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312
The Analysis of Designed Experiments and Longitudinal Data Using Smoothing Splines
, 1997
"... this paper provides the mechanism for including cubic smoothing splines in models for the analysis of designed experiments and longitudinal data. Thus nonlinear curves can be included with random effects and random coefficients, and this leads to very flexible and informative modelling within the li ..."
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Cited by 55 (4 self)
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this paper provides the mechanism for including cubic smoothing splines in models for the analysis of designed experiments and longitudinal data. Thus nonlinear curves can be included with random effects and random coefficients, and this leads to very flexible and informative modelling within the linear mixed model framework. Variance heterogeneity can also be accommodated. The advantage of using the cubic smoothing spline in the case of longitudinal data is particularly pronounced, because covariance modelling is achieved implicitly as for random coefficient models. Several examples are considered to illustrate the ideas.
Bayesian MixedEffects Models for Recommender Systems
 In ACM SIGIR ’99 Workshop on Recommender Systems: Algorithms and Evaluation
, 1999
"... We propose a Bayesian methodology for recommender systems that incorporates user ratings, user features, and item features in a single unified framework. In principle our approach should address the coldstart issue and can address both scalability issues as well as sparse ratings. However, our earl ..."
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Cited by 54 (6 self)
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We propose a Bayesian methodology for recommender systems that incorporates user ratings, user features, and item features in a single unified framework. In principle our approach should address the coldstart issue and can address both scalability issues as well as sparse ratings. However, our early experiments have shown mixed results. 1 Introduction Recommender systems have emerged as an important application area and have been the focus of considerable recent academic and commercial interest. The 1997 special issue of the Communications of the ACM [14] contains some key papers. Other important contributions include [2], [4], [8], [13], [16], [9], [1], [12], and [15]. In addition, many online retailers are using this technology to recommend new items to their customers, based on what they have bought in the past. Currently, most recommender systems are either contentbased or collaborative, depending on the type of information that the system uses to recommend items to a user. Co...
Functional Modeling and Classification of Longitudinal Data
"... We review and extend some statistical tools that have proved useful for analyzing functional data. Functional data analysis primarily is designed for the analysis of random trajectories and infinitedimensional data, and there exists a need for the development of adequate statistical estimation and ..."
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Cited by 40 (11 self)
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We review and extend some statistical tools that have proved useful for analyzing functional data. Functional data analysis primarily is designed for the analysis of random trajectories and infinitedimensional data, and there exists a need for the development of adequate statistical estimation and inference techniques. While this field is in flux, some methods have proven useful. These include warping methods, functional principal component analysis, and conditioning under Gaussian assumptions for the case of sparse data. The latter is a recent development that may provide a bridge between functional and more classical longitudinal data analysis. Besides presenting a brief review of functional principal components and functional regression, we develop some concepts for estimating functional principal component scores in the sparse situation. An extension of the socalled generalized functional linear model to the case of sparse longitudinal predictors is proposed. This extension includes functional binary regression models for longitudinal data and is illustrated with data on primary biliary cirrhosis.
Polynomial spline estimation and inference for varying coefficient models with longitudinal data
 Statist. Sinica
, 2004
"... We consider nonparametric estimation of coefficient functions in a varying coefficient model of the form Yij = XTi (tij)β(tij)+ i(tij) based on longitudinal observations {(Yij, Xi(tij), tij), i = 1,..., n, j = 1,..., ni}, where tij and ni are the time of the jth measurement and the number of repeate ..."
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Cited by 34 (4 self)
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We consider nonparametric estimation of coefficient functions in a varying coefficient model of the form Yij = XTi (tij)β(tij)+ i(tij) based on longitudinal observations {(Yij, Xi(tij), tij), i = 1,..., n, j = 1,..., ni}, where tij and ni are the time of the jth measurement and the number of repeated measurements for the ith subject, and Yij and Xi(tij) = (Xi0(tij),..., XiL(tij))T for L ≥ 0 are the ith subject’s observed outcome and covariates at tij. We approximate each coefficient function by a polynomial spline and employ the least squares method to do the estimation. An asymptotic theory for the resulting estimates is established, including consistency, rate of convergence and asymptotic distribution. The asymptotic distribution results are used as a guideline to construct approximate confidence intervals and confidence bands for components of β(t). We also propose a polynomial spline estimate of the covariance structure of (t), which is used to estimate the variance of the spline estimate β̂(t). A data example in epidemiology and a simulation study are used to demonstrate our methods. Key words and phrases: Asymptotic normality; confidence intervals; nonparametric regression; repeated measurements, varying coefficient models. 1 1
Population HIV1 dynamics in vivo: applicable models and inferential tools for virological data from AIDS clinical trials
 Biometrics
, 1999
"... In this paper we introduce a novel application of hierarchical nonlinear mixedeffect models to HIV dynamics. We show that a simple model with a sum of exponentials can give a good fit to the observed clinical data of HIV1 dynamics (HIV1 RNA copies) after initiation of potent antiviral treatments ..."
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Cited by 30 (8 self)
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In this paper we introduce a novel application of hierarchical nonlinear mixedeffect models to HIV dynamics. We show that a simple model with a sum of exponentials can give a good fit to the observed clinical data of HIV1 dynamics (HIV1 RNA copies) after initiation of potent antiviral treatments, and can also be justified by a biological compartment model for the interaction between HIV and its host cells. This kind of model enjoys both biological interpretability and mathematical simplicity after reparameterization and simplification. A model simplification procedure is proposed and illustrated through examples. We interpret and justify various simplified models based on clinical data taken during different phases of viral dynamics during antiviral treatments. We suggest the hierarchical nonlinear mixedeffect model approach for parameter estimation and other statistical inferences. In the context of an AIDS clinical trial involving patients treated with a combination of potent antiviral agents, we show how the models may be used to draw biologically relevant interpretations from repeated HIV1 RNA measurements and demonstrate the potential use of the models in clinical decisionmaking. ∗ Corresponding author’s
HIV dynamics: modeling, data analysis, and optimal treatment protocols
 J. Comput. Appl. Math
, 2005
"... We present an overview of some concepts and methodologies we believe useful in modeling HIV pathogenesis. After a brief discussion of motivation for and previous efforts in the development of mathematical models for progression of HIV infection and treatment, we discuss mathematical and statistical ..."
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Cited by 25 (10 self)
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We present an overview of some concepts and methodologies we believe useful in modeling HIV pathogenesis. After a brief discussion of motivation for and previous efforts in the development of mathematical models for progression of HIV infection and treatment, we discuss mathematical and statistical ideas relevant to Structured Treatment Interruptions (STI). Among these are model development and validation procedures including parameter estimation, data reduction and representation, and optimal control relative to STI. Results from initial attempts in each of these areas by an interdisciplinary team of applied mathematicians, statisticians and clinicians are presented. Key words: HIV models, parameter estimation, data and model reduction, structured treatment interruptions, optimal control
An inverse problem statistical methodology summary
 North Carolina State University
"... We discuss statistical and computational aspects of inverse or parameter estimation problems based on Ordinary Least Squares and Generalized Least Squares with appropriate corresponding data noise assumptions of constant variance and nonconstant variance (relative error), respectively. Among the t ..."
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Cited by 24 (18 self)
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We discuss statistical and computational aspects of inverse or parameter estimation problems based on Ordinary Least Squares and Generalized Least Squares with appropriate corresponding data noise assumptions of constant variance and nonconstant variance (relative error), respectively. Among the topics included here are mathematical model, statistical model and data assumptions, and some techniques (residual plots, sensitivity analysis, model comparison tests) for verifying these. The ideas are illustrated throughout with the popular logistic growth model of Verhulst and Pearl as well as with a recently developed population level model of pneumococcal disease spread.
Fitting Nonlinear Mixed Models with the New NLMIXED Procedure
"... Statistical models in which both fixed and random effects enter nonlinearly are becoming increasingly popular. These models have a wide variety of applications, two of the most common being nonlinear growth curves and overdispersed binomial data. A new SAS/STAT procedure, NLMIXED, fits these models ..."
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Cited by 20 (0 self)
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Statistical models in which both fixed and random effects enter nonlinearly are becoming increasingly popular. These models have a wide variety of applications, two of the most common being nonlinear growth curves and overdispersed binomial data. A new SAS/STAT procedure, NLMIXED, fits these models using likelihoodbased methods. This paper presents some of the primary features of PROC NLMIXED and illustrates its use with two examples. INTRODUCTION The NLMIXED procedure fits nonlinear mixed models, that is, models in which both fixed and random effects are permitted to have a nonlinear relationship to the response variable. These models can take various forms, but the most common ones involve a conditional distribution for the response variable given the random effects. PROC NLMIXED enables you to specify such a distribution by using either a keyword for a standard form (normal, binomial, Poisson) or SAS programming statements to specify a general distribution. PROC NLMIXED fits the ...
A Bayesian population model with hierarchical mixture priors applied to blood count data
 JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
, 1997
"... Population pharmacokinetic and pharmacodynamic studies require one to analyze nonlinear growth curves fit to multiple measurements from study subjects. We propose a class of nonlinear population models with nonparametric secondstage priors for analyzing such data. The proposed models apply a flexib ..."
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Cited by 20 (5 self)
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Population pharmacokinetic and pharmacodynamic studies require one to analyze nonlinear growth curves fit to multiple measurements from study subjects. We propose a class of nonlinear population models with nonparametric secondstage priors for analyzing such data. The proposed models apply a flexible class of mixtures to implement the nonparametric second stage. The discussion is based on a pharmacodynamic study involving longitudinal data consisting of hematologic profiles (i.e., blood counts measured over time) of cancer patients undergoing chemotherapy. We describe a full posterior analysis in a Bayesian framework. This includes prediction of future observations (profiles and end points for new patients), estimation of the mean response function for observed individuals, and inference on population characteristics. The mixture model is specified and given a hyperprior distribution by means of a Dirichlet processes prior on the mixing measure. Estimation is implemented by a combinat...
Stochastic and deterministic models for agricultural production networks
 Math. Biosci. Eng
"... An approach to modeling the impact of disturbances in an agricultural production network is presented. A stochastic model and its approximate deterministic model for averages over sample paths of the stochastic system are developed. Simulations, sensitivity and generalized sensitivity analyses are g ..."
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Cited by 19 (13 self)
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An approach to modeling the impact of disturbances in an agricultural production network is presented. A stochastic model and its approximate deterministic model for averages over sample paths of the stochastic system are developed. Simulations, sensitivity and generalized sensitivity analyses are given. Finally, it is shown how diseases may be introduced into the network and corresponding simulations are discussed.