AIM:To build a functional generalized estimating equation(GEE)model to detect glaucomatous visual field progression and compare the performance of the proposed method with that of commonly employed algorithms.METHODS:...AIM:To build a functional generalized estimating equation(GEE)model to detect glaucomatous visual field progression and compare the performance of the proposed method with that of commonly employed algorithms.METHODS:Totally 716 eyes of 716 patients with primary open angle glaucoma(POAG)with at least 5 reliable 24-2 test results and 2y of follow-up were selected.The functional GEE model was used to detect perimetric progression in the training dataset(501 eyes).In the testing dataset(215 eyes),progression was evaluated the functional GEE model,mean deviation(MD)and visual field index(VFI)rates of change,Advanced Glaucoma Intervention Study(AGIS)and Collaborative Initial Glaucoma Treatment Study(CIGTS)scores,and pointwise linear regression(PLR).RESULTS:The proposed method showed the highest proportion of eyes detected as progression(54.4%),followed by the VFI rate(34.4%),PLR(23.3%),and MD rate(21.4%).The CIGTS and AGIS scores had a lower proportion of eyes detected as progression(7.9%and 5.1%,respectively).The time to detection of progression was significantly shorter for the proposed method than that of other algorithms(adjusted P≤0.019).The VFI rate displayed moderate pairwise agreement with the proposed method(k=0.47).CONCLUSION:The functional GEE model shows the highest proportion of eyes detected as perimetric progression and the shortest time to detect perimetric progression in patients with POAG.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
Issues concerning spatial dependence among cross-sectional units in econometrics have received more and more attention,while in statistical modeling,rarely can the analysts have a priori knowledge of the dependency re...Issues concerning spatial dependence among cross-sectional units in econometrics have received more and more attention,while in statistical modeling,rarely can the analysts have a priori knowledge of the dependency relationship of the response variable with respect to independent variables.This paper proposes an automatic structure identification and variable selection procedure for semiparametric spatial autoregressive model,based on the generalized method of moments and the smooth-threshold estimating equations.The novel method is easily implemented without solving any convex optimization problems.Model identification consistency is theoretically established in the sense that the proposed method can automatically separate the linear and zero components from the varying ones with probability approaching to one.Detailed issues on computation and turning parameter selection are discussed.Some Monte Carlo simulations are conducted to demonstrate the finite sample performance of the proposed procedure.Two empirical applications on Boston housing price data and New York leukemia data are further considered.展开更多
In this article, empirical likelihood inference for estimating equation with missing data is considered. Based on the weighted-corrected estimating function, an empirical log-likelihood ratio is proved to be a standar...In this article, empirical likelihood inference for estimating equation with missing data is considered. Based on the weighted-corrected estimating function, an empirical log-likelihood ratio is proved to be a standard chiqsquare distribution asymptotically under some suitable conditions. This result is different from those derived before. So it is convenient to construct confidence regions for the parameters of interest. We also prove that our proposed maximum empirical likelihood estimator θ is asymptotically normal and attains the semiparametric efficiency bound of missing data. Some simulations indicate that the proposed method performs the best.展开更多
The method of generalized estimating equations （GEE） introduced by K. Y. Liang and S. L. Zeger has been widely used to analyze longitudinal data. Recently, this method has been criticized for a failure to protect ag...The method of generalized estimating equations （GEE） introduced by K. Y. Liang and S. L. Zeger has been widely used to analyze longitudinal data. Recently, this method has been criticized for a failure to protect against misspecification of working correlation models, which in some cases leads to loss of efficiency or infeasibility of solutions. In this paper, we present a new method named as ＇weighted estimating equations （WEE）＇ for estimating the correlation parameters. The new estimates of correlation parameters are obtained as the solutions of these weighted estimating equations. For some commonly assumed correlation structures, we show that there exists a unique feasible solution to these weighted estimating equations regardless the correlation structure is correctly specified or not. The new feasible estimates of correlation parameters are consistent when the working correlation structure is correctly specified. Simulation results suggest that the new method works well in finite samples.展开更多
This paper presents a novel class of semiparametric estimating functions for the additive model with right-censored data that are obtained from general biased-sampling. The new estimator can be obtained using a weight...This paper presents a novel class of semiparametric estimating functions for the additive model with right-censored data that are obtained from general biased-sampling. The new estimator can be obtained using a weighted estimating equation for the covariate coefficients, by embedding the biased-sampling data into left-truncated and right-censored data. The asymptotic properties(consistency and asymptotic normality) of the proposed estimator are derived via the modern empirical processes theory. Based on the cumulative residual processes, we also propose graphical and numerical methods to assess the adequacy of the additive risk model.The good finite-sample performance of the proposed estimator is demonstrated by simulation studies and two applications of real datasets.展开更多
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
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
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
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
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
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
Estimates of the type L1-L∞ for the Schrödinger Equation on the Line and on Half-Line with a regular potential V(x), express the dispersive nature of the Schrödinger Equation and are the essential e...Estimates of the type L1-L∞ for the Schrödinger Equation on the Line and on Half-Line with a regular potential V(x), express the dispersive nature of the Schrödinger Equation and are the essential elements in the study of the problems of initial values, the asymptotic times for large solutions and Scattering Theory for the Schrödinger equation and non-linear in general;for other equations of Non-linear Evolution. In general, the estimates Lp-Lp' express the dispersive nature of this equation. And its study plays an important role in problems of non-linear initial values;likewise, in the study of problems nonlinear initial values;see [1] [2] [3]. On the other hand, following a series of problems proposed by V. Marchenko [4], that we will name Marchenko’s formulation, and relate it to a generalized version of Theorem 1 given in [1], the main theorem (Theorem 1) of this article provides a transformation operator W?that transforms the Reduced Radial Schrödinger Equation (RRSE) (whose main characteristic is the addition a singular term of quadratic order to a regular potential V(x)) in the Schrödinger Equation on Half-Line (RSEHL) under W. That is to say;W?eliminates the singular term of quadratic order of potential V(x) in the asymptotic development towards zero and adds to the potential V(x) a bounded term and a term exponentially decrease fast enough in the asymptotic development towards infinity, which continues guaranteeing the uniqueness of the potential V(x) in the condition of the infinity boundary. Then the L1-L∞ estimates for the (RRSE) are preserved under the transformation operator , as in the case of (RSEHL) where they were established in [3]. Finally, as an open question, the possibility of extending the L1-L∞ estimates for the case (RSEHL), where added to the potential V(x) an analytical perturbation is mentioned.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
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
基金Supported by the Korea Health Technology R&D Project through the Korea Health Industry Development Institute(KHIDI),funded by the Ministry of Health&Welfare,Republic of Korea(No.HR20C0026)the National Research Foundation of Korea(NRF)(No.RS-2023-00247504)the Patient-Centered Clinical Research Coordinating Center,funded by the Ministry of Health&Welfare,Republic of Korea(No.HC19C0276).
文摘AIM:To build a functional generalized estimating equation(GEE)model to detect glaucomatous visual field progression and compare the performance of the proposed method with that of commonly employed algorithms.METHODS:Totally 716 eyes of 716 patients with primary open angle glaucoma(POAG)with at least 5 reliable 24-2 test results and 2y of follow-up were selected.The functional GEE model was used to detect perimetric progression in the training dataset(501 eyes).In the testing dataset(215 eyes),progression was evaluated the functional GEE model,mean deviation(MD)and visual field index(VFI)rates of change,Advanced Glaucoma Intervention Study(AGIS)and Collaborative Initial Glaucoma Treatment Study(CIGTS)scores,and pointwise linear regression(PLR).RESULTS:The proposed method showed the highest proportion of eyes detected as progression(54.4%),followed by the VFI rate(34.4%),PLR(23.3%),and MD rate(21.4%).The CIGTS and AGIS scores had a lower proportion of eyes detected as progression(7.9%and 5.1%,respectively).The time to detection of progression was significantly shorter for the proposed method than that of other algorithms(adjusted P≤0.019).The VFI rate displayed moderate pairwise agreement with the proposed method(k=0.47).CONCLUSION:The functional GEE model shows the highest proportion of eyes detected as perimetric progression and the shortest time to detect perimetric progression in patients with POAG.
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 Natural Science Foundation of Hunan Province(Grant 2022JJ30368)the National Natural Science Foundation of China(Grants 11801168,11801169,12071124)the Discovery Grants(RG/PIN261567-2013)from National Science and Engineering Council of Canada.
文摘Issues concerning spatial dependence among cross-sectional units in econometrics have received more and more attention,while in statistical modeling,rarely can the analysts have a priori knowledge of the dependency relationship of the response variable with respect to independent variables.This paper proposes an automatic structure identification and variable selection procedure for semiparametric spatial autoregressive model,based on the generalized method of moments and the smooth-threshold estimating equations.The novel method is easily implemented without solving any convex optimization problems.Model identification consistency is theoretically established in the sense that the proposed method can automatically separate the linear and zero components from the varying ones with probability approaching to one.Detailed issues on computation and turning parameter selection are discussed.Some Monte Carlo simulations are conducted to demonstrate the finite sample performance of the proposed procedure.Two empirical applications on Boston housing price data and New York leukemia data are further considered.
基金supported by National Natural Science Foundation of China (Grant Nos.11171188, 11201499 and 10921101)Natural Science Foundation of Shandong Province (Grant Nos. ZR2010AZ001 and ZR2011AQ007)+1 种基金Shandong Provincial Scientific Research Reward Foundation for Excellent Young and MiddleAged Scientists (Grant No. BS2011SF006)K.C. Wong-HKBU Fellowship Program for Mainland Visiting Scholars 2010-11
文摘In this article, empirical likelihood inference for estimating equation with missing data is considered. Based on the weighted-corrected estimating function, an empirical log-likelihood ratio is proved to be a standard chiqsquare distribution asymptotically under some suitable conditions. This result is different from those derived before. So it is convenient to construct confidence regions for the parameters of interest. We also prove that our proposed maximum empirical likelihood estimator θ is asymptotically normal and attains the semiparametric efficiency bound of missing data. Some simulations indicate that the proposed method performs the best.
文摘The method of generalized estimating equations （GEE） introduced by K. Y. Liang and S. L. Zeger has been widely used to analyze longitudinal data. Recently, this method has been criticized for a failure to protect against misspecification of working correlation models, which in some cases leads to loss of efficiency or infeasibility of solutions. In this paper, we present a new method named as ＇weighted estimating equations （WEE）＇ for estimating the correlation parameters. The new estimates of correlation parameters are obtained as the solutions of these weighted estimating equations. For some commonly assumed correlation structures, we show that there exists a unique feasible solution to these weighted estimating equations regardless the correlation structure is correctly specified or not. The new feasible estimates of correlation parameters are consistent when the working correlation structure is correctly specified. Simulation results suggest that the new method works well in finite samples.
基金supported by National Natural Science Foundation of China(Grant Nos.11771133 and 11401194)the Natural Science Foundation of Hunan Province of China(Grant No.2017JJ3021)+2 种基金Zhao’s work was supported by National Natural Science Foundation of China(Grant No.11771366)Zhou’s work was supported by the State Key Program of National Natural Science Foundation of China(Grant No.71331006)the State Key Program in the Major Research Plan of National Natural Science Foundation of China(Grant No.91546202)
文摘This paper presents a novel class of semiparametric estimating functions for the additive model with right-censored data that are obtained from general biased-sampling. The new estimator can be obtained using a weighted estimating equation for the covariate coefficients, by embedding the biased-sampling data into left-truncated and right-censored data. The asymptotic properties(consistency and asymptotic normality) of the proposed estimator are derived via the modern empirical processes theory. Based on the cumulative residual processes, we also propose graphical and numerical methods to assess the adequacy of the additive risk model.The good finite-sample performance of the proposed estimator is demonstrated by simulation studies and two applications of real datasets.
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 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.
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Estimates of the type L1-L∞ for the Schrödinger Equation on the Line and on Half-Line with a regular potential V(x), express the dispersive nature of the Schrödinger Equation and are the essential elements in the study of the problems of initial values, the asymptotic times for large solutions and Scattering Theory for the Schrödinger equation and non-linear in general;for other equations of Non-linear Evolution. In general, the estimates Lp-Lp' express the dispersive nature of this equation. And its study plays an important role in problems of non-linear initial values;likewise, in the study of problems nonlinear initial values;see [1] [2] [3]. On the other hand, following a series of problems proposed by V. Marchenko [4], that we will name Marchenko’s formulation, and relate it to a generalized version of Theorem 1 given in [1], the main theorem (Theorem 1) of this article provides a transformation operator W?that transforms the Reduced Radial Schrödinger Equation (RRSE) (whose main characteristic is the addition a singular term of quadratic order to a regular potential V(x)) in the Schrödinger Equation on Half-Line (RSEHL) under W. That is to say;W?eliminates the singular term of quadratic order of potential V(x) in the asymptotic development towards zero and adds to the potential V(x) a bounded term and a term exponentially decrease fast enough in the asymptotic development towards infinity, which continues guaranteeing the uniqueness of the potential V(x) in the condition of the infinity boundary. Then the L1-L∞ estimates for the (RRSE) are preserved under the transformation operator , as in the case of (RSEHL) where they were established in [3]. Finally, as an open question, the possibility of extending the L1-L∞ estimates for the case (RSEHL), where added to the potential V(x) an analytical perturbation is mentioned.
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.
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.
