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
High-dimensional longitudinal data arise frequently in biomedical and genomic research. It is important to select relevant covariates when the dimension of the parameters diverges as the sample size increases. We cons...High-dimensional longitudinal data arise frequently in biomedical and genomic research. It is important to select relevant covariates when the dimension of the parameters diverges as the sample size increases. We consider the problem of variable selection in high-dimensional linear models with longitudinal data. A new variable selection procedure is proposed using the smooth-threshold generalized estimating equation and quadratic inference functions (SGEE-QIF) to incorporate correlation information. The proposed procedure automatically eliminates inactive predictors by setting the corresponding parameters to be zero, and simultaneously estimates the nonzero regression coefficients by solving the SGEE-QIF. The proposed procedure avoids the convex optimization problem and is flexible and easy to implement. We establish the asymptotic properties in a high-dimensional framework where the number of covariates increases as the number of cluster increases. Extensive Monte Carlo simulation studies are conducted to examine the finite sample performance of the proposed variable selection procedure.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
Generalized linear models are usually adopted to model the discrete or nonnegative responses.In this paper,empirical likelihood inference for fixed design generalized linear models with longitudinal data is investigat...Generalized linear models are usually adopted to model the discrete or nonnegative responses.In this paper,empirical likelihood inference for fixed design generalized linear models with longitudinal data is investigated.Under some mild conditions,the consistency and asymptotic normality of the maximum empirical likelihood estimator are established,and the asymptotic χ^(2) distribution of the empirical log-likelihood ratio is also obtained.Compared with the existing results,the new conditions are more weak and easy to verify.Some simulations are presented to illustrate these asymptotic properties.展开更多
Although hierarchical correlated data are increasingly available and are being used in evidence-based medical practices and health policy decision making, there is a lack of information about the strengths and weaknes...Although hierarchical correlated data are increasingly available and are being used in evidence-based medical practices and health policy decision making, there is a lack of information about the strengths and weaknesses of the methods of analysis with such data. In this paper, we describe the use of hierarchical data in a family study of alcohol abuse conducted in Edmonton, Canada, that attempted to determine whether alcohol abuse in probands is associated with abuse in their first-degree relatives. We review three methods of analyzing discrete hierarchical data to account for correlations among the relatives. We conclude that the best analytic choice for typical correlated discrete hierarchical data is by nonlinear mixed effects modeling using a likelihood-based approach or multilevel (hierarchical) modeling using a quasilikelihood approach, especially when dealing with heterogeneous patient data.展开更多
Modeling the mean and covariance simultaneously is a common strategy to efficiently estimate the mean parameters when applying generalized estimating equation techniques to longitudinal data. In this article, using ge...Modeling the mean and covariance simultaneously is a common strategy to efficiently estimate the mean parameters when applying generalized estimating equation techniques to longitudinal data. In this article, using generalized estimation equation techniques, we propose a new kind of regression models for parameterizing covariance structures. Using a novel Cholesky factor, the entries in this decomposition have moving average and log innovation interpretation and are modeled as the regression coefficients in both the mean and the linear functions of covariates. The resulting estimators for eovarianee are shown to be consistent and asymptotically normally distributed. Simulation studies and a real data analysis show that the proposed approach yields highly efficient estimators for the parameters in the mean, and provides parsimonious estimation for the covariance structure.展开更多
In this paper, we study the local asymptotic behavior of the regression spline estimator in the framework of marginal semiparametric model. Similarly to Zhu, Fung and He (2008), we give explicit expression for the asy...In this paper, we study the local asymptotic behavior of the regression spline estimator in the framework of marginal semiparametric model. Similarly to Zhu, Fung and He (2008), we give explicit expression for the asymptotic bias of regression spline estimator for nonparametric function f. Our results also show that the asymptotic bias of the regression spline estimator does not depend on the working covariance matrix, which distinguishes the regression splines from the smoothing splines and the seemingly unrelated kernel. To understand the local bias result of the regression spline estimator, we show that the regression spline estimator can be obtained iteratively by applying the standard weighted least squares regression spline estimator to pseudo-observations. At each iteration, the bias of the estimator is unchanged and only the variance is updated.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
The generalized estimating equations(GEE) approach is perhaps one of the most widely used methods for longitudinal data analysis. While the GEE method guarantees the consistency of its estimators under working correla...The generalized estimating equations(GEE) approach is perhaps one of the most widely used methods for longitudinal data analysis. While the GEE method guarantees the consistency of its estimators under working correlation structure misspecification, the corresponding efficiency can be severely affected. In this paper, we propose a new two-step estimation method in which the correlation matrix is assumed to be a linear combination of some known working matrices. Asymptotic properties of the new estimators are developed.Simulation studies are conducted to examine the performance of the proposed estimators. We illustrate the methodology with an epileptic data set.展开更多
Based on the generalized estimating equation approach,the authors propose a parsimonious mean-covariance model for longitudinal data with autoregressive and moving average error process,which not only unites the exist...Based on the generalized estimating equation approach,the authors propose a parsimonious mean-covariance model for longitudinal data with autoregressive and moving average error process,which not only unites the existing autoregressive Cholesky factor model and moving average Cholesky factor model but also provides a wide variety of structures of covariance matrix.The resulting estimators for the regression coefficients in both the mean and the covariance are shown to be consistent and asymptotically normally distributed under mild conditions.The authors demonstrate the effectiveness,parsimoniousness and desirable performance of the proposed approach by analyzing the CD4-I-cell counts data set and conducting extensive simulations.展开更多
Longitudinal data often occur in follow-up studies, and in many situations, there may exist informative observation times and a dependent terminal event such as death that stops the follow-up. We propose a semiparamet...Longitudinal data often occur in follow-up studies, and in many situations, there may exist informative observation times and a dependent terminal event such as death that stops the follow-up. We propose a semiparametric mixed effect model with time-varying latent effects in the analysis of longitudinal data with informative observation times and a dependent terminal event. Estimating equation approaches are developed for parameter estimation, and asymptotic properties of the resulting estimators are established. The finite sample behavior of the proposed estimators is evaluated through simulation studies, and an application to a bladder cancer study is provided.展开更多
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.
文摘High-dimensional longitudinal data arise frequently in biomedical and genomic research. It is important to select relevant covariates when the dimension of the parameters diverges as the sample size increases. We consider the problem of variable selection in high-dimensional linear models with longitudinal data. A new variable selection procedure is proposed using the smooth-threshold generalized estimating equation and quadratic inference functions (SGEE-QIF) to incorporate correlation information. The proposed procedure automatically eliminates inactive predictors by setting the corresponding parameters to be zero, and simultaneously estimates the nonzero regression coefficients by solving the SGEE-QIF. The proposed procedure avoids the convex optimization problem and is flexible and easy to implement. We establish the asymptotic properties in a high-dimensional framework where the number of covariates increases as the number of cluster increases. Extensive Monte Carlo simulation studies are conducted to examine the finite sample performance of the proposed variable selection procedure.
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>
基金supported by the Natural Science Foundation of China under Grant Nos.12031016,11061002,11801033,12071014 and 12131001the National Social Science Fund of China under Grant No.19ZDA121the Natural Science Foundation of Guangxi under Grant Nos.2015GXNSFAA139006 and LMEQF。
文摘Generalized linear models are usually adopted to model the discrete or nonnegative responses.In this paper,empirical likelihood inference for fixed design generalized linear models with longitudinal data is investigated.Under some mild conditions,the consistency and asymptotic normality of the maximum empirical likelihood estimator are established,and the asymptotic χ^(2) distribution of the empirical log-likelihood ratio is also obtained.Compared with the existing results,the new conditions are more weak and easy to verify.Some simulations are presented to illustrate these asymptotic properties.
文摘Although hierarchical correlated data are increasingly available and are being used in evidence-based medical practices and health policy decision making, there is a lack of information about the strengths and weaknesses of the methods of analysis with such data. In this paper, we describe the use of hierarchical data in a family study of alcohol abuse conducted in Edmonton, Canada, that attempted to determine whether alcohol abuse in probands is associated with abuse in their first-degree relatives. We review three methods of analyzing discrete hierarchical data to account for correlations among the relatives. We conclude that the best analytic choice for typical correlated discrete hierarchical data is by nonlinear mixed effects modeling using a likelihood-based approach or multilevel (hierarchical) modeling using a quasilikelihood approach, especially when dealing with heterogeneous patient data.
基金supported by National Natural Science Foundation of China(Grant Nos.11271347 and 11171321)
文摘Modeling the mean and covariance simultaneously is a common strategy to efficiently estimate the mean parameters when applying generalized estimating equation techniques to longitudinal data. In this article, using generalized estimation equation techniques, we propose a new kind of regression models for parameterizing covariance structures. Using a novel Cholesky factor, the entries in this decomposition have moving average and log innovation interpretation and are modeled as the regression coefficients in both the mean and the linear functions of covariates. The resulting estimators for eovarianee are shown to be consistent and asymptotically normally distributed. Simulation studies and a real data analysis show that the proposed approach yields highly efficient estimators for the parameters in the mean, and provides parsimonious estimation for the covariance structure.
基金supported by National Natural Science Foundation of China (Grant Nos.10671038,10801039)Youth Science Foundation of Fudan University (Grant No.08FQ29)Shanghai Leading Academic Discipline Project (Grant No.B118)
文摘In this paper, we study the local asymptotic behavior of the regression spline estimator in the framework of marginal semiparametric model. Similarly to Zhu, Fung and He (2008), we give explicit expression for the asymptotic bias of regression spline estimator for nonparametric function f. Our results also show that the asymptotic bias of the regression spline estimator does not depend on the working covariance matrix, which distinguishes the regression splines from the smoothing splines and the seemingly unrelated kernel. To understand the local bias result of the regression spline estimator, we show that the regression spline estimator can be obtained iteratively by applying the standard weighted least squares regression spline estimator to pseudo-observations. At each iteration, the bias of the estimator is unchanged and only the variance is updated.
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 the National Natural Science Foundation of China(No.11471068)
文摘The generalized estimating equations(GEE) approach is perhaps one of the most widely used methods for longitudinal data analysis. While the GEE method guarantees the consistency of its estimators under working correlation structure misspecification, the corresponding efficiency can be severely affected. In this paper, we propose a new two-step estimation method in which the correlation matrix is assumed to be a linear combination of some known working matrices. Asymptotic properties of the new estimators are developed.Simulation studies are conducted to examine the performance of the proposed estimators. We illustrate the methodology with an epileptic data set.
基金supported by the National Key Research and Development Plan under Grant No.2016YFC0800100the National Science Foundation of China under Grant Nos.11671374,71771203,71631006
文摘Based on the generalized estimating equation approach,the authors propose a parsimonious mean-covariance model for longitudinal data with autoregressive and moving average error process,which not only unites the existing autoregressive Cholesky factor model and moving average Cholesky factor model but also provides a wide variety of structures of covariance matrix.The resulting estimators for the regression coefficients in both the mean and the covariance are shown to be consistent and asymptotically normally distributed under mild conditions.The authors demonstrate the effectiveness,parsimoniousness and desirable performance of the proposed approach by analyzing the CD4-I-cell counts data set and conducting extensive simulations.
基金supported by National Natural Science Foundation of China (Grant Nos. 11231010, 11171330 and 11201315)Key Laboratory of Random Complex Structures and Data Science, Chinese Academy of Sciences (Grant No. 2008DP173182)Beijing Center for Mathematics and Information Interdisciplinary Sciences
文摘Longitudinal data often occur in follow-up studies, and in many situations, there may exist informative observation times and a dependent terminal event such as death that stops the follow-up. We propose a semiparametric mixed effect model with time-varying latent effects in the analysis of longitudinal data with informative observation times and a dependent terminal event. Estimating equation approaches are developed for parameter estimation, and asymptotic properties of the resulting estimators are established. The finite sample behavior of the proposed estimators is evaluated through simulation studies, and an application to a bladder cancer study is provided.
