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Variable selection for generalized partially linear models with longitudinal data

EVOLUTIONARY INTELLIGENCE 2022年第4期15卷 2473-2483页

作者： Zhang, Jinghua Xue, Liugen Jingdezhen Ceram Inst Dept Informat Engn Jingdezhen Jiangxi Peoples R China Beijing Univ Technol Coll Appl Sci Beijing Peoples R China

Variables selection and parameter estimation are of great significance in all regression analysis. A variety of approaches have been proposed to tackle this problem. Among those, the penalty-based shrinkage approach has been most popular for the ability to carry out the variable selection and parameter estimation simultaneously. However, not much work is available on the variable selection for the generalized partially models (GPLMs) with longitudinal data. In this paper, we proposed a variable selection procedure for GPLMs with longitudinal data. The inference is based on the SCAD-penalized quadratic inference functions, which is obtained after the B-spline approximating to non-parametric function in the model. The proposed approach efficiently utilized the within-cluster correlation information, which can improve estimating efficiency. The proposed approach also has the virtue of low computational cost. With the tuning parameter chosen by BIC, the correct model is identified with probability tends to 1. The resulted estimator of the parametric component is asymptotic to a normal distribution, and that of the non-parametric function achieves the optimal convergence rate. The performance of the proposed methods is evaluated through extensive simulation studies. A real data analysis shows that the proposed approach succeeds in excluding the insignificant variable.

关键词： Variable selection Longitudinal data quadratic inference functions Generalized partially linear models

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Orthogonality-based bias-corrected empirical likelihood inference for partial linear varying coefficient EV models with longitudinal data

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2024年 443卷

作者： Zhou, Yan Mei, Ruoxi Zhao, Yichuan Hu, Zongliang Zhao, Mingtao Shenzhen Univ Inst Stat Sci Sch Math Sci Shenzhen Key Lab Adv Machine Learning & Applicat Shenzhen 518061 Peoples R China Georgia State Univ Dept Math & Stat Atlanta GA 30303 USA Anhui Univ Finance & Econ Inst Stat & Appl Math Bengbu 233000 Anhui Peoples R China

In this paper, we study the model estimation for the partial linear varying coefficient errors -invariables (EV) models with longitudinal data. Based on the empirical likelihood and quadratic inference functions, we propose an orthogonality -based bias -corrected empirical likelihood estimation method using the QR decomposition method of matrix. The proposed method can handle the measurement errors of covariates and unknown within -subject correlation simultaneously, estimate the parametric and nonparametric components separately. Under some regularity conditions, the resulting estimator of the parametric component is asymptotic normal and the estimators of the nonparametric varying coefficients achieve the optimal convergence rate. Furthermore, we conduct simulation studies and a real data analysis to compare the performance of the proposed method with existing methods in finite samples. The results show that the feasibility of the proposed method is obvious.

关键词： Longitudinal data Partial linear varying coefficient EV models Empirical likelihood quadratic inference functions

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Efficient regression modeling for correlated and overdispersed count data

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2019年第24期48卷 6005-6018页

作者： Niu, Xiaomeng Cho, Hyunkeun Ryan Western Michigan Univ Dept Stat Kalamazoo MI 49008 USA Univ Iowa Dept Biostat Iowa City IA 52242 USA

The objective of this paper is to propose an efficient estimation procedure in a marginal mean regression model for longitudinal count data and to develop a hypothesis test for detecting the presence of overdispersion. We extend the matrix expansion idea of quadratic inference functions to the negative binomial regression framework that entails accommodating both the within-subject correlation and overdispersion issue. Theoretical and numerical results show that the proposed procedure yields a more efficient estimator asymptotically than the one ignoring either the within-subject correlation or overdispersion. When the overdispersion is absent in data, the proposed method might hinder the estimation efficiency in practice, yet the Poisson regression based regression model is fitted to the data sufficiently well. Therefore, we construct the hypothesis test that recommends an appropriate model for the analysis of the correlated count data. Extensive simulation studies indicate that the proposed test can identify the effective model consistently. The proposed procedure is also applied to a transportation safety study and recommends the proposed negative binomial regression model.

关键词： Estimation efficiency negative binomial regression overdispersion detection Poisson regression quadratic inference functions within-subject correlation

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Subgroup Analysis and Growth Curve Models for Longitudinal Data

Subgroup Analysis and Growth Curve Models for Longitudinal D...

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作者： Andrews Nichole Western Michigan University

学位级别：Ph . D

In clinical trials and biomedical studies, treatments are compared to determine which one is effective against illness. Growth curve analysis can be beneficial in longitudinal biomedical studies, as we can evaluate the treatment effect on the response over time. The generalized growth curve model using polynomial regression is proposed for longitudinal data. An optimal degree for the polynomial is obtained using the BIQIF, an adaptation of the Bayesian information criterion. quadratic inference functions are used to estimate the parameters of the model, which takes into account the fact that repeated measurements from the same subject are more likely to be correlated. The equality of the growth curves is assessed using an asymptotically chi-square test statistic. Through this test, it could be shown that multiple treatments perform similarly, leading to the recommendation of either, however individuals can react to the same treatment very differently. A complete process for longitudinal data is also proposed that identifies subgroups of the population that would benefit from a specific treatment. A random effects linear model is used to evaluate individual treatment effects longitudinally where the random effects identify a positive or negative reaction to the treatment over. With the individual treatment effects and characteristics of the patients, various classification algorithms are applied to build prediction models for subgrouping. While many subgrouping approaches have been developed recently, most of them do not check its validity. As such, a simple validation approach is proposed which not only determines if the subgroups used are appropriate and beneficial, but also compares methods to predict individual treatment effects. All proposed methods are confirmed with simulation studies and analysis of data from the Women Entering Care study on depression.

关键词： Pure sciences Biological sciences Growth curve model quadratic inference functions Random effects linear model Subgrouping Validation

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Improved methods for the marginal analysis of longitudinal data in the presence of time-dependent covariates

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STATISTICS IN MEDICINE 2017年第16期36卷 2533-2546页

作者： Chen, I-Chen Westgate, Philip M. Univ Kentucky Dept Biostat Coll Publ Hlth Lexington KY 40536 USA

Generalized estimating equations (GEEs) are commonly used for the marginal analysis of longitudinal data. In order to obtain consistent regression parameter estimates, these estimating equations must be unbiased. However, in the presence of certain types of time-dependent covariates, these equations can be biased unless they incorporate the independence working correlation structure. Moreover, in this case, regression parameter estimation can be very inefficient because not all valid moment conditions are incorporated within the corresponding estimating equations. Therefore, approaches based on the generalized method of moments or quadratic inference functions have been proposed in order to utilize all valid moment conditions. However, we have found in previous studies, as well as the current study, that such methods will not always provide valid inference and can also be improved upon in terms of finite-sample regression parameter estimation. Therefore, we propose both a modified GEE approach and a method selection strategy in order to ensure valid inference with the goal of improving regression parameter estimation. In a simulation study and application example, we compare existing and proposed methods and demonstrate that our modified GEE approach performs well, and the correlation information criterion has good accuracy with respect to selecting the best approach in terms of regression parameter estimation. Copyright (C) 2017 JohnWiley & Sons, Ltd.

关键词： correlation selection empirical covariance matrix generalized estimating equations generalized method of moments quadratic inference functions

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An Association of Platelet Indices with Blood Pressure in Beijing Adults: Applying quadratic inference Function for A Longitudinal Study

An Association of Platelet Indices with Blood Pressure in Be...

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2016年中国生物统计学术年会

作者： Kun Yang Lixin Tao Gehendra Mahara Kai Cao Xiuhua Guo Aoshuang Yan Department of Epidemiology and Health Statistics School of Public Health Capital Medical Universit Department of Epidemiology and Health Statistics School of Public Health Capital Medical Universit

Objective The quadratic inference function (QIF) method becomes more acceptable for correlated data because of its advantages over generalized estimating equations (GEE).This study aimed to evaluate the relationship between platelet indices and blood pressure using QIF method, which has not been studied extensively in real data *** A population based longitudinal study was conducted in Beijing from 2007 to 2012, and the median of follow-up was 6-years.A total of 6515 cases, who were aged between 20-65 years at baseline and underwent routine physical examinations every year from three Beijing hospitals, were enrolled to explore the association between platelet indices and blood pressure by QIF *** original continuous platelet indices were categorized into 4 levels (Q1-Q4) using the 3 quartiles of P25, P50 and P75 as a critical *** was preformed to make a comparison with *** After adjusting for age, usage of drugs and other confounding factors, mean platelet volume was negatively associated with diastolic blood pressure (DBP) (Q4:(β)/95% CI, P value;-0.7649/-1.1313 to-0.3985, 0.00004) in males and positively linked with systolic blood pressure (SBP) (Q4: (β)/95% CI, P value;3.1926/2.0853 to 4.2999, 0.00001 in female;1.8477/1.3148 to 2.3806, 0.00001 for male).Platelet distribution width was negatively associated with SBP (Q4: (β)/95% CI, P value;-1.5926/-2.5921 to-0.5931, 0.00179 for female;-1.0568/-1.5335 to-0.5801, 0.00001for male).Blood platelet count was associated with DBP (Q4: (β)/95% CI, P value;0.4212/0.0200 to 0.8223, 0.03958) in *** Adults in Beijing with prolonged exposure to extreme value of platelet indices have elevated risk for future hypertension and evidences in support of using some platelet indices for early diagnosis of hypertension were provided.

关键词： quadratic inference functions Generalized estimating equations Blood pressure Platelet indices Association

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Penalized quadratic inference functions for single-index models with longitudinal data

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JOURNAL OF MULTIVARIATE ANALYSIS 2009年第1期100卷 152-161页

作者： Bai, Yang Fung, Wing K. Zhu, Zhong Yi Univ Hong Kong Dept Stat & Actuarial Sci Hong Kong Hong Kong Peoples R China Fudan Univ Dept Stat Shanghai 200433 Peoples R China

In this paper, we focus on single-index models for longitudinal data. We propose a procedure to estimate the single-index component and the unknown link function based on the combination of the penalized splines and quadratic inference functions. It is shown that the proposed estimation method has good asymptotic properties. We also evaluate the finite sample performance of the proposed method via Monte Carlo simulation studies. Furthermore, the proposed method is illustrated in the analysis of a real data set. (C) 2008 Elsevier Inc. All rights reserved.

关键词： Longitudinal data P-splines quadratic inference functions Single-index models

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Criterion for the simultaneous selection of a working correlation structure and either generalized estimating equations or the quadratic inference function approach

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BIOMETRICAL JOURNAL 2014年第3期56卷 461-476页

作者： Westgate, Philip M. Univ Kentucky Coll Publ Hlth Dept Biostat Lexington KY 40536 USA

Generalized estimating equations (GEE) are commonly used for the marginal analysis of correlated data, although the quadratic inference function (QIF) approach is an alternative that is increasing in popularity. This method optimally combines distinct sets of unbiased estimating equations that are based upon a working correlation structure, therefore asymptotically increasing or maintaining estimation efficiency relative to GEE. However, in finite samples, additional estimation variability arises when combining these sets of estimating equations, and therefore the QIF approach is not guaranteed to work as well as GEE. Furthermore, estimation efficiency can be improved for both analysis methods by accurate modeling of the correlation structure. Our goal is to improve parameter estimation, relative to existing methods, by simultaneously selecting a working correlation structure and choosing between GEE and two versions of the QIF approach. To do this, we propose the use of a criterion based upon the trace of the empirical covariance matrix (TECM). To make GEE and both QIF versions directly comparable for any given working correlation structure, the proposed TECM utilizes a penalty to account for the finite-sample variance inflation that can occur with either version of the QIF approach. Via a simulation study and in application to a longitudinal study, we show that penalizing the variance inflation that occurs with the QIF approach is necessary and that the proposed criterion works very well.

关键词： Correlation selection Efficiency Empirical covariance matrix Generalized estimating equations quadratic inference functions

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Empirical likelihood for generalized linear models with longitudinal data

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JOURNAL OF MULTIVARIATE ANALYSIS 2013年第1期114卷 63-73页

作者： Li, Daoji Pan, Jianxin Univ Manchester Sch Math Manchester M13 9PL Lancs England

In this paper, empirical likelihood-based inference for longitudinal data within the framework of generalized linear model is investigated. The proposed procedure takes into account the within-subject correlation without involving direct estimation of nuisance parameters in the correlation matrix and retains optimal even if the working correlation structure is misspecified. The proposed approach yields more efficient estimators than conventional generalized estimating equations and achieves the same asymptotic variance as quadratic inference function based methods. Furthermore, hypothesis testing procedures are developed to test whether or not the model assumption is met and whether or not regression coefficients are significant. The finite sample performance of the proposed methods is evaluated through simulation studies. Application to the Ohio Children Wheeze Status data is also discussed. (C) 2012 Elsevier Inc. All rights reserved.

关键词： Empirical likelihood Generalized estimating equations Longitudinal data quadratic inference functions Quasi-likelihood Hypothesis testing

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Partial linear models for longitudinal data based on quadratic inference functions

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SCANDINAVIAN JOURNAL OF STATISTICS 2008年第1期35卷 104-118页

作者： Bai, Yang Zhu, Zhongyi Fung, Wing K. Univ Hong Kong Dept Stat & Actuarial Sci Hong Kong Hong Kong Peoples R China Fudan Univ Dept Stat Shanghai Peoples R China

In this paper, we consider improved estimating equations for semiparametric partial linear models (PLM) for longitudinal data, or clustered data in general. We approximate the non-parametric function in the PLM by a regression spline, and utilize quadratic inference functions (QIF) in the estimating equations to achieve a more efficient estimation of the parametric part in the model, even when the correlation structure is misspecified. Moreover, we construct a test which is an analogue to the likelihood ratio inference function for inferring the parametric component in the model. The proposed methods perform well in simulation studies and real data analysis conducted in this paper.

关键词： B-spline estimating equations longitudinal data partial linear models quadratic inference functions

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