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Articles 181 - 204 of 204

Full-Text Articles in Numerical Analysis and Computation

A Population Pharmacokinetic Model With Time-Dependent Covariates Measured With Errors, Lang Lil, Xihong Lin, Mort B. Brown, Suneel Gupta, Kyung-Hoon Lee Oct 2003

A Population Pharmacokinetic Model With Time-Dependent Covariates Measured With Errors, Lang Lil, Xihong Lin, Mort B. Brown, Suneel Gupta, Kyung-Hoon Lee

The University of Michigan Department of Biostatistics Working Paper Series

We propose a population pharmacokinetic (PK) model with time-dependent covariates measured with errors. This model is used to model S-oxybutynin's kinetics following an oral administration of Ditropan, and allows the distribution rate to depend on time-dependent covariates blood pressure and heart rate, which are measured with errors. We propose two two-step estimation methods: the second order two-step method with numerical solutions of differential equations (2orderND), and the second order two-step method with closed form approximate solutions of differential equations (2orderAD). The proposed methods are computationally easy and require fitting a linear mixed model at the first step and a nonlinear …

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Cross-Calibration Of Stroke Disability Measures: Bayesian Analysis Of Longitudinal Ordinal Categorical Data Using Negative Dependence, Giovanni Parmigiani, Heidi W. Ashih, Gregory P. Samsa, Pamela W. Duncan, Sue Min Lai, David B. Matchar Aug 2003

Cross-Calibration Of Stroke Disability Measures: Bayesian Analysis Of Longitudinal Ordinal Categorical Data Using Negative Dependence, Giovanni Parmigiani, Heidi W. Ashih, Gregory P. Samsa, Pamela W. Duncan, Sue Min Lai, David B. Matchar

Johns Hopkins University, Dept. of Biostatistics Working Papers

It is common to assess disability of stroke patients using standardized scales, such as the Rankin Stroke Outcome Scale (RS) and the Barthel Index (BI). The Rankin Scale, which was designed for applications to stroke, is based on assessing directly the global conditions of a patient. The Barthel Index, which was designed for general applications, is based on a series of questions about the patient’s ability to carry out 10 basis activities of daily living. As both scales are commonly used, but few studies use both, translating between scales is important in gaining an overall understanding of the efficacy of …

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An Extended General Location Model For Causal Inference From Data Subject To Noncompliance And Missing Values, Yahong Peng, Rod Little, Trivellore E. Raghuanthan Aug 2003

An Extended General Location Model For Causal Inference From Data Subject To Noncompliance And Missing Values, Yahong Peng, Rod Little, Trivellore E. Raghuanthan

The University of Michigan Department of Biostatistics Working Paper Series

Noncompliance is a common problem in experiments involving randomized assignment of treatments, and standard analyses based on intention-to treat or treatment received have limitations. An attractive alternative is to estimate the Complier-Average Causal Effect (CACE), which is the average treatment effect for the subpopulation of subjects who would comply under either treatment (Angrist, Imbens and Rubin, 1996, henceforth AIR). We propose an Extended General Location Model to estimate the CACE from data with non-compliance and missing data in the outcome and in baseline covariates. Models for both continuous and categorical outcomes and ignorable and latent ignorable (Frangakis and Rubin, 1999) …

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Locally Efficient Estimation Of Nonparametric Causal Effects On Mean Outcomes In Longitudinal Studies, Romain Neugebauer, Mark J. Van Der Laan Jul 2003

Locally Efficient Estimation Of Nonparametric Causal Effects On Mean Outcomes In Longitudinal Studies, Romain Neugebauer, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Marginal Structural Models (MSM) have been introduced by Robins (1998a) as a powerful tool for causal inference as they directly model causal curves of interest, i.e. mean treatment-specific outcomes possibly adjusted for baseline covariates. Two estimators of the corresponding MSM parameters of interest have been proposed, see van der Laan and Robins (2002): the Inverse Probability of Treatment Weighted (IPTW) and the Double Robust (DR) estimators. A parametric MSM approach to causal inference has been favored since the introduction of MSM. It relies on correct specification of a parametric MSM to consistently estimate the parameter of interest using the IPTW …

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Resampling-Based Multiple Testing: Asymptotic Control Of Type I Error And Applications To Gene Expression Data, Katherine S. Pollard, Mark J. Van Der Laan Jun 2003

Resampling-Based Multiple Testing: Asymptotic Control Of Type I Error And Applications To Gene Expression Data, Katherine S. Pollard, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

We define a general statistical framework for multiple hypothesis testing and show that the correct null distribution for the test statistics is obtained by projecting the true distribution of the test statistics onto the space of mean zero distributions. For common choices of test statistics (based on an asymptotically linear parameter estimator), this distribution is asymptotically multivariate normal with mean zero and the covariance of the vector influence curve for the parameter estimator. This test statistic null distribution can be estimated by applying the non-parametric or parametric bootstrap to correctly centered test statistics. We prove that this bootstrap estimated null …

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Maximization By Parts In Likelihood Inference, Peter Xuekun Song, Yanqin Fan, Jack Kalbfleisch Jun 2003

Maximization By Parts In Likelihood Inference, Peter Xuekun Song, Yanqin Fan, Jack Kalbfleisch

The University of Michigan Department of Biostatistics Working Paper Series

This paper presents and examines a new algorithm for solving a score equation for the maximum likelyhood estimate in certain problems of practical interest. The method circumvents the need to compute second order derivaties of the full likelihood function. It exploits the structure of certain models that yield a natural decomposition of a very complicated likelihood function. In this decomposition, the first part is a log likelihood from a simply analyzed model and the second part is used to update estimates from the first. Convergence properties of this fixed point algorithm are examined and asymptotics are derived for estimators obtained …

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Double Robust Estimation In Longitudinal Marginal Structural Models, Zhuo Yu, Mark J. Van Der Laan Jun 2003

Double Robust Estimation In Longitudinal Marginal Structural Models, Zhuo Yu, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Consider estimation of causal parameters in a marginal structural model for the discrete intensity of the treatment specific counting process (e.g. hazard of a treatment specific survival time) based on longitudinal observational data on treatment, covariates and survival. We assume the sequential randomization assumption (SRA) on the treatment assignment mechanism and the so called experimental treatment assignment assumption which is needed to identify the causal parameters from the observed data distribution. Under SRA, the likelihood of the observed data structure factorizes in the auxiliary treatment mechanism and the partial likelihood consisting of the product over time of conditional distributions of …

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A Bootstrap Confidence Interval Procedure For The Treatment Effect Using Propensity Score Subclassification, Wanzhu Tu, Xiao-Hua Zhou May 2003

A Bootstrap Confidence Interval Procedure For The Treatment Effect Using Propensity Score Subclassification, Wanzhu Tu, Xiao-Hua Zhou

UW Biostatistics Working Paper Series

In the analysis of observational studies, propensity score subclassification has been shown to be a powerful method for adjusting unbalanced covariates for the purpose of causal inferences. One practical difficulty in carrying out such an analysis is to obtain a correct variance estimate for such inferences, while reducing bias in the estimate of the treatment effect due to an imbalance in the measured covariates. In this paper, we propose a bootstrap procedure for the inferences concerning the average treatment effect; our bootstrap method is based on an extension of Efron’s bias-corrected accelerated (BCa) bootstrap confidence interval to a two-sample problem. …

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Estimating The Accuracy Of Polymerase Chain Reaction-Based Tests Using Endpoint Dilution, Jim Hughes, Patricia Totten Mar 2003

Estimating The Accuracy Of Polymerase Chain Reaction-Based Tests Using Endpoint Dilution, Jim Hughes, Patricia Totten

UW Biostatistics Working Paper Series

PCR-based tests for various microorganisms or target DNA sequences are generally acknowledged to be highly "sensitive" yet the concept of sensitivity is ill-defined in the literature on these tests. We propose that sensitivity should be expressed as a function of the number of target DNA molecules in the sample (or specificity when the target number is 0). However, estimating this "sensitivity curve" is problematic since it is difficult to construct samples with a fixed number of targets. Nonetheless, using serially diluted replicate aliquots of a known concentration of the target DNA sequence, we show that it is possible to disentangle …

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Checking Assumptions In Latent Class Regression Models Via A Markov Chain Monte Carlo Estimation Approach: An Application To Depression And Socio-Economic Status, Elizabeth Garrett, Richard Miech, Pamela Owens, William W. Eaton, Scott L. Zeger Jan 2003

Checking Assumptions In Latent Class Regression Models Via A Markov Chain Monte Carlo Estimation Approach: An Application To Depression And Socio-Economic Status, Elizabeth Garrett, Richard Miech, Pamela Owens, William W. Eaton, Scott L. Zeger

Johns Hopkins University, Dept. of Biostatistics Working Papers

Latent class regression models are useful tools for assessing associations between covariates and latent variables. However, evaluation of key model assumptions cannot be performed using methods from standard regression models due to the unobserved nature of latent outcome variables. This paper presents graphical diagnostic tools to evaluate whether or not latent class regression models adhere to standard assumptions of the model: conditional independence and non-differential measurement. An integral part of these methods is the use of a Markov Chain Monte Carlo estimation procedure. Unlike standard maximum likelihood implementations for latent class regression model estimation, the MCMC approach allows us to …

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Impulse Control Of Stochastic Navier-Stokes Equations, J. L. Menaldi, S. S. Sritharan Jan 2003

Impulse Control Of Stochastic Navier-Stokes Equations, J. L. Menaldi, S. S. Sritharan

Mathematics Faculty Research Publications

In this paper we study stopping time and impulse control problems for stochastic Navier-Stokes equation. Exploiting a local monotonicity property of the nonlinearity, we establish existence and uniqueness of strong solutions in two dimensions which gives a Markov-Feller process. The variational inequality associated with the stopping time problem and the quasi-variational inequality associated with the impulse control problem are resolved in a weak sense, using semigroup approach with a convergence uniform over path.

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An Empirical Study Of Marginal Structural Models For Time-Independent Treatment, Tanya A. Henneman, Mark J. Van Der Laan Oct 2002

An Empirical Study Of Marginal Structural Models For Time-Independent Treatment, Tanya A. Henneman, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

In non-randomized treatment studies a significant problem for statisticians is determining how best to adjust for confounders. Marginal structural models (MSMs) and inverse probability of treatment weighted (IPTW) estimators are useful in analyzing the causal effect of treatment in observational studies. Given an IPTW estimator a doubly robust augmented IPTW (AIPTW) estimator orthogonalizes it resulting in a more e±cient estimator than the IPTW estimator. One purpose of this paper is to make a practical comparison between the IPTW estimator and the doubly robust AIPTW estimator via a series of Monte- Carlo simulations. We also consider the selection of the optimal …

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Bivariate Current Status Data, Mark J. Van Der Laan, Nicholas P. Jewell Sep 2002

Bivariate Current Status Data, Mark J. Van Der Laan, Nicholas P. Jewell

U.C. Berkeley Division of Biostatistics Working Paper Series

In many applications, it is often of interest to estimate a bivariate distribution of two survival random variables. Complete observation of such random variables is often incomplete. If one only observes whether or not each of the individual survival times exceeds a common observed monitoring time C, then the data structure is referred to as bivariate current status data (Wang and Ding, 2000). For such data, we show that the identifiable part of the joint distribution is represented by three univariate cumulative distribution functions, namely the two marginal cumulative distribution functions, and the bivariate cumulative distribution function evaluated on the …

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A New Partitioning Around Medoids Algorithm, Mark J. Van Der Laan, Katherine S. Pollard, Jennifer Bryan Feb 2002

A New Partitioning Around Medoids Algorithm, Mark J. Van Der Laan, Katherine S. Pollard, Jennifer Bryan

U.C. Berkeley Division of Biostatistics Working Paper Series

Kaufman & Rousseeuw (1990) proposed a clustering algorithm Partitioning Around Medoids (PAM) which maps a distance matrix into a specified number of clusters. A particularly nice property is that PAM allows clustering with respect to any specified distance metric. In addition, the medoids are robust representations of the cluster centers, which is particularly important in the common context that many elements do not belong well to any cluster. Based on our experience in clustering gene expression data, we have noticed that PAM does have problems recognizing relatively small clusters in situations where good partitions around medoids clearly exist. In this …

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Maximum Likelihood Estimation Of Ordered Multinomial Parameters, Nicholas P. Jewell, John D. Kalbfleisch Oct 2001

Maximum Likelihood Estimation Of Ordered Multinomial Parameters, Nicholas P. Jewell, John D. Kalbfleisch

U.C. Berkeley Division of Biostatistics Working Paper Series

The pool-adjacent violator-algorithm (Ayer, et al., 1955) has long been known to give the maximum likelihood estimator of a series of ordered binomial parameters, based on an independent observation from each distribution (see Barlow et al., 1972). This result has immediate application to estimation of a survival distribution based on current survival status at a set of monitoring times. This paper considers an extended problem of maximum likelihood estimation of a series of ‘ordered’ multinomial parameters. By making use of variants of the pool adjacent violator algorithm, we obtain a simple algorithm to compute the maximum likelihood estimator and demonstrate …

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Stochastic Hybrid Control, A. Bensoussan, J. L. Menaldi Sep 2000

Stochastic Hybrid Control, A. Bensoussan, J. L. Menaldi

Mathematics Faculty Research Publications

The objective of this paper is to study the stochastic version of a previous paper of the authors, in which hybrid control for deterministic systems was considered. The modelling is quite similar to the deterministic case. We have a system whose state is composed of a continuous part and a discrete part. They are affected by a continuous type control and an impulse control. The dynamics is moreover perturbed by noise, also a continuous and a discrete noise process. The Markovian character of the state process is preserved. We develop the model and show how the dynamic programming approach leads …

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Invariant Measure For Diffusions With Jumps, Jose-Luis Menaldi, Maurice Robin Feb 1999

Invariant Measure For Diffusions With Jumps, Jose-Luis Menaldi, Maurice Robin

Mathematics Faculty Research Publications

Our purpose is to study an ergodic linear equation associated to diffusion processes with jumps in the whole space. This integro-differential equation plays a fundamental role in ergodic control problems of second order Markov processes. The key result is to prove the existence and uniqueness of an invariant density function for a jump diffusion, whose lower order coefficients are only Borel measurable. Based on this invariant probability, existence and uniqueness (up to an additive constant) of solutions to the ergodic linear equation are established.

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Ergodic Control Of Reflected Diffusions With Jumps, Jose-Luis Menaldi, Maurice Robin Mar 1997

Ergodic Control Of Reflected Diffusions With Jumps, Jose-Luis Menaldi, Maurice Robin

Mathematics Faculty Research Publications

No abstract provided.

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On An Investment-Consumption Model With Transaction Costs, Marianne Akian, José Luis Menaldi, Agnès Sulem Jan 1996

On An Investment-Consumption Model With Transaction Costs, Marianne Akian, José Luis Menaldi, Agnès Sulem

Mathematics Faculty Research Publications

This paper considers the optimal consumption and investment policy for an investor who has available one bank account paying a fixed interest rate and n risky assets whose prices are log-normal diffusions. We suppose that transactions between the assets incur a cost proportional to the size of the transaction. The problem is to maximize the total utility of consumption. Dynamic programming leads to a variational inequality for the value function. Existence and uniqueness of a viscosity solution are proved. The variational inequality is solved by using a numerical algorithm based on policies, iterations, and multigrid methods. Numerical results are displayed …

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Optimal Control And Differential Games With Measures, E. N. Barron, R. Jensen, J. L. Menaldi Jan 1993

Optimal Control And Differential Games With Measures, E. N. Barron, R. Jensen, J. L. Menaldi

Mathematics Faculty Research Publications

We consider control problems with trajectories which involve ordinary measureable control functions and controls which are measures. The payoff involves a running cost in time and a running cost against the control measures. In the optimal control problem we are trying to minimize this payoff with both controls. In the differential game problem we are trying to minimize the cost with the ordinary controls assuming that the measure controls are chosen to maximize the cost. We will characterize the value functions in both cases using viscosity solution theory by deriving the Bellman and Isaacs equations.

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Singular Ergodic Control For Multidimensional Gaussian Processes, J. L. Menaldi, M. Robin, M. I. Taksar Mar 1992

Singular Ergodic Control For Multidimensional Gaussian Processes, J. L. Menaldi, M. Robin, M. I. Taksar

Mathematics Faculty Research Publications

A multidimensional Wiener process is controlled by an additive process of bounded variation. A convex nonnegative function measures the cost associated with the position of the state process, and the cost of controlling is proportional to the displacement induced. We minimize a limiting time-average expected (ergodic) criterion. Under reasonable assumptions, we prove that the optimal discounted cost converges to the optimal ergodic cost. Moreover, under some additional conditions there exists a convex Lipschitz continuous function solution to the corresponding Hamilton-Jacobi-Bellman equation which provides an optimal stationary feedback control.

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On The Optimal Reward Function Of The Continuous Time Multiarmed Bandit Problem, José Luis Menaldi, Maurice Robin Jan 1990

On The Optimal Reward Function Of The Continuous Time Multiarmed Bandit Problem, José Luis Menaldi, Maurice Robin

Mathematics Faculty Research Publications

The optimal reward function associated with the so-called "multiarmed bandit problem" for general Markov-Feller processes is considered. It is shown that this optimal reward function has a simple expression (product form) in terms of individual stopping problems, without any smoothness properties of the optimal reward function neither for the global problem nor for the individual stopping problems. Some results relative to a related problem with switching cost are obtained.

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Some Estimates For Finite Difference Approximations, José-Luis Menaldi May 1989

Some Estimates For Finite Difference Approximations, José-Luis Menaldi

Mathematics Faculty Research Publications

Some estimates for the approximation of optimal stochastic control problems by discrete time problems are obtained. In particular an estimate for the solutions of the continuous time versus the discrete time Hamilton-Jacobi-Bellman equations is given. The technique used is more analytic than probabilistic.

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On Asymptotic Behavior Of Stopping Time Problems, Jose Luis Menaldi, Maurice Robin Jan 1989

On Asymptotic Behavior Of Stopping Time Problems, Jose Luis Menaldi, Maurice Robin

Mathematics Faculty Research Publications

No abstract provided.

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