THE LARGE SAMPLE PROPERTIES OF THE SOLUTIONS OF GENERAL ESTIMATING EQUATIONS

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.

A class of weighted estimating equations for additive hazards models with covariates missing at random

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.

Construction of an Early Warning Model for Ischemic Stroke Recurrence Based on Generalized Estimating Equation

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.

Empirical Likelihood Based Longitudinal Data Analysis

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 characteristics and asymptotic properties. We also provide an algorithm based 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.

Modeling Individual Patient Count/Rate Data over Time with Applications to Cancer Pain Flares and Cancer Pain Medication Usage

The purpose of this article is to investigate approaches for modeling individual patient count/rate data over time accounting for temporal correlation and non-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, because in example analyses, it either generates better LCV scores or more parsimonious models and requires substantially less time.

Usefulness of fecal lactoferrin in predicting and monitoring the clinical severity of infectious diarrhea

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.

A Model-calibration Approach to Using Complete Auxiliary Information from Stratified Sampling Survey Data

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）.

Longitudinal Changes in Liver Aminotransferases Predict Metabolic Syndrome in Chinese Patients with Nonviral Hepatitis

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.

Hepatitis B virus persistent infection-related single nucleotide polymorphisms in HLA regions are associated with viral load in hepatoma families

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.

Explanatory Variables as Evidence for Precision in Intramuscular Long-Acting Injections of Patients with Schizophrenia

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.

A computational model of the human glucose-insulin regulatory system

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.

ROBUST ESTIMATION IN PARTIAL LINEAR MIXED MODEL FOR LONGITUDINAL DATA

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.

The Additive-multiplicative Hazards Model for Multiple Type of Recurrent Gap Times

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.

Reduced finite difference scheme and error estimates based on POD method for non-stationary Stokes equation

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.

The simultaneity in human capital estimations： The case of China

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.

Body Surface Area Prediction in Odorrana grahami

Body surface area（BSA）was regarded as a more readily quantifiable parameter relative to body mass in the normalization of comparative biochemistry and physiology.The BSA prediction has attracted unceasing research back more than a century on animals,especially on humans and rats.Few studies in this area for anurans were reported,and the equation for body surface area（S）and body mass（W）：S=9.9 W 0.56,which was concluded from toads of four species in 1969,was generally adopted to estimate the body surface areas for anurans until recent years.However,this equation was not applicable to Odorrana grahami.The relationship between body surface area and body mass for this species was established as：S=15.4 W 0.579.Our current results suggest estimation equations should be used cautiously across different species and body surface area predictions on more species need to be conducted.

Efficient Shrinkage Estimation about the Partially Linear Varying Coefficient Model with Random Effect for Longitudinal Data

In this paper, an efficient shrinkage estimation procedure for the partially linear varying coefficient model (PLVC) with random effect is considered. By selecting the significant variable and estimating the nonzero coefficient, the model structure specification is accomplished by introducing a novel penalized estimating equation. Under some mild conditions, the asymptotic properties for the proposed model selection and estimation results, such as the sparsity and oracle property, are established. Some numerical simulation studies and a real data analysis are presented to examine the finite sample performance of the procedure.

SOME DIAGNOSTICS IN NONLINEAR REPRODUCTIVE DISPERSION MODELS

This article discusses the problem of the detection of influential cases in nonlinear reproductive dispersion models (NRDM). A diagnostic based on case\|deletion approach in estimating equations is proposed. The relationships between the generalized leverage defined by Wei et al. in 1998, statistical curvature, and the local influence of the response vector perturbations are investigated in NRDM. Two numerical examples are given to illustrate the results.

The Estimates L_(1)-L_(∞) for the Reduced Radial Equation of Schrodinger

Estimates of the type L1-L∞ for the Schr&#246;dinger Equation on the Line and on Half-Line with a regular potential V(x), express the dispersive nature of the Schr&#246;dinger 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 Schr&#246;dinger 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 Schr&#246;dinger Equation (RRSE) (whose main characteristic is the addition a singular term of quadratic order to a regular potential V(x)) in the Schr&#246;dinger 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.

Estimating Survival Treatment Effects with Covariate Adjustment Using Propensity Score

Propensity score is widely used to estimate treatment effects in observational studies.The covariate adjustment using propensity score is the most straightforward method in the literature of causal inference.In this article,we estimate the survival treatment effect with covariate adjustment using propensity score in the semiparametric accelerated failure time model.We establish the asymptotic properties of the proposed estimator by simultaneous estimating equations.We conduct simulation studies to evaluate the finite sample performance of the proposed method.A real data set from the German Breast Cancer Study Group is analyzed to illustrate the proposed method.