertension, obesity, hyperlipidemia, and hyperglycemia. Generalized estimating equation （GEE） model was used to analyze multivariate relative risk （RR） of repeated observations of ALT and AST in quartiles for Mets or its components according to gender. Results In all, 826 Mets cases were reported. Adjustment of relevant parameters indicated that time-varying changes in ALT and AST levels were positively associated with the incidence of Mets in a dose-response manner. Positive association between high ALT levels and fatty liver was much stronger than that between high AST levels and fatty liver, particularly in male participants. These associations were consistently observed in the following subgroups： participants with ALT and AST levels of 〈40 U/L, participants with of 〈25 kg/m2, and participants with non-fatty liver. Furthermore, participants with 2 Mets components at baseline showed lower multivariate adjusted RRs of ALT and AST for Mets than participants with 0-1 Mets component. Conclusion These results suggested that elevated serum ALT and AST levels were early biomarkers of Mets or its components.展开更多
BACKGROUND Genome-wide association studies from Asia indicate that HLA-DP and HLA-DQ loci are important in persistent hepatitis B virus(HBV)infections.One of the key elements for HBV-related carcinogenesis is persiste...BACKGROUND Genome-wide association studies from Asia indicate that HLA-DP and HLA-DQ loci are important in persistent hepatitis B virus(HBV)infections.One of the key elements for HBV-related carcinogenesis is persistent viral replication and inflammation.AIM To examine genetic and nongenetic factors with persistent HBV infection and viral load in families with hepatocellular carcinoma(HCC).METHODS The HCC families included 301 hepatitis B surface antigen(HBsAg)carriers and 424 noncarriers born before the nationwide vaccination program was initiated in 1984.Five HBV-related single nucleotide polymorphisms(SNPs)—rs477515,rs9272105,rs9276370,rs7756516,and rs9277535—were genotyped.Factors associated with persistent HBV infection and viral load were analyzed by a generalized estimating equation.RESULTS In the first-stage persistent HBV study,all SNPs except rs9272105 were associated with persistent infection.A significantly higher area under the reciprocal operating characteristic curve for nongenetic factors vs genetic factors(P<0.001)suggests that the former play a major role in persistent HBV infection.In the second-stage viral load study,we added 8 HBsAg carriers born after 1984.The 309 HBsAg carriers were divided into low(n=162)and high viral load(n=147)groups with an HBV DNA cutoff of 105 cps/mL.Sex,relationship to the index case,rs477515,rs9272105,and rs7756516 were associated with viral load.Based on the receiver operating characteristic curve analysis,genetic and nongenetic factors affected viral load equally in the HCC family cohort(P=0.3117).CONCLUSION In these east Asian adults,the mechanism of persistent HBV infection-related SNPs was a prolonged viral replication phase.展开更多
Multivariate failure time data are frequently encountered in biomedical research.In this article,we model marginal hazards with accelerated hazards model to analyze multivariate failure time data.Estimating equations ...Multivariate failure time data are frequently encountered in biomedical research.In this article,we model marginal hazards with accelerated hazards model to analyze multivariate failure time data.Estimating equations are derived analogous to generalized estimating equation method.Under certain regular conditions,the resultant estimators for the regression parameters are shown to be asymptotically normal.Furthermore,we also establish the weak convergence of estimators for the baseline cumulative hazard functions.展开更多
Intramuscular injections can cause damage to arteries, veins and nerves. Achieving maximum effects of medications through precise intramuscular (IM) injections must be assured and with certainty, particularly with lon...Intramuscular injections can cause damage to arteries, veins and nerves. Achieving maximum effects of medications through precise intramuscular (IM) injections must be assured and with certainty, particularly with long-acting injection drugs (LAI). The purpose of this study is to determine precision in IM LAIs of patients with schizophrenia. These evidences estimate “Distance from the Epidermis to the Under-Fascia” (DEUF) and “Distance from Epidermis to the Upper-Arm Bone” (DEB) of the deltoid muscle. Explanatory variables include body height, weight, body-mass index (BMI), deltoid-muscle circumference, fat percentage and muscle mass measured by body composition monitor. Sixty nine subjects are included based on the Diagnostic Statistical Manual of Mental Disorders (DSM-IV, 1994), and receive treatments of typical and atypical antipsychotic LAI. There are 46 males and 23 females with average age of 51.41 (Standard Deviation = 13.58) and ranging from 21 to 81 years who are all right-handed. Ultrasonographic data and those from explanatory variables are calculated using Spearman’s rank correlation coefficients. Multiple regression analysis (step-wise method/forced input method) is performed assuming DEUF or DEB as dependent variables. Significant correlations are found with highest adjusted R-square. Paired t-tests show differences in average values of actual ultrasonographic measurements assigned to DEUF or DEB, and the regression equations for accuracy. Ultrasonographic values are assigned multiple-regression equations as true values, and the calculated values are compared with those obtained by regression equations. There are no significant differences observed for either the right or left arm. The multiple regression equations for BMI and fat percentages (upper extremity estimation) of DEUF, and for BMI and injection site circumference of estimated DEB, successfully value the DEUF and DEB. By using these multiple regression equations for IM injection to the deltoid-muscle, DEUF can better ensure accurate LAI into the muscle through body monitor, DEB, and measured values of the deltoid-muscle injection site circumference.展开更多
Objective：A computational model of insulin secretion and glucose metabolism for assisting the diagnosis of diabetes mellitus in clinical research is introduced.The proposed method for the estimation of parameters for...Objective：A computational model of insulin secretion and glucose metabolism for assisting the diagnosis of diabetes mellitus in clinical research is introduced.The proposed method for the estimation of parameters for a system of ordinary differential equations（ODEs）that represent the time course of plasma glucose and insulin concentrations during glucose tolerance test（GTT）in physiological studies is presented.The aim of this study was to explore how to interpret those laboratory glucose and insulin data as well as enhance the Ackerman mathematical model.Methods：Parameters estimation for a system of ODEs was performed by minimizing the sum of squared residuals（SSR）function,which quantifies the difference between theoretical model predictions and GTT＇s experimental observations.Our proposed perturbation search and multiple-shooting methods were applied during the estimating process.Results：Based on the Ackerman＇s published data,we estimated the key parameters by applying R-based iterative computer programs.As a result,the theoretically simulated curves perfectly matched the experimental data points.Our model showed that the estimated parameters,computed frequency and period values,were proven a good indicator of diabetes.Conclusion：The present paper introduces a computational algorithm to biomedical problems,particularly to endocrinology and metabolism fields,which involves two coupled differential equations with four parameters describing the glucose-insulin regulatory system that Ackerman proposed earlier.The enhanced approach may provide clinicians in endocrinology and metabolism field insight into the transition nature of human metabolic mechanism from normal to impaired glucose tolerance.展开更多
In this article, robust generalized estimating equation for the analysis of partial linear mixed model for longitudinal data is used. The authors approximate the nonparametric function by a regression spline. Under so...In this article, robust generalized estimating equation for the analysis of partial linear mixed model for longitudinal data is used. The authors approximate the nonparametric function by a regression spline. Under some regular conditions, the asymptotic properties of the estimators are obtained. To avoid the computation of high-dimensional integral, a robust Monte Carlo Newton-Raphson algorithm is used. Some simulations are carried out to study the performance of the proposed robust estimators. In addition, the authors also study the robustness and the efficiency of the proposed estimators by simulation. Finally, two real longitudinal data sets are analyzed.展开更多
Quantitative traits often underlie risk for complex diseases. Many studies collect multiple correlated quantitative phenotypes and perform univariate analyses on each of them respectively. However, this strategy may n...Quantitative traits often underlie risk for complex diseases. Many studies collect multiple correlated quantitative phenotypes and perform univariate analyses on each of them respectively. However, this strategy may not be powerful and has limitations to detect plei- otropic genes that may underlie correlated quantitative traits. In addition, testing multiple traits individually will exacerbate perplexing problem of multiple testing. In this study, generalized estimating equation 2 （GEE2） is applied to association mapping of two correlated quantitative traits. We suppose that a quantitative trait locus is located in a chromosome region that exerts pleiotropic effects on multiple quantitative traits. In that region, multiple SNPs are genotyped. Genotypes of these SNPs and the two quantitative traits affected by a causal SNP were simulated under various parameter values： residual correlation coefficient between two traits, causal SNP heritability, minor allele frequency of the causal SNP, extent of linkage disequilibrium with the causal SNP, and the test sample size. By power ana- lytical analyses, it is showed that the bivariate method is generally more powerful than the univariate method. This method is robust and yields false-positive rates close to the pre-set nominal significance level. Our real data analyses attested to the usefulness of the method.展开更多
Recurrent event gap times data frequently arise in biomedical studies and often more than one type of event is of interest. To evaluate the effects of covariates on the marginal recurrent event hazards functions, ther...Recurrent event gap times data frequently arise in biomedical studies and often more than one type of event is of interest. To evaluate the effects of covariates on the marginal recurrent event hazards functions, there exist two types of hazards models： the multiplicative hazards model and the additive hazards model. In the paper, we propose a more flexible additive-multiplicative hazards model for multiple type of recurrent gap times data, wherein some covariates are assumed to be additive while others are multiplicative. An estimating equation approach is presented to estimate the regression parameters. We establish asymptotic properties of the proposed estimators.展开更多
The proper orthogonal decomposition （POD） is a model reduction technique for the simulation Of physical processes governed by partial differential equations （e.g., fluid flows）. It has been successfully used in th...The proper orthogonal decomposition （POD） is a model reduction technique for the simulation Of physical processes governed by partial differential equations （e.g., fluid flows）. It has been successfully used in the reduced-order modeling of complex systems. In this paper, the applications of the POD method are extended, i.e., the POD method is applied to a classical finite difference （FD） scheme for the non-stationary Stokes equation with a real practical applied background. A reduced FD scheme is established with lower dimensions and sufficiently high accuracy, and the error estimates are provided between the reduced and the classical FD solutions. Some numerical examples illustrate that the numerical results are consistent with theoretical conclusions. Moreover, it is shown that the reduced FD scheme based on the POD method is feasible and efficient in solving the FD scheme for the non-stationary Stokes equation.展开更多
Existing papers on human capital and growth in China has been using single equation estimations.This might cause a simultaneity bias if a two-way causality between the two variables exists.In this paper,the author per...Existing papers on human capital and growth in China has been using single equation estimations.This might cause a simultaneity bias if a two-way causality between the two variables exists.In this paper,the author performs vector autoregressive estimations using panel data on the number of graduates at each level of education as a proxy for human capital in China during 1991-2005.The results show that investment in human capital increases output per worker at all three levels of education.Regarding the effects of output per worker on the accumulation of human capital,the author finds mixed results with the primary-school graduates'benefits the most from increases in per capita output.展开更多
基金supported by NSFC 11171065NSFJS BK2011058+3 种基金China Postdoctoral Science Foundation funded project under Grant No.2010471366Jiangsu Planned Projects for Postdoctoral Research Funds under Grant No.1001068CNUST Research Funding under Grant No.2010ZYTS071National Social Science Foundation of China under Grant No.09BTJ004
文摘This paper develops the large sample properties of the solutions of the general estimating equations which are unbiased or asymptotically unbiased or with nuisance parameters for correlated data.The authors do not make the assumption that the estimating equations come from some objective function when we establish the large sample properties of the solutions.So these results extend the work of Newey and McFadden(1994) and are more widely applicable.Furthermore,we provide some examples to justify the importance of our work.
基金supported by National Natural Science Foundation of China(Grant Nos.11771431,11690015,11926341,11601080 and 11671275)Key Laboratory of Random Complex Structures and Data Science,Chinese Academy of Sciences(Grant No.2008DP173182)the Fundamental Research Funds for the Central Universities in University of International Business and Economics(Grant No.CXTD10-09)。
文摘Missing covariate data arise frequently in biomedical studies.In this article,we propose a class of weighted estimating equations for the additive hazards regression model when some of the covariates are missing at random.Time-specific and subject-specific weights are incorporated into the formulation of weighted estimating equations.Unified results are established for estimating selection probabilities that cover both parametric and non-parametric modelling schemes.The resulting estimators have closed forms and are shown to be consistent and asymptotically normal.Simulation studies indicate that the proposed estimators perform well for practical settings.An application to a mouse leukemia study is illustrated.
基金Supported by Research Grant of Department of Education of Hubei Province(Q20142803)
文摘This paper is devoted to the pointwise estimate of solutions for the initial value problem to the three-dimensional compressible magnetohydrodynamic equations, which models the dynamics of compressible quasi-neutrally ionized fluids under the influence of electromagnetic fields. Based on the detailed analysis of the Green function of the linearized system, we obtain the pointwise estimates of smooth solutions when the initial data is sufficiently small with the algebraic decay to the constant equilibrium. As the by-product, we also show the corresponding pL-estimates of the smooth solutions.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1130123111171235)
文摘In this paper, we consider a class of Monge-Ampere equations in relative differential geometry. Given these equations with zero boundary values in a smooth strictly convex bounded domain, we obtain second order derivative estimates of the convex solutions.
基金National Key R&D Program of the Ministry of Science and TechnologyConstruction of the Technical System for"Treating the Disease"in Traditional Chinese Medicine(No.2018YFC1704705)2015 Special Research Project of the Chinese Medicine Industry of the National Administration of Traditional Chinese Medicine:R&D and Demonstration of Recurrence Risk Assessment System for Ischemic Stroke Disease with Chinese Medicine Characteristic Health Management(No.201507003-8).
文摘Objective:To explore the appropriate modeling method of the early warning model of ischemic stroke recurrence in TCM.Methods:This was a prospective,multi-center and registered study conducted in 7 clinical subcenters from 8 provinces and 10 cities in China between 3rd November 2016 and 27th April,2019.1,741 patients with first-ever ischemic stroke were recruited.Univariate analysis was carried out using distance correlation coefficient,mutual information entropy,and statistical correlation test.Multivariate analysis adopted multi-factor Cox regression model and combined with expert opinions in the field of stroke to determine modeling variables.The generalized estimating equation of longitudinal data and the Cox proportional hazard regression model of cross-sectional data were used to construct and compare in the early warning model of ischemic stroke recalls.The area under the ROC curve(AUC value)was used to evaluate the early warning capability of the model.Results:The follow-up time was 1-3 years,and the median follow-up time was 1.42 years(95%CI:1.37-1.47).Recurrence events occurred in 175 cases,and the cumulative recurrence rate was 10.05%(95%CI:8.64%-11.47%).The AUC values of the TCM syndrome and TCM constitution model were 0.71809 and 0.72668 based on the generalized estimating equation and the AUC values.Conclusion:The generalized estimating equation may be more suitable for the construction of early warning models of stroke recurrence with TCM characteristics,which provides a certain reference for the evaluation of secondary prevention of ischemic stroke.
基金Supported by the National Natural Science Foundation of China(Grant No.11171349)the Science Foundation of Hebei Province(Grant No.A2010000346)
文摘In this article, we first propose the Riemann-Hilbert problem for uniformly elliptic complex equations of first order and its well-posed-ness in multiply connected domains.Then we give the integral representation of solutions for modified Riemann-Hilbert problem of the complex equations. Moreover we shall obtain a priori estimates of solutions of the modified Riemann-Hilbert problem and verify its solvability. Finally the solvability results of the original boundary value problem can be obtained.
文摘In longitudinal data analysis, our primary interest is in the estimation of regression parameters for the marginal expectations of the longitudinal responses, and the longitudinal correlation parameters are of secondary interest. The joint likelihood function for longitudinal data is challenging, particularly due to correlated responses. Marginal models, such as generalized estimating equations (GEEs), have received much attention based on the assumption of the first two moments of the data and a working correlation structure. The confidence regions and hypothesis tests are constructed based on the asymptotic normality. This approach is sensitive to the misspecification of the variance function and the working correlation structure which may yield inefficient and inconsistent estimates leading to wrong conclusions. To overcome this problem, we propose an empirical likelihood (EL) procedure based on a set of estimating equations for the parameter of interest and discuss its <span style="font-family:Verdana;">characteristics and asymptotic properties. We also provide an algorithm base</span><span style="font-family:Verdana;">d on EL principles for the estimation of the regression parameters and the construction of its confidence region. We have applied the proposed method in two case examples.</span>
文摘The purpose of this article is to investigate approaches for modeling individual patient count/rate data over time accounting for temporal correlation and non</span><span style="font-family:Verdana;">-</span><span style="font-family:Verdana;">constant dispersions while requiring reasonable amounts of time to search over alternative models for those data. This research addresses formulations for two approaches for extending generalized estimating equations (GEE) modeling. These approaches use a likelihood-like function based on the multivariate normal density. The first approach augments standard GEE equations to include equations for estimation of dispersion parameters. The second approach is based on estimating equations determined by partial derivatives of the likelihood-like function with respect to all model parameters and so extends linear mixed modeling. Three correlation structures are considered including independent, exchangeable, and spatial autoregressive of order 1 correlations. The likelihood-like function is used to formulate a likelihood-like cross-validation (LCV) score for use in evaluating models. Example analyses are presented using these two modeling approaches applied to three data sets of counts/rates over time for individual cancer patients including pain flares per day, as needed pain medications taken per day, and around the clock pain medications taken per day per dose. Means and dispersions are modeled as possibly nonlinear functions of time using adaptive regression modeling methods to search through alternative models compared using LCV scores. The results of these analyses demonstrate that extended linear mixed modeling is preferable for modeling individual patient count/rate data over time</span><span style="font-family:Verdana;">,</span><span style="font-family:Verdana;"> because in example analyses</span><span style="font-family:Verdana;">,</span><span style="font-family:Verdana;"> it either generates better LCV scores or more parsimonious models and requires substantially less time.
基金Supported by Chang Gung Memorial Hospital research project grants CMRPG470051-470052
文摘AIM:To explore the value of fecal lactoferrin in predicting and monitoring the clinical severity of infectious diarrhea.METHODS:Patients with acute infectious diarrhea ranging from 3 mo to 10 years in age were enrolled,and one to three stool samples from each subject were collected.Certain parameters,including white blood cells /differential count,C-reactive protein,fecal mucus,fecal pus cells,duration of fever,vomiting,diarrhea and severity(indicated by Clark and Vesikari scores),were recorded and analyzed.Fecal lactoferrin was determined by enzyme-linked immunosorbent assay and compared in different pathogen and disease activity.Generalized estimating equations(GEE) were also used for analysis.RESULTS:Data included 226 evaluations for 117 individuals across three different time points.Fecal lactoferrin was higher in patients with Salmonella(11.17 μg/g ± 2.73 μg/g) or Campylobacter(10.32 μg/g ± 2.94 μg/g) infections and lower in patients with rotavirus(2.82 μg/g ± 1.27 μg/g) or norovirus(3.16 μg/g ± 1.18 μg/g) infections.Concentrations of fecal lactoferrin were significantly elevated in patients with severe(11.32 μg/g ± 3.29 μg/g) or moderate(3.77 μg/g ± 2.08 μg/g) disease activity compared with subjects with mild(1.51 μg/g ± 1.36 μg/g) disease activity(P < 0.05).GEE analysis suggests that this marker could be used to monitor the severity and course of gastrointestinal infections and may provide information for disease management.CONCLUSION:Fecal lactoferrin increased during bacterial infection and with greater disease severity and may be a good marker for predicting and monitoring intestinal inflammation in children with infectious diarrhea.
基金Supported by the National Natural Science Foundation of China(10571093)
文摘In stratified survey sampling, sometimes we have complete auxiliary information. One of the fundamental questions is how to effectively use the complete auxiliary information at the estimation stage. In this paper, we extend the model-calibration method to obtain estimators of the finite population mean by using complete auxiliary information from stratified sampling survey data. We show that the resulting estimators effectively use auxiliary information at the estimation stage and possess a number of attractive features such as asymptotically design-unbiased irrespective of the working model and approximately model-unbiased under the model. When a linear working-model is used, the resulting estimators reduce to the usual calibration estimator（or GREG）.
文摘Objective This study explored the correlation of longitudinal changes in serum alanine aminotransferase （ALT） and aspartate aminotransferase （AST） levels with the incidence of metabolic syndrome （Mets） based on a dynamic health examination cohort. Methods A Mets-free dynamic cohort involving 4541 participants who underwent at least three health examinations from 2006 to 2011 was included in the study. Mets was defined according to the Chinese Medical Association Diabetes Branch definition that included hypertension, obesity, hyperlipidemia, and hyperglycemia. Generalized estimating equation （GEE） model was used to analyze multivariate relative risk （RR） of repeated observations of ALT and AST in quartiles for Mets or its components according to gender. Results In all, 826 Mets cases were reported. Adjustment of relevant parameters indicated that time-varying changes in ALT and AST levels were positively associated with the incidence of Mets in a dose-response manner. Positive association between high ALT levels and fatty liver was much stronger than that between high AST levels and fatty liver, particularly in male participants. These associations were consistently observed in the following subgroups： participants with ALT and AST levels of 〈40 U/L, participants with of 〈25 kg/m2, and participants with non-fatty liver. Furthermore, participants with 2 Mets components at baseline showed lower multivariate adjusted RRs of ALT and AST for Mets than participants with 0-1 Mets component. Conclusion These results suggested that elevated serum ALT and AST levels were early biomarkers of Mets or its components.
基金Supported by Chang Gung Memorial Hospital,No.CMRPG3C0701and National Science Council,No.NSC101-2314-B-182A-025-MY3 and No.MOST 107-2314-B-039-059.
文摘BACKGROUND Genome-wide association studies from Asia indicate that HLA-DP and HLA-DQ loci are important in persistent hepatitis B virus(HBV)infections.One of the key elements for HBV-related carcinogenesis is persistent viral replication and inflammation.AIM To examine genetic and nongenetic factors with persistent HBV infection and viral load in families with hepatocellular carcinoma(HCC).METHODS The HCC families included 301 hepatitis B surface antigen(HBsAg)carriers and 424 noncarriers born before the nationwide vaccination program was initiated in 1984.Five HBV-related single nucleotide polymorphisms(SNPs)—rs477515,rs9272105,rs9276370,rs7756516,and rs9277535—were genotyped.Factors associated with persistent HBV infection and viral load were analyzed by a generalized estimating equation.RESULTS In the first-stage persistent HBV study,all SNPs except rs9272105 were associated with persistent infection.A significantly higher area under the reciprocal operating characteristic curve for nongenetic factors vs genetic factors(P<0.001)suggests that the former play a major role in persistent HBV infection.In the second-stage viral load study,we added 8 HBsAg carriers born after 1984.The 309 HBsAg carriers were divided into low(n=162)and high viral load(n=147)groups with an HBV DNA cutoff of 105 cps/mL.Sex,relationship to the index case,rs477515,rs9272105,and rs7756516 were associated with viral load.Based on the receiver operating characteristic curve analysis,genetic and nongenetic factors affected viral load equally in the HCC family cohort(P=0.3117).CONCLUSION In these east Asian adults,the mechanism of persistent HBV infection-related SNPs was a prolonged viral replication phase.
基金Supported by the National Natural Science Foundation of China (11171263)
文摘Multivariate failure time data are frequently encountered in biomedical research.In this article,we model marginal hazards with accelerated hazards model to analyze multivariate failure time data.Estimating equations are derived analogous to generalized estimating equation method.Under certain regular conditions,the resultant estimators for the regression parameters are shown to be asymptotically normal.Furthermore,we also establish the weak convergence of estimators for the baseline cumulative hazard functions.
文摘Intramuscular injections can cause damage to arteries, veins and nerves. Achieving maximum effects of medications through precise intramuscular (IM) injections must be assured and with certainty, particularly with long-acting injection drugs (LAI). The purpose of this study is to determine precision in IM LAIs of patients with schizophrenia. These evidences estimate “Distance from the Epidermis to the Under-Fascia” (DEUF) and “Distance from Epidermis to the Upper-Arm Bone” (DEB) of the deltoid muscle. Explanatory variables include body height, weight, body-mass index (BMI), deltoid-muscle circumference, fat percentage and muscle mass measured by body composition monitor. Sixty nine subjects are included based on the Diagnostic Statistical Manual of Mental Disorders (DSM-IV, 1994), and receive treatments of typical and atypical antipsychotic LAI. There are 46 males and 23 females with average age of 51.41 (Standard Deviation = 13.58) and ranging from 21 to 81 years who are all right-handed. Ultrasonographic data and those from explanatory variables are calculated using Spearman’s rank correlation coefficients. Multiple regression analysis (step-wise method/forced input method) is performed assuming DEUF or DEB as dependent variables. Significant correlations are found with highest adjusted R-square. Paired t-tests show differences in average values of actual ultrasonographic measurements assigned to DEUF or DEB, and the regression equations for accuracy. Ultrasonographic values are assigned multiple-regression equations as true values, and the calculated values are compared with those obtained by regression equations. There are no significant differences observed for either the right or left arm. The multiple regression equations for BMI and fat percentages (upper extremity estimation) of DEUF, and for BMI and injection site circumference of estimated DEB, successfully value the DEUF and DEB. By using these multiple regression equations for IM injection to the deltoid-muscle, DEUF can better ensure accurate LAI into the muscle through body monitor, DEB, and measured values of the deltoid-muscle injection site circumference.
基金supported by a grant from the NIH(No.U42 RR16607)
文摘Objective：A computational model of insulin secretion and glucose metabolism for assisting the diagnosis of diabetes mellitus in clinical research is introduced.The proposed method for the estimation of parameters for a system of ordinary differential equations（ODEs）that represent the time course of plasma glucose and insulin concentrations during glucose tolerance test（GTT）in physiological studies is presented.The aim of this study was to explore how to interpret those laboratory glucose and insulin data as well as enhance the Ackerman mathematical model.Methods：Parameters estimation for a system of ODEs was performed by minimizing the sum of squared residuals（SSR）function,which quantifies the difference between theoretical model predictions and GTT＇s experimental observations.Our proposed perturbation search and multiple-shooting methods were applied during the estimating process.Results：Based on the Ackerman＇s published data,we estimated the key parameters by applying R-based iterative computer programs.As a result,the theoretically simulated curves perfectly matched the experimental data points.Our model showed that the estimated parameters,computed frequency and period values,were proven a good indicator of diabetes.Conclusion：The present paper introduces a computational algorithm to biomedical problems,particularly to endocrinology and metabolism fields,which involves two coupled differential equations with four parameters describing the glucose-insulin regulatory system that Ackerman proposed earlier.The enhanced approach may provide clinicians in endocrinology and metabolism field insight into the transition nature of human metabolic mechanism from normal to impaired glucose tolerance.
基金the Natural Science Foundation of China(10371042,10671038)
文摘In this article, robust generalized estimating equation for the analysis of partial linear mixed model for longitudinal data is used. The authors approximate the nonparametric function by a regression spline. Under some regular conditions, the asymptotic properties of the estimators are obtained. To avoid the computation of high-dimensional integral, a robust Monte Carlo Newton-Raphson algorithm is used. Some simulations are carried out to study the performance of the proposed robust estimators. In addition, the authors also study the robustness and the efficiency of the proposed estimators by simulation. Finally, two real longitudinal data sets are analyzed.
基金supported by grants from the Natural Science Foundation of China (No.30600364,30470534,and 30230210)the NSFC-Canadian Institutes of Health Research (CIHR) Joint Health Research Initia-tive Proposal (No.30811120436)+3 种基金the NSFC/RGC Joint Research Scheme (No.30731160618)Shanghai Leading Academic Discipline Project (No.S30501)supported by grants from NIH (No.P50AR055081,R01AG026564,R01AR050496,and R01AR057049)the Dickson/Missouri endowment
文摘Quantitative traits often underlie risk for complex diseases. Many studies collect multiple correlated quantitative phenotypes and perform univariate analyses on each of them respectively. However, this strategy may not be powerful and has limitations to detect plei- otropic genes that may underlie correlated quantitative traits. In addition, testing multiple traits individually will exacerbate perplexing problem of multiple testing. In this study, generalized estimating equation 2 （GEE2） is applied to association mapping of two correlated quantitative traits. We suppose that a quantitative trait locus is located in a chromosome region that exerts pleiotropic effects on multiple quantitative traits. In that region, multiple SNPs are genotyped. Genotypes of these SNPs and the two quantitative traits affected by a causal SNP were simulated under various parameter values： residual correlation coefficient between two traits, causal SNP heritability, minor allele frequency of the causal SNP, extent of linkage disequilibrium with the causal SNP, and the test sample size. By power ana- lytical analyses, it is showed that the bivariate method is generally more powerful than the univariate method. This method is robust and yields false-positive rates close to the pre-set nominal significance level. Our real data analyses attested to the usefulness of the method.
基金The Science Foundation(JA12301)of Fujian Educational Committeethe Teaching Quality Project(ZL0902/TZ(SJ))of Higher Education in Fujian Provincial Education Department
文摘Recurrent event gap times data frequently arise in biomedical studies and often more than one type of event is of interest. To evaluate the effects of covariates on the marginal recurrent event hazards functions, there exist two types of hazards models： the multiplicative hazards model and the additive hazards model. In the paper, we propose a more flexible additive-multiplicative hazards model for multiple type of recurrent gap times data, wherein some covariates are assumed to be additive while others are multiplicative. An estimating equation approach is presented to estimate the regression parameters. We establish asymptotic properties of the proposed estimators.
基金Project supported by the National Natural Science Foundation of China (Nos. 10871022, 11061009, and 40821092)the National Basic Research Program of China (973 Program) (Nos. 2010CB428403, 2009CB421407, and 2010CB951001)the Natural Science Foundation of Hebei Province of China (No. A2010001663)
文摘The proper orthogonal decomposition （POD） is a model reduction technique for the simulation Of physical processes governed by partial differential equations （e.g., fluid flows）. It has been successfully used in the reduced-order modeling of complex systems. In this paper, the applications of the POD method are extended, i.e., the POD method is applied to a classical finite difference （FD） scheme for the non-stationary Stokes equation with a real practical applied background. A reduced FD scheme is established with lower dimensions and sufficiently high accuracy, and the error estimates are provided between the reduced and the classical FD solutions. Some numerical examples illustrate that the numerical results are consistent with theoretical conclusions. Moreover, it is shown that the reduced FD scheme based on the POD method is feasible and efficient in solving the FD scheme for the non-stationary Stokes equation.
文摘Existing papers on human capital and growth in China has been using single equation estimations.This might cause a simultaneity bias if a two-way causality between the two variables exists.In this paper,the author performs vector autoregressive estimations using panel data on the number of graduates at each level of education as a proxy for human capital in China during 1991-2005.The results show that investment in human capital increases output per worker at all three levels of education.Regarding the effects of output per worker on the accumulation of human capital,the author finds mixed results with the primary-school graduates'benefits the most from increases in per capita output.
