Browsing by Author "Marie Davidian, Committee Member"

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Cost-effectiveness analysis of Vaccination and Self-isolation in case of an H1N1 outbreak
(2010-04-04) Yarmand, Hamed; Marie Davidian, Committee Member; Alun Lloyd, Committee Member; Stephen D Roberts, Committee Co-Chair; Julie S Ivy, Committee Co-Chair
In this research, we have conducted a cost-effectiveness analysis to examine the relative importance of vaccination and self-isolation, two common measures for controlling the spread of infectious diseases, with respect to the current H1N1 outbreak. We have developed a continuous-time simulation model for the spread of H1N1 which allows for three types of interventions: antiviral prophylaxis and treatment, vaccination, and self-isolation and mandatory quarantine. We have used the North Carolina State University undergraduate students as our target population. We have developed an optimization model with two decision variables: vaccination fraction and self-isolation fraction among infectives. By considering the relative marginal costs associated with each of these decision variables, we have a linear objective function representing the total relative cost for each control policy. We have also considered upper bound constraints for two of the most critical performance measures: maximum number of individuals under treatment (which is related to surge capacity), and percentage of infected individuals. We used grid search to obtain insight into the model, find the feasible region, and conduct the cost-effectiveness analysis. Then we integrated the simulation and optimization models via the Arena optimization toolbox, OptQuest, to find â€œnear optimalâ€ feasible solutions. Using the estimated model parameters from the target population and literature, our results show that in low levels of interventions, vaccination is more effective and also incrementally cost-effective in controlling the disease spread than self-isolation. While vaccination decreases the number of both susceptibles and infectives (with a delay), self-isolation only affects the number of infectives. On the other hand, in high levels of interventions, self-isolation is more effective and also incrementally cost-effective than vaccination, due to the delay in the vaccine effectiveness and also the incapability of distinguishing between the susceptible and exposed individuals to receive the vaccine. Also our results show that self-isolation is incrementally more cost-effective than vaccination if the ratio of the vaccination marginal cost to the self-isolation marginal cost is greater than 0.3, which should be the case for our target population. To validate the model and to have a realistic estimate of the model parameters, we have taken advantage of the cooperation of the NCSU Health Center Director as an expert. Finally we have conducted a sensitivity analysis on the key input parameters to ensure robust results and conclusions.
Generalized Estimators of the Attributable Benefit of an Optimal Treatment Regime
(2008-09-12) Brinkley, Jason Scott; Wenbin Lu, Committee Member; Daowen Zhang, Committee Member; Marie Davidian, Committee Member; Anastasios Tsiatis, Committee Chair
Improving the Efficiency of Tests and Estimators of Treatment Effect with Auxiliary Covariates in the Presence of Censoring
(2008-05-30) Lu, Xiaomin; Marie Davidian, Committee Member; Anastasios A. Tsiatis, Committee Chair; Hao Zhang, Committee Member; Wenbin Lu, Committee Member
Model Diagnostics for the Nonlinear Mixed Effects Model with Balanced Longitudinal Data
(2007-10-04) Chiswell, Karen Elizabeth; John Monahan, Committee Chair; Marie Davidian, Committee Member; Hao Zhang, Committee Member; H. T. Banks, Committee Member
Model Selection and Estimation in Additive Regression Models
(2009-09-14) Miao, Huiping; Hao Zhang, Committee Member; Marie Davidian, Committee Member; Dennis Boos, Committee Member; Daowen Zhang, Committee Chair
We propose a method of simultaneous model selection and estimation in additive regression models (ARMs) for independent normal data. We use the mixed model representation of the smoothing spline estimators of the nonparametric functions in ARMs, where the importance of these functions is controlled by treating the inverse of the smoothing parameters as extra variance components. The selection of important nonparametric functions is achieved by maximizing the penalized likelihood with an adaptive LASSO. A unified EM algorithm is provided to obtain the maximum penalized likelihood estimates of the nonparametric functions and the residual variance. In the same framework, we also consider forward selection based on score tests, and a two stage approach that imposes an early stage screening using an individual score test on each induced variance component of the smoothing parameter. For longitudinal data, we propose to extend the adaptive LASSO and the two-stage selection with score test screening to the additive mixed models (AMMs), by introducing subject-specific random effects to the additive models to accommodate the correlation in responses. We use the eigenvalue-eigenvector decomposition approach to approximate the working random effects in the linear mixed model presentation of the AMMs, so as to reduce the dimensions of matrices involved in the algorithm while keeping most data information, hence to tackle the computational problems caused by large sample sizes in longitudinal data. Simulation studies are provided and the methods are illustrated with data applications.
Modeling, Analysis, and Estimation of an in vitro HIV Infection Using Functional Differential Equations
(2002-09-05) Bortz, David Matthew; H. Thomas Banks, Committee Chair; Marie Davidian, Committee Member; Kazufumi Ito, Committee Member; Hien T. Tran, Committee Member
This dissertation focuses on developing mathematical and computational tools for use as an aid in understanding the cellular population dynamics of an in vitro HIV experiment. We carefully develop a functional differential equation model which incorporates mathematical mechanisms that account for both the biological delays and the parameter uncertainty inherent in the system. We present the theoretical foundations for our methodology which then allow us to develop a numerical approximation scheme and perform parameter identifications (even on the delay distributions) and sensitivity analyses. We summarize the results of a numerical investigation of the delays followed by the results from the nonlinear least squares inverse problem. We then present a statistical significance argument for the importance of the delay mechanism as well as the results of a sample sensitivity analysis of the system with respect to select parameters.
Non-parametric Parameter Estimation and Clinical Data Fitting with a Model of HIV Infection
(2005-07-29) Adams, Brian Michael; Robert H. Martin, Committee Member; Hien T. Tran, Committee Member; H.T. Banks, Committee Chair; Marie Davidian, Committee Member
The focus of this dissertation is to develop a combined mathematical and statistical modeling approach for analyzing clinical data from an HIV acute infection study. We amalgamate two existing models from the literature to create a nonlinear differential equation model of in-host infection dynamics that is capable of predicting sustained low-level viral loads and multiple stable equilibria. Using this example system of differential equations we demonstrate two contrasting parameter identification problem formulations for estimating the distribution of model parameters across a population: the first at the individual patient level and the second directly at the population level itself. In the latter case one leverages data from all patients to estimate a probability density function representing the distribution. We discuss well-posedness and computational implementation for such inverse problems. Directly estimating the distribution in this way may offer computational advantages over estimating parameters for individual patients. In the context of the model, we implement the Expectation Maximization (EM) Algorithm for maximum likelihood estimation to handle patient measurements censored by assay resolution limits. This censored data method is beneficial since with it we do not arbitrarily assign values for measurements below the limit of detection, but rather compute their expected value based on the dynamics model and conditioned on the knowledge that they are censored. In addition, in both inverse problem contexts (estimating a vector of parameters for a single patient and the distribution of a parameter across all patients) we develop and apply methods for estimating variability of the resulting parameter estimates by using sensitivity analysis to calculate confidence intervals. We validate each of the methods with simulated data and demonstrate typical results. Finally we present results for the application of the methods to actual clinical data and give examples of conclusions that one might draw from them. This model fitting approach may help clinicians better understand patient behaviors and notably, could alert them to the expected long-term trend for a particular patient.
An Optimization Approach for the Parameter Estimation of the Nonlinear Mixed Effects Models
(2004-07-29) Wang, Jing; Bhattacharyya, Bibhuti, Committee Member; John F. Monahan, Committee Chair; Marie Davidian, Committee Member; Dickey, David, Committee Member
Nonlinear mixed-effects models (NLMM) have received a great deal of attention in the statistical literature in recent years because of the flexibility they offer in handling the unbalanced repeated-measurements data that arise in different areas of investigation, such as pharmacokinetics. We concentrate here on maximum likelihood estimation for the parameters in nonlinear mixed-effects models. A rather complex numerical issue for maximum likelihood estimation in nonlinear mixed-effects models is the evaluation of a multiple integral that, in most cases, does not have a closed-form expression. We restrict our attention in this article on numerical methods that are based on approximation for the likelihood. Several numerical approximations for the likelihood have been proposed such as first-order linearization (FOL), Laplace approximation, Importance Sampling, and Gaussian Quadrature (GQ). In addition, for a general optimization problem, iterative methods are usually required to update the parameter estimates iteratively. A large number of parameter updating methods have been developed such as Newton-Raphson, Steepest Descent, Stochastic optimization, etc. Many current optimization algorithms implement a Newton iterative method to update the parameter estimates in NLMM. The objective of this thesis is to propose an optimization approach for the parameter estimation in nonlinear mixed-effects models. This optimization method implements Importance Sampling for approximating likelihood and a stochastic recursive procedure for updating parameter estimates in NLMM. In Chapter 1, we describe the model and introduce several likelihood approximations and parameter updating procedures for these models. The proposed optimization approach is illustrated in Chapter 2. In order to compare this approach to the other optimization methods, simulations are performed and conclusions are drawn based on simulation results in Chapter 3. Some future work is presented in Chapter 4.
Semiparametric Estimators for the Regression Coefficients in the Linear Transformation Competing Risks Models with Missing Cause of Failure
(2006-06-01) Gao, Guozhi; Marie Davidian, Committee Member; Zhang Daowen, Committee Member; Lu Wenbin, Committee Member; Anastasios A. Tsiatis, Committee Chair
In many clinical studies, researchers are mainly interested in studying the effects of some prognostic factors on the hazard of failure from a specific cause while individuals may failure from multiple causes. This leads to a competing risks problem. Often, due to various reasons such as finite study duration, loss to follow-up, or withdrawal from the study, the time-to-failure is right-censored for some individuals. Although the proportional hazards model has been commonly used in analyzing survival data, there are circumstances where other models are more appropriate. Here we consider the class of linear transformation models that contains the proportional hazards model and the proportional odds model as special cases. Sometimes, patients are known to die but the cause of death is unavailable. It is well known that when cause of failure is missing, ignoring the observations with missing cause or treating them as censored may result in erroneous inferences. Under the Missing At Random assumption, we propose two methods to estimate the regression coefficients in the linear transformation models. The augmented inverse probability weighting method is highly efficient and doubly robust. In addition, it allows the possibility of using auxiliary covariates to model the missing mechanism. The multiple imputation method is very efficient, is straightforward and easy to implement and also allows for the use of auxiliary covariates. The asymptotic properties of these estimators are developed using theory of counting processes and semiparametric theory for missing data problems. Simulation studies demonstrate the relevance of the theory in finite samples. These methods are also illustrated using data from a breast cancer stage II clinical trial.
Semiparametric Mixed Models for Censored Longitudinal Data.
(2010-11-01) Huang, Mingyan; Daowen Zhang, Committee Chair; Hao Zhang, Committee Chair; Marie Davidian, Committee Member; Wenbin Lu, Committee Member; Richard Braham, Committee Member
Statistical Analysis in Two Stage Randomization Designs in Clinical Trials
(2005-06-25) Guo, Xiang; Daowen Zhang, Committee Member; John Monahan, Committee Member; Marie Davidian, Committee Member; Anastasios A. Tsiatis, Committee Chair
Two-stage randomization designs are becoming more common in many clinical trials related to diseases such as cancer and HIV, where an induction therapy is given followed by a maintenance therapy depending on patients' response and consent. The main interest is to compare combinations of induction and maintenance therapies and to find the combination leading to the longest average survival time. However, in practice, the data analysis is typically conducted separately in two stages. In this Thesis, we tackle the problem based on treatment policies. We use the concepts of counting process and risk set as described by Fleming and Harrington (1991) to find weighted estimating equations whose solution gives an estimator for the cumulative hazard function which, in turn, is used to derive an estimator for the overall survival distribution under a treatment policy with right-censored data. We call this estimator as the Weighted Risk Set Estimator (WRSE). We show that the WRSE is consistent and asymptotically normally distributed. In addition to survival distribution estimation, we also consider the hypothesis testing problem. Since the log rank test is the common method for hypothesis testing in survival analysis, we propose a test statistic using an inverse weighted version of the log rank test. We use simulation studies to demonstrate the properties of our method and use data from a clinical trial, Protocol 88923, conducted by the Cancer and Leukemia Group B (CALGB) to illustrate how to implement the method.
Topics in Design and Analysis of Clinical Trials (DRAFT)
(2005-08-04) Lokhnygina, Yuliya; Marie Davidian, Committee Member; Dennis Boos, Committee Member; Anastasios A. Tsiatis, Committee Chair; Daowen Zhang, Committee Member
In the first part of this dissertation we derive optimal two-stage adaptive group-sequential designs for normally distributed data which achieve the minimum of a mixture of expected sample sizes at the range of plausible values of a normal mean. Unlike standard group-sequential tests, our method is adaptive in that it allows the group size at the second look to be a function of the observed test statistic at the first look. Using optimality criteria, we construct two-stage designs which we show have advantage over other popular adaptive methods. The employed computational method is a modification of the backward induction algorithm applied to a Bayesian decision problem. Two-stage randomization designs (TSRD) are becoming increasingly common in oncology and AIDS clinical trials as they make more efficient use of study participants to examine therapeutic regimens. In these designs patients are initially randomized to an induction treatment, followed by randomization to a maintenance treatment conditional on their induction response and consent to further study treatment. Broader acceptance of TSRDs in drug development may hinge on the ability to make appropriate intent-to-treat type inference as to whether an experimental induction regimen is better than a standard regimen in the absence of maintenance treatment within this design framework. Lunceford, Davidian, and Tsiatis (2002, Biometrics 58, 48-57) introduced an inverse-probability-weighting based analytical framework for estimating survival distributions and mean restricted survival times, as well as for comparing treatment policies in the TSRD setting. In practice Cox regression is widely used, and in the second part of this dissertation we extend the analytical framework of Lunceford et. al. to derive a consistent estimator for the log hazard in the Cox model and a robust score test to compare treatment policies. Large sample properties of these methods are derived and illustrated via a simulation study. Considerations regarding the application of TSRDs compared to single randomization designs are discussed.
Topics in Longitudinal Studies with Coarsened Data
(2007-01-11) Jiang, Liqiu; Anastasios A. Tsiatis, Committee Chair; John F. Monahan, Committee Member; Wenbin Lu, Committee Member; Marie Davidian, Committee Member
In the first part of the dissertation, we derive two methods for responders analysis in longitudinal data with random missing data. Often a binary variable is generated by dichotomizing an underlying continuous variable measured at a specific point in time according to a prespecified threshold value. Ordinarily, a logistic regression model is used to estimate the effects of covariates on the binary response. In the event that the underlying continuous measurements are from a longitudinal study, the repeated measurements are often analyzed using a repeated measures model because of mathematical and computational convenience of available off-the-shelf software. This practical advantage motivates us to propose two methods: one is to use repeated measures model as an imputation approach in the presence of missing data on the responder status as a result of patient drop-out before completion of the study. We then apply the logistic regression model on the observed or otherwise imputed responder status; the other is to construct estimating equations based on the relationship of repeated measures model and logistic regression model. Large sample properties of the resulting estimators are derived and simulation studies carried out to assess the performance of the estimators in situations where either the model for the continuous repeated measurements is misspecified as following a multinormal distribution, when, in truth, it follows a logistic distribution that is compatible with the logistic regression model for the probability of response or when the model that the probability of response following a logistic regression model is misspecified because, in truth, the longitudinal data follow a multinormal distribution. We show that the resulting estimators are robust to misspecification and apply them to data from a clinical trial on a toenail disease. We adopt a semiparametric estimator to a longitudinal data with measurement error in the second part of the dissertation. In longitudinal studies, we are often interested in the relationship between a primary response and the profile of repeated measurements collected over time for a subject, which can be dictated by individual random effects in the framework of a generalized linear model. For example, if the longitudinal profile is linear, the relationship of individual intercept and slope and primary response would be of interest. The naive method by fitting a regression model to obtain estimates for individual random effects can lead to biased results. Li, Zhang, and Davidian (Biometrics 2004) developed conditional score approaches for generalized linear models which require no assumption on the distribution of the random effects and yield consistent inference regardless of the true distribution. However, the estimator can only be used for generalized linear models in canonical form with normally distributed measurement error. To overcome this limitation, we adopt locally efficient semiparametric estimators proposed by Tsiatis and Ma (Biometrika 2004) for functional measurement error models to use for such longitudinal studies. The distribution of random effects is allowed to be misspecified and the method will still yield consistent inference. Simulation studies are carried out to assess the performance of the estimator. We show that the estimator can give much better inference than the naive method in terms of bias and empirical probability coverage. The approach is applied to data from a study on woman's bone disease.
Variable Selection in Linear Mixed Model for Longitudinal Data
(2006-08-17) Lan, Lan; Daowen Zhang, Committee Chair; Hao Helen Zhang, Committee Co-Chair; Marie Davidian, Committee Member; Dennis Boos, Committee Member
Fan and Li (JASA, 2001) proposed a family of variable selection procedures for certain parametric models via a nonconcave penalized likelihood approach, where significant variable selection and parameter estimation were done simultaneously, and the procedures were shown to have the oracle property. In this presentation, we extend the nonconcave penalized likelihood approach to linear mixed models for longitudinal data. Two new approaches are proposed to select significant covariates and estimate fixed effect parameters and variance components. In particular, we show the new approaches also possess the oracle property when the tuning parameter is chosen appropriately. We assess the performance of the proposed approaches via simulation and apply the procedures to data from the Multicenter AIDS Cohort Study.
Variable Selection in Partial Linear Models and Semiparametric Mixed Models
(2008-07-25) Ni, Xiao; Hao Helen Zhang, Committee Co-Chair; Marie Davidian, Committee Member; Jason Osborne, Committee Member; Daowen Zhang, Committee Chair
Variable Selection Procedures for Generalized Linear Mixed Models in Longitudinal Data Analysis
(2007-08-03) Yang, Hongmei; Daowen Zhang, Committee Chair; Hao Helen Zhang, Committee Co-Chair; Dennis Boos, Committee Member; Marie Davidian, Committee Member
Model selection is important for longitudinal data analysis. But up to date little work has been done on variable selection for generalized linear mixed models (GLMM). In this paper we propose and study a class of variable selection methods. Full likelihood (FL) approach is proposed for simultaneous model selection and parameter estimation. Due to the intensive computation involved in FL approach, Penalized Quasi-Likelihood (PQL) procedure is developed so that model selection in GLMMs can proceed in the framework of linear mixed models. Since the PQL approach will produce biased parameter estimates for sparse binary longitudinal data, Two-stage Penalized Quasi-Likelihood approach (TPQL) is proposed to bias correct PQL in terms of estimation: use PQL to do model selection at the first stage and existing software to do parameter estimation at the second stage. Marginal approach for some special types of data is also developed. A robust estimator of standard error for the fitted parameters is derived based on a sandwich formula. A bias correction is proposed to improve the estimation accuracy of PQL for binary data. The sampling performance of four proposed procedures is evaluated through extensive simulations and their application to real data analysis. In terms of model selection, all of them perform closely. As for parameter estimation, FL, AML and TPQL yield similar results. Compared with FL, the other procedures greatly reduce computational load. The proposed procedures can be extended to longitudinal data analysis involving missing data, and the shrinkage penalty based approach allows them to work even when the number of observations n is less than the number of parameters d.
Variations on the Accelerated Failure Time Model: Mixture Distributions, Cure Rates, and Di fferent Censoring Scenarios
(2009-10-06) Krachey, Elizabeth Catherine; Sujit Ghosh, Committee Co-Chair; Marie Davidian, Committee Member; Brian Reich, Committee Member; Wenbin Lu, Committee Chair
The accelerated failure time (AFT) model is a popular model for time-to-event data. It provides a useful alternative when the proportional hazards assumption is in question and it provides an intuitive linear regression interpretation where the logarithm of the survival time is regressed on the covariates. We have explored several deviations from the standard AFT model. Standard survival analysis assumes that in the case of perfect follow-up, every patient will eventually experience the event of interest. However, in some clinical trials, a number of patients may never experience such an event, and in essence, are considered cured from the disease. In such a scenario, the Kaplan-Meier survival curve will level off at a nonzero proportion. Hence there is a window of time in which most or all of the events occur, while heavy censoring occurs in the tail. The two-component mixture cure model provides a means of adjusting the AFT model to account for this cured fraction. Chapters 1 and 2 propose parametric and semiparametric estimation procedures for this cure rate AFT model. Survival analysis methods for interval-censoring have been much slower to develop than for the right-censoring case. This is in part because interval-censored data have a more complex censoring mechanism and because the counting process theory developed for right-censored data does not generalize or extend to interval-censored data. Because of the analytical difficulty associated with interval-censored data, recent estimation strategies have focused on the implementation rather than the large sample theoretical justifications of the semiparametric AFT model. Chapter 3 proposes a semiparametric Bayesian estimation procedure for the AFT model under interval-censored data.