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Identifying significant covariates for anti-HIV treatment response: mechanism-based differential equation models and empirical semiparametric regression models

Huang, Yangxin; Liang, Hua; Wu, Hulin
Fonte: PubMed Publicador: PubMed
Tipo: Artigo de Revista Científica
Publicado em 15/10/2008 Português
Relevância na Pesquisa
46.54%
In this paper, the mechanism-based ordinary differential equation (ODE) model and the flexible semiparametric regression model are employed to identify the significant covariates for antiretroviral response in AIDS clinical trials. We consider the treatment effect as a function of three factors (or covariates) including pharmacokinetics, drug adherence and susceptibility. Both clinical and simulated data examples are given to illustrate these two different kinds of modeling approaches. We found that the ODE model is more powerful to model the mechanism-based nonlinear relationship between treatment effects and virological response biomarkers. The ODE model is also better in identifying the significant factors for virological response, although it is a little bit liberal and there is a trend to include more factors (or covariates) in the model. The semiparametric mixed-effects regression model is very flexible to fit the virological response data, but it is too liberal to identify correct factors for virological response; sometimes it may miss the correct factors. The ODE model is also biologically justifiable and good for predictions and simulations for various biological scenarios. The limitations of the ODE models include the high cost of computation and the requirement of biological assumptions that sometimes may not be easy to validate. The methodologies reviewed in this paper are also generally applicable to studies of other viruses such as hepatitis B virus (HBV) or hepatitis C virus (HCV).

Variable Selection in Semiparametric Regression Modeling1

LI, RUNZE; LIANG, HUA
Fonte: PubMed Publicador: PubMed
Tipo: Artigo de Revista Científica
Publicado em //2008 Português
Relevância na Pesquisa
46.71%
In this paper, we are concerned with how to select significant variables in semiparametric modeling. Variable selection for semiparametric regression models consists of two components: model selection for nonparametric components and select significant variables for parametric portion. Thus, it is much more challenging than that for parametric models such as linear models and generalized linear models because traditional variable selection procedures including stepwise regression and the best subset selection require model selection to nonparametric components for each submodel. This leads to very heavy computational burden. In this paper, we propose a class of variable selection procedures for semiparametric regression models using nonconcave penalized likelihood. The newly proposed procedures are distinguished from the traditional ones in that they delete insignificant variables and estimate the coefficients of significant variables simultaneously. This allows us to establish the sampling properties of the resulting estimate. We first establish the rate of convergence of the resulting estimate. With proper choices of penalty functions and regularization parameters, we then establish the asymptotic normality of the resulting estimate...

Semiparametric Regression of Multidimensional Genetic Pathway Data: Least-Squares Kernel Machines and Linear Mixed Models

Liu, Dawei; Lin, Xihong; Ghosh, Debashis
Fonte: PubMed Publicador: PubMed
Tipo: Artigo de Revista Científica
Publicado em /12/2007 Português
Relevância na Pesquisa
46.66%
We consider a semiparametric regression model that relates a normal outcome to covariates and a genetic pathway, where the covariate effects are modeled parametrically and the pathway effect of multiple gene expressions is modeled parametrically or nonparametrically using least-squares kernel machines (LSKMs). This unified framework allows a flexible function for the joint effect of multiple genes within a pathway by specifying a kernel function and allows for the possibility that each gene expression effect might be nonlinear and the genes within the same pathway are likely to interact with each other in a complicated way. This semiparametric model also makes it possible to test for the overall genetic pathway effect. We show that the LSKM semiparametric regression can be formulated using a linear mixed model. Estimation and inference hence can proceed within the linear mixed model framework using standard mixed model software. Both the regression coefficients of the covariate effects and the LSKM estimator of the genetic pathway effect can be obtained using the best linear unbiased predictor in the corresponding linear mixed model formulation. The smoothing parameter and the kernel parameter can be estimated as variance components using restricted maximum likelihood. A score test is developed to test for the genetic pathway effect. Model/variable selection within the LSKM framework is discussed. The methods are illustrated using a prostate cancer data set and evaluated using simulations.

Semiparametric regression during 2003–2007*

Ruppert, David; Wand, M.P.; Carroll, Raymond J.
Fonte: PubMed Publicador: PubMed
Tipo: Artigo de Revista Científica
Publicado em 01/01/2009 Português
Relevância na Pesquisa
46.61%
Semiparametric regression is a fusion between parametric regression and nonparametric regression that integrates low-rank penalized splines, mixed model and hierarchical Bayesian methodology – thus allowing more streamlined handling of longitudinal and spatial correlation. We review progress in the field over the five-year period between 2003 and 2007. We find semiparametric regression to be a vibrant field with substantial involvement and activity, continual enhancement and widespread application.

Penalized Estimating Functions and Variable Selection in Semiparametric Regression Models

Johnson, Brent A.; Lin, D. Y.; Zeng, Donglin
Fonte: PubMed Publicador: PubMed
Tipo: Artigo de Revista Científica
Publicado em 01/06/2008 Português
Relevância na Pesquisa
46.71%
We propose a general strategy for variable selection in semiparametric regression models by penalizing appropriate estimating functions. Important applications include semiparametric linear regression with censored responses and semiparametric regression with missing predictors. Unlike the existing penalized maximum likelihood estimators, the proposed penalized estimating functions may not pertain to the derivatives of any objective functions and may be discrete in the regression coefficients. We establish a general asymptotic theory for penalized estimating functions and present suitable numerical algorithms to implement the proposed estimators. In addition, we develop a resampling technique to estimate the variances of the estimated regression coefficients when the asymptotic variances cannot be evaluated directly. Simulation studies demonstrate that the proposed methods perform well in variable selection and variance estimation. We illustrate our methods using data from the Paul Coverdell Stroke Registry.

Adjustment for Missingness Using Auxiliary Information in Semiparametric Regression

Zeng, Donglin; Chen, Qingxia
Fonte: PubMed Publicador: PubMed
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
46.42%
In this article, we study the estimation of mean response and regression coefficient in semiparametric regression problems when response variable is subject to nonrandom missingness. When the missingness is independent of the response conditional on high-dimensional auxiliary information, the parametric approach may misspecify the relationship between covariates and response while the nonparametric approach is infeasible because of the curse of dimensionality. To overcome this, we study a model-based approach to condense the auxiliary information and estimate the parameters of interest nonparametrically on the condensed covariate space. Our estimators possess the double robustness property, i.e., they are consistent whenever the model for the response given auxiliary covariates or the model for the missingness given auxiliary covariate is correct. We conduct a number of simulations to compare the numerical performance between our estimators and other existing estimators in the current missing data literature, including the propensity score approach and the inverse probability weighted estimating equation. A set of real data is used to illustrate our approach.

Variable selection for semiparametric regression models with iterated penalization

Dai, Ying; Ma, Shuangge
Fonte: PubMed Publicador: PubMed
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
46.54%
Semiparametric regression models with multiple covariates are commonly encountered. When there are covariates not associated with response variable, variable selection may lead to sparser models, more lucid interpretations and more accurate estimation. In this study, we adopt a sieve approach for the estimation of nonparametric covariate effects in semiparametric regression models. We adopt a two-step iterated penalization approach for variable selection. In the first step, a mixture of the Lasso and group Lasso penalties are employed to conduct the first-round variable selection and obtain the initial estimate. In the second step, a mixture of the weighted Lasso and weighted group Lasso penalties, with weights constructed using the initial estimate, are employed for variable selection. We show that the proposed iterated approach has the variable selection consistency property, even when number of unknown parameters diverges with sample size. Numerical studies, including simulation and analysis of a diabetes dataset, show satisfactory performance of the proposed approach.

Semiparametric Regression Pursuit

Huang, Jian; Wei, Fengrong; Ma, Shuangge
Fonte: PubMed Publicador: PubMed
Tipo: Artigo de Revista Científica
Publicado em 01/10/2012 Português
Relevância na Pesquisa
46.63%
The semiparametric partially linear model allows flexible modeling of covariate effects on the response variable in regression. It combines the flexibility of nonparametric regression and parsimony of linear regression. The most important assumption in the existing methods for the estimation in this model is to assume a priori that it is known which covariates have a linear effect and which do not. However, in applied work, this is rarely known in advance. We consider the problem of estimation in the partially linear models without assuming a priori which covariates have linear effects. We propose a semiparametric regression pursuit method for identifying the covariates with a linear effect. Our proposed method is a penalized regression approach using a group minimax concave penalty. Under suitable conditions we show that the proposed approach is model-pursuit consistent, meaning that it can correctly determine which covariates have a linear effect and which do not with high probability. The performance of the proposed method is evaluated using simulation studies, which support our theoretical results. A real data example is used to illustrated the application of the proposed method.

Profile local linear estimation of generalized semiparametric regression model for longitudinal data

Sun, Yanqing; Sun, Liuquan; Zhou, Jie
Fonte: PubMed Publicador: PubMed
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
46.42%
This paper studies the generalized semiparametric regression model for longitudinal data where the covariate effects are constant for some and time-varying for others. Different link functions can be used to allow more flexible modelling of longitudinal data. The nonparametric components of the model are estimated using a local linear estimating equation and the parametric components are estimated through a profile estimating function. The method automatically adjusts for heterogeneity of sampling times, allowing the sampling strategy to depend on the past sampling history as well as possibly time-dependent covariates without specifically model such dependence. A K -fold cross-validation bandwidth selection is proposed as a working tool for locating an appropriate bandwidth. A criteria for selecting the link function is proposed to provide better fit of the data. Large sample properties of the proposed estimators are investigated. Large sample pointwise and simultaneous confidence intervals for the regression coefficients are constructed. Formal hypothesis testing procedures are proposed to check for the covariate effects and whether the effects are time-varying. A simulation study is conducted to examine the finite sample performances of the proposed estimation and hypothesis testing procedures. The methods are illustrated with a data example.

Statistical properties on semiparametric regression for evaluating pathway effects

Kim, Inyoung; Pang, Herbert; Zhao, Hongyu
Fonte: PubMed Publicador: PubMed
Tipo: Artigo de Revista Científica
Publicado em /04/2013 Português
Relevância na Pesquisa
46.69%
Most statistical methods for microarray data analysis consider one gene at a time, and they may miss subtle changes at the single gene level. This limitation may be overcome by considering a set of genes simultaneously where the gene sets are derived from prior biological knowledge. We call a pathway as a predefined set of genes that serve a particular cellular or physiological function. Limited work has been done in the regression settings to study the effects of clinical covariates and expression levels of genes in a pathway on a continuous clinical outcome. A semiparametric regression approach for identifying pathways related to a continuous outcome was proposed by Liu et al. (2007), who demonstrated the connection between a least squares kernel machine for nonparametric pathway effect and a restricted maximum likelihood (REML) for variance components. However, the asymptotic properties on a semiparametric regression for identifying pathway have never been studied. In this paper, we study the asymptotic properties of the parameter estimates on semiparametric regression and compare Liu et al.’s REML with our REML obtained from a profile likelihood. We prove that both approaches provide consistent estimators, have n convergence rate under regularity conditions...

Semiparametric penalty function method in partially linear model selection

Dong, C.; Gao, J.; Tong, H.
Fonte: Statistica Sinica Publicador: Statistica Sinica
Tipo: Artigo de Revista Científica
Publicado em //2007 Português
Relevância na Pesquisa
46.6%
Model selection in nonparametric and semiparametric regression is of both theoretical and practical interest. Gao and Tong (2004) proposed a semiparametric leave-more-out cross-validation selection procedure for the choice of both the parametric and nonparametric regressors in a nonlinear time series regression model. As recognized by the authors, the implementation of the proposed procedure requires the availability of relatively large sample sizes. In order to address the model selection problem with small or medium sample sizes, we propose a model selection procedure for practical use. By extending the so-called penalty function method proposed in Zheng and Loh (1995, 1997) through the incorporation of features of the leave-one-out cross-validation approach, we develop a semiparametric, consistent selection procedure suitable for the choice of optimum subsets in a partially linear model. The newly proposed method is implemented using the full set of data, and simulations show that it works well for both small and medium sample sizes.; Chaohua Dong, Jiti Gao and Howell Tong

Statistical inference of nonlinear Granger causality: a semiparametric time series regression analysis.

Lee, Sooyoung
Fonte: Universidade de Adelaide Publicador: Universidade de Adelaide
Tipo: Tese de Doutorado
Publicado em //2013 Português
Relevância na Pesquisa
56.82%
Since the seminal work of Granger (1969), Granger causality has become a useful concept and tool in the study of the dynamic linkages between economic variables and to explore whether or not an economic variable helps forecast another one. Researchers have suggested a variety of methods to test the existence of Grangercausality in the literature. In particular, linear Granger causality testing has been remarkably developed; (see, for example, Toda & Philips (1993), Sims, Stock & Watson (1990), Geweke (1982), Hosoya (1991) and Hidalgo (2000)). However, in practice, the real economic relationship between different variables may often be nonlinear. Hiemstra & Jones (1994) and Nishiyama, Hitomi, Kawasaki & Jeong (2011) recently proposed different methods to test the existence of any non-linear Granger causality between a pair of economic variables under a α-mixing framework of data generating process. Their methods are general with nonparametric features, which however suffer from curse of dimensionality when high lag orders need to be taken into consideration in applications. In this thesis, the main objective is to develop a class of semiparametric time series regression models that are of partially linear structures, with statistical theory established under a more general framework of near epoch dependent (NED) data generating processes...

A Robbins-Monro procedure for estimation in semiparametric regression models

Bercu, Bernard; Fraysse, Philippe
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
46.61%
This paper is devoted to the parametric estimation of a shift together with the nonparametric estimation of a regression function in a semiparametric regression model. We implement a very efficient and easy to handle Robbins-Monro procedure. On the one hand, we propose a stochastic algorithm similar to that of Robbins-Monro in order to estimate the shift parameter. A preliminary evaluation of the regression function is not necessary to estimate the shift parameter. On the other hand, we make use of a recursive Nadaraya-Watson estimator for the estimation of the regression function. This kernel estimator takes into account the previous estimation of the shift parameter. We establish the almost sure convergence for both Robbins-Monro and Nadaraya--Watson estimators. The asymptotic normality of our estimates is also provided. Finally, we illustrate our semiparametric estimation procedure on simulated and real data.; Comment: Published in at http://dx.doi.org/10.1214/12-AOS969 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

Variational inference for count response semiparametric regression

Luts, Jan; Wand, Matt P.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 17/09/2013 Português
Relevância na Pesquisa
46.54%
Fast variational approximate algorithms are developed for Bayesian semiparametric regression when the response variable is a count, i.e. a non-negative integer. We treat both the Poisson and Negative Binomial families as models for the response variable. Our approach utilizes recently developed methodology known as non-conjugate variational message passing. For concreteness, we focus on generalized additive mixed models, although our variational approximation approach extends to a wide class of semiparametric regression models such as those containing interactions and elaborate random effect structure.; Comment: 19 pages, 7 figures

Semiparametric regression estimation using noisy nonlinear non invertible functions of the observations

Gassiat, Elisabeth; Landelle, Benoit
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 16/12/2008 Português
Relevância na Pesquisa
46.47%
We investigate a semiparametric regression model where one gets noisy non linear non invertible functions of the observations. We focus on the application to bearings-only tracking. We first investigate the least squares estimator and prove its consistency and asymptotic normality under mild assumptions. We study the semiparametric likelihood process and prove local asymptotic normality of the model. This allows to define the efficient Fisher information as a lower bound for the asymptotic variance of regular estimators, and to prove that the parametric likelihood estimator is regular and asymptotically efficient. Simulations are presented to illustrate our results.

Real-time semiparametric regression for distributed data sets

Luts, Jan
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 18/06/2013 Português
Relevância na Pesquisa
46.61%
This paper proposes a method for semiparametric regression analysis of large-scale data which are distributed over multiple hosts. This enables modeling of nonlinear relationships and both the batch approach, where analysis starts after all data have been collected, and the real-time setting are addressed. The methodology is extended to operate in evolving environments, where it can no longer be assumed that model parameters remain constant over time. Two areas of application for the methodology are presented: regression modeling when there are multiple data owners and regression modeling within the MapReduce framework. A website, realtime-semiparametric-regression.net, illustrates the use of the proposed method on United States domestic airline data in real-time.

Variable selection in semiparametric regression modeling

Li, Runze; Liang, Hua
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 13/03/2008 Português
Relevância na Pesquisa
46.75%
In this paper, we are concerned with how to select significant variables in semiparametric modeling. Variable selection for semiparametric regression models consists of two components: model selection for nonparametric components and selection of significant variables for the parametric portion. Thus, semiparametric variable selection is much more challenging than parametric variable selection (e.g., linear and generalized linear models) because traditional variable selection procedures including stepwise regression and the best subset selection now require separate model selection for the nonparametric components for each submodel. This leads to a very heavy computational burden. In this paper, we propose a class of variable selection procedures for semiparametric regression models using nonconcave penalized likelihood. We establish the rate of convergence of the resulting estimate. With proper choices of penalty functions and regularization parameters, we show the asymptotic normality of the resulting estimate and further demonstrate that the proposed procedures perform as well as an oracle procedure. A semiparametric generalized likelihood ratio test is proposed to select significant variables in the nonparametric component. We investigate the asymptotic behavior of the proposed test and demonstrate that its limiting null distribution follows a chi-square distribution which is independent of the nuisance parameters. Extensive Monte Carlo simulation studies are conducted to examine the finite sample performance of the proposed variable selection procedures.; Comment: Published in at http://dx.doi.org/10.1214/009053607000000604 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

Real-time semiparametric regression

Luts, Jan; Broderick, Tamara; Wand, Matt P.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
46.78%
We develop algorithms for performing semiparametric regression analysis in real time, with data processed as it is collected and made immediately available via modern telecommunications technologies. Our definition of semiparametric regression is quite broad and includes, as special cases, generalized linear mixed models, generalized additive models, geostatistical models, wavelet nonparametric regression models and their various combinations. Fast updating of regression fits is achieved by couching semiparametric regression into a Bayesian hierarchical model or, equivalently, graphical model framework and employing online mean field variational ideas. An internet site attached to this article, realtime-semiparametric-regression.net, illustrates the methodology for continually arriving stock market, real estate and airline data. Flexible real-time analyses, based on increasingly ubiquitous streaming data sources stand to benefit.

Consistent covariate selection and post model selection inference in semiparametric regression

Bunea, Florentina
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 23/06/2004 Português
Relevância na Pesquisa
46.54%
This paper presents a model selection technique of estimation in semiparametric regression models of the type Y_i=\beta^{\prime}\underbarX_i+f(T_i)+W_i, i=1,...,n. The parametric and nonparametric components are estimated simultaneously by this procedure. Estimation is based on a collection of finite-dimensional models, using a penalized least squares criterion for selection. We show that by tailoring the penalty terms developed for nonparametric regression to semiparametric models, we can consistently estimate the subset of nonzero coefficients of the linear part. Moreover, the selected estimator of the linear component is asymptotically normal.

Semiparametric regression analysis under imputation for missing response data

Hardle, Wolfgang; Linton, Oliver; Wang, Qihua
Fonte: Suntory and Toyota International Centres for Economics and Related Disciplines, London School of Economics and Political Science Publicador: Suntory and Toyota International Centres for Economics and Related Disciplines, London School of Economics and Political Science
Tipo: Monograph; NonPeerReviewed Formato: application/pdf
Publicado em /05/2003 Português
Relevância na Pesquisa
46.71%
We develop inference tools in a semiparametric regression model with missing response data. A semiparametric regression imputation estimator, a marginal average estimator and a (marginal) propensity score weighted estimator are defined. All the estimators are proved to be asymptotically normal, with the same asymptotic variance. They achieve the semiparametric efficiency bound in the homoskedastic Gaussian case. We show that the Jackknife method can be used to consistently estimate the asymptotic variance. Our model and estimators are defined with a view to avoid the curse of dimensionality, and that severely limits the applicability of existing methods. The empirical likelihood method is developed. It is shown that when missing responses are imputed using the semiparametric regression method the empirical log-likelihood is asymptotically a scaled chi-square variable. An adjusted empirical log-likelihood ratio, which is asymptotically standard chi-square, is obtained. Also, a bootstrap empirical log-likelihood ratio is derived and its distribution is used to approximate that of the imputed empirical log-likelihood ratio. A simulation study is conducted to compare the adjusted and bootstrap empirical likelihood with the normal approximation-based method in terms of coverage accuracies and average lengths of confidence intervals. Based on biases and standard errors...