Applied Mathematics Commons^™

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 …

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) …

Computational Models For Diffusion Of Second Messengers In Visual Transduction, Harihar Khanal

Publications

The process of phototransduction, whereby light is converted into an electrical response in retinal rod and cone photoreceptors, involves, as a crucial step, the diffusion of cytoplasmic signaling molecules, termed second messengers. A barrier to mathematical and computational modeling is the complex geometry of the rod outer segment which contains about 1000 thin discs. Most current investigations on the subject assume a well-stirred bulk aqueous environment thereby avoiding such geometrical complexity. We present theoretical and computational spatio-temporal models for phototransduction in vertebrate rod photoreceptors, which are pointwise in nature and thus take into account the complex geometry of the …

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. …

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 …

Detectability Of Excitatory Versus Inhibitory Drive In An Integrate-And-Fire-Or-Burst Thalamocortical Relay Neuron Model, Gregory D. Smith, S. M. Sherman

Arts & Sciences Articles

Although inhibitory inputs are often viewed as equal but opposite to excitatory inputs, excitatory inputs may alter the firing of postsynaptic cells more effectively than inhibitory inputs. This is because spike cancellation produced by an inhibitory input requires coincidence in time, whereas an excitatory input can add spikes with less temporal constraint. To test for such potential differences, especially in the context of the function of thalamocortical (TC) relay nuclei, we used a stochastic “integrate-and-fire-or-burst” TC neuron model to quantify the detectability of excitatory and inhibitory drive in the presence and absence of the low-threshold Ca 2+ current, IT, and …

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 …

Modeling Control Of Hiv Infection Through Structured Treatment Interruptions With Recommendations For Experimental Protocol, Shannon Kubiak, Heather Lehr, Rachel Levy, Todd Moeller, Albert Parker, Edward Swim

All HMC Faculty Publications and Research

Highly Active Anti-Retroviral Therapy (HAART) of HIV infection has significantly reduced morbidity and mortality in developed countries. However, since these treatments can cause side effects and require strict adherence to treatment protocol, questions about whether or not treatment can be interrupted or discontinued with control of infection maintained by the host immune system remain to be answered. We present sensitivity analysis of a compartmental model for HIV infection that allows for treatment interruptions, including the sensitivity of the compartments themselves to our parameters as well as the sensitivity of the cost function used in parameter estimation. Recommendations are made about …

Methods For Volume Measurement In 3d Images, Kevin J. Black

Kevin J. Black, MD

Mathematical Models Of Chemotherapy, John Carl Panetta

Mathematics & Statistics Theses & Dissertations

Several mathematical models are developed to describe the effects of chemotherapy on both cancerous and normal tissue. Each model is defined by either a single homogeneous equation or a system of heterogeneous equations which describe the states of the normal and/or cancer cells. Periodic terms are added to model the effects of the chemotherapy. What we obtain are regions, in parameter space (dose and period), of acceptable drug regimens.

The models take into account various aspects of chemotherapy. These include, interactions between the cancer and normal tissue, cell specific chemotherapeutic drug, the use of non-constant parameters to aid in modeling …

A Logistic Model Of Periodic Chemotherapy, J. C. Panetta

Mathematics & Statistics Faculty Publications

A logistic differential equation with a time-varying periodic parameter is used to model the growth of cells, in particular cancer cells, in the presences of chemotherapeutic drugs. The chemotherapeutic effects are modeled by a periodic parameter that modifies the growth rate of the cell tissue. A negative growth rate represents the detrimental effects of the drugs. A simple criterion is obtained for the behavior of the chemotherapy.

Optical Properties Of Human Uterus At 630 Nm, Steen J. Madsen, Bruce J. Tromberg, Yona Tadir, Pius Wyss, Lars O. Svaasand, Richard C. Haskell

All HMC Faculty Publications and Research

The optical properties of normal and fibriotic human uteri were determined using frequency-domain and steady-state techniques .

Tracking Plasma Lactate Concentration In Vivo With A Catheter-Tip L-Lactate Sensor, Brett T. Weinzapfel, Mark D. Ball, Lee R. Waite, Nacer E. Abrouk, Shun P. Lim

Mathematical Sciences Technical Reports (MSTR)

To circumvent the problems of repeated blood sampling for in vitro analysis, a catheter-tip L-lactate sensor has been developed. The sensor was tested in anesthetized pigs (n=6). The sensor in vivo tracked the lactate concentration non-linearly, seeming to obey Michaelis-Menten kinetics. Calibration time was short, typically 1.5 min per lactate standard. Furthermore, time drift was small, typically -1.3% to -3.3% per hour of in vivo use.

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Estimation Of Growth Curves By Least Square Splines, Dorothy Rybaczyk Pathak

Mathematics & Statistics ETDs

The primary object of this dissertation is to present some con­tributions to the theory of estimation of growth curves by least square splines in the presence of unknown unequal variances. The theoretical developments rest heavily on the standard least square theory and the theory of polynomial spline functions. A modifica­tion of the Aitken procedure of weighted least squares is used to estimate regression parameters. It is shown that this modification of the Aitken procedure does not unduly influence the nice least square properties of estimators so obtained; the estimators re­ main unbiased, consistent and asymptotically efficient.

The techniques developed in …

The Theoretical Distribution Of Forces In The Rigid Component Of The Buccal Arch Positioner, Dennis H. Teruya

Loma Linda University Electronic Theses, Dissertations & Projects

The distribution of an applied force to the rigid component of the Buccal Arch Positioner was determined with a theoretically formulated model. The rigid component was assumed to be a free body without the semi-rigid attachments and was evaluated at four points for the force distribution. The summation of the forces and the moments were equated to zero and were utilized to derive equations to solve for the unknown forces. The unknown forces at each point of the rigid component were solved for in terms of the given force applications.

A laterally directed force application at one of the posterior …