Model Checking for ROC Regression Analysis

The Receiver Operating Characteristic (ROC) curve is a prominent tool for characterizing the accuracy of continuous diagnostic test. To account for factors that might invluence the test accuracy, various ROC regression methods have been proposed. However, as in any regression analysis, when the assumed models do not fit the data well, these methods may render invalid and misleading results. To date practical model checking techniques suitable for validating existing ROC regression models are not yet available. In this paper, we develop cumulative residual based procedures to graphically and numerically assess the goodness-of-fit for some commonly used ROC regression models, and show how specific components of these models can be examined within this framework. We derive asymptotic null distributions for the residual process and discuss resampling procedures to approximate these distributions in practice. We illustrate our methods with a dataset from the Cystic Fibrosis registry.

Predicting asthma control and exacerbations: chronic asthma as a complex dynamic model

PURPOSE OF REVIEW: Predicting asthma episodes is notoriously difficult but has potentially significant consequences for the individual, as well as for healthcare services. The purpose of this review is to describe recent insights into the prediction of acute asthma episodes in relation to classical clinical, functional or inflammatory variables, as well as present a new concept for evaluating asthma as a dynamically regulated homeokinetic system. RECENT FINDINGS: Risk prediction for asthma episodes or relapse has been attempted using clinical scoring systems, considerations of environmental factors and lung function, as well as inflammatory and immunological markers in induced sputum or exhaled air, and these are summarized here. We have recently proposed that newer mathematical methods derived from statistical physics may be used to understand the complexity of asthma as a homeokinetic, dynamic system consisting of a network comprising multiple components, and also to assess the risk for future asthma episodes based on fluctuation analysis of long time series of lung function. SUMMARY: Apart from the classical analysis of risk factor and functional parameters, this new approach may be used to assess asthma control and treatment effects in the individual as well as in future research trials.

FUNCTIONAL PRINCIPAL COMPONENTS MODEL FOR HIGH-DIMENSIONAL BRAIN IMAGING

We establish a fundamental equivalence between singular value decomposition (SVD) and functional principal components analysis (FPCA) models. The constructive relationship allows to deploy the numerical efficiency of SVD to fully estimate the components of FPCA, even for extremely high-dimensional functional objects, such as brain images. As an example, a functional mixed effect model is fitted to high-resolution morphometric (RAVENS) images. The main directions of morphometric variation in brain volumes are identified and discussed.

Studying Effects of Primary Care Physicians and Patients on the Trade-Off Between Charges for Primary Care and Specialty Care Using a Hierarchical Multivariate Two-Part Model

Objective. To examine effects of primary care physicians (PCPs) and patients on the association between charges for primary care and specialty care in a point-of-service (POS) health plan. Data Source. Claims from 1996 for 3,308 adult male POS plan members, each of whom was assigned to one of the 50 family practitioner-PCPs with the largest POS plan member-loads. Study Design. A hierarchical multivariate two-part model was fitted using a Gibbs sampler to estimate PCPs' effects on patients' annual charges for two types of services, primary care and specialty care, the associations among PCPs' effects, and within-patient associations between charges for the two services. Adjusted Clinical Groups (ACGs) were used to adjust for case-mix. Principal Findings. PCPs with higher case-mix adjusted rates of specialist use were less likely to see their patients at least once during the year (estimated correlation: –.40; 95% CI: –.71, –.008) and provided fewer services to patients that they saw (estimated correlation: –.53; 95% CI: –.77, –.21). Ten of 11 PCPs whose case-mix adjusted effects on primary care charges were significantly less than or greater than zero (p < .05) had estimated, case-mix adjusted effects on specialty care charges that were of opposite sign (but not significantly different than zero). After adjustment for ACG and PCP effects, the within-patient, estimated odds ratio for any use of primary care given any use of specialty care was .57 (95% CI: .45, .73). Conclusions. PCPs and patients contributed independently to a trade-off between utilization of primary care and specialty care. The trade-off appeared to partially offset significant differences in the amount of care provided by PCPs. These findings were possible because we employed a hierarchical multivariate model rather than separate univariate models.

A BAYESIAN HIERARCHICAL MODEL FOR CONSTRAINED DISTRIBUTED LAG FUNCTIONS: ESTIMATING THE TIME COURSE OF HOSPITALIZATION ASSOCIATED WITH AIR POLLUTION EXPOSURE

Numerous time series studies have provided strong evidence of an association between increased levels of ambient air pollution and increased levels of hospital admissions, typically at 0, 1, or 2 days after an air pollution episode. An important research aim is to extend existing statistical models so that a more detailed understanding of the time course of hospitalization after exposure to air pollution can be obtained. Information about this time course, combined with prior knowledge about biological mechanisms, could provide the basis for hypotheses concerning the mechanism by which air pollution causes disease. Previous studies have identified two important methodological questions: (1) How can we estimate the shape of the distributed lag between increased air pollution exposure and increased mortality or morbidity? and (2) How should we estimate the cumulative population health risk from short-term exposure to air pollution? Distributed lag models are appropriate tools for estimating air pollution health effects that may be spread over several days. However, estimation for distributed lag models in air pollution and health applications is hampered by the substantial noise in the data and the inherently weak signal that is the target of investigation. We introduce an hierarchical Bayesian distributed lag model that incorporates prior information about the time course of pollution effects and combines information across multiple locations. The model has a connection to penalized spline smoothing using a special type of penalty matrix. We apply the model to estimating the distributed lag between exposure to particulate matter air pollution and hospitalization for cardiovascular and respiratory disease using data from a large United States air pollution and hospitalization database of Medicare enrollees in 94 counties covering the years 1999-2002.

A Mechanistic Latent Variable Model for Estimating Drug Concentrations in the Male Genital Tract

The purpose of this study is to develop statistical methodology to facilitate indirect estimation of the concentration of antiretroviral drugs and viral loads in the prostate gland and the seminal vesicle. The differences in antiretroviral drug concentrations in these organs may lead to suboptimal concentrations in one gland compared to the other. Suboptimal levels of the antiretroviral drugs will not be able to fully suppress the virus in that gland, lead to a source of sexually transmissible virus and increase the chance of selecting for drug resistant virus. This information may be useful selecting antiretroviral drug regimen that will achieve optimal concentrations in most of male genital tract glands. Using fractionally collected semen ejaculates, Lundquist (1949) measured levels of surrogate markers in each fraction that are uniquely produced by specific male accessory glands. To determine the original glandular concentrations of the surrogate markers, Lundquist solved a simultaneous series of linear equations. This method has several limitations. In particular, it does not yield a unique solution, it does not address measurement error, and it disregards inter-subject variability in the parameters. To cope with these limitations, we developed a mechanistic latent variable model based on the physiology of the male genital tract and surrogate markers. We employ a Bayesian approach and perform a sensitivity analysis with regard to the distributional assumptions on the random effects and priors. The model and Bayesian approach is validated on experimental data where the concentration of a drug should be (biologically) differentially distributed between the two glands. In this example, the Bayesian model-based conclusions are found to be robust to model specification and this hierarchical approach leads to more scientifically valid conclusions than the original methodology. In particular, unlike existing methods, the proposed model based approach was not affected by a common form of outliers.

Statistical evaluation of time-dependent metabolite concentrations: estimation of post-mortem intervals based on in situ 1H-MRS of the brain

Knowledge of the time interval from death (post-mortem interval, PMI) has an enormous legal, criminological and psychological impact. Aiming to find an objective method for the determination of PMIs in forensic medicine, 1H-MR spectroscopy (1H-MRS) was used in a sheep head model to follow changes in brain metabolite concentrations after death. Following the characterization of newly observed metabolites (Ith et al., Magn. Reson. Med. 2002; 5: 915-920), the full set of acquired spectra was analyzed statistically to provide a quantitative estimation of PMIs with their respective confidence limits. In a first step, analytical mathematical functions are proposed to describe the time courses of 10 metabolites in the decomposing brain up to 3 weeks post-mortem. Subsequently, the inverted functions are used to predict PMIs based on the measured metabolite concentrations. Individual PMIs calculated from five different metabolites are then pooled, being weighted by their inverse variances. The predicted PMIs from all individual examinations in the sheep model are compared with known true times. In addition, four human cases with forensically estimated PMIs are compared with predictions based on single in situ MRS measurements. Interpretation of the individual sheep examinations gave a good correlation up to 250 h post-mortem, demonstrating that the predicted PMIs are consistent with the data used to generate the model. Comparison of the estimated PMIs with the forensically determined PMIs in the four human cases shows an adequate correlation. Current PMI estimations based on forensic methods typically suffer from uncertainties in the order of days to weeks without mathematically defined confidence information. In turn, a single 1H-MRS measurement of brain tissue in situ results in PMIs with defined and favorable confidence intervals in the range of hours, thus offering a quantitative and objective method for the determination of PMIs.

Accurate and robust reconstruction of proximal femur from sparse intraoperative data and dense point distribution model for surgical navigation

Constructing a 3D surface model from sparse-point data is a nontrivial task. Here, we report an accurate and robust approach for reconstructing a surface model of the proximal femur from sparse-point data and a dense-point distribution model (DPDM). The problem is formulated as a three-stage optimal estimation process. The first stage, affine registration, is to iteratively estimate a scale and a rigid transformation between the mean surface model of the DPDM and the sparse input points. The estimation results of the first stage are used to establish point correspondences for the second stage, statistical instantiation, which stably instantiates a surface model from the DPDM using a statistical approach. This surface model is then fed to the third stage, kernel-based deformation, which further refines the surface model. Handling outliers is achieved by consistently employing the least trimmed squares (LTS) approach with a roughly estimated outlier rate in all three stages. If an optimal value of the outlier rate is preferred, we propose a hypothesis testing procedure to automatically estimate it. We present here our validations using four experiments, which include 1 leave-one-out experiment, 2 experiment on evaluating the present approach for handling pathology, 3 experiment on evaluating the present approach for handling outliers, and 4 experiment on reconstructing surface models of seven dry cadaver femurs using clinically relevant data without noise and with noise added. Our validation results demonstrate the robust performance of the present approach in handling outliers, pathology, and noise. An average 95-percentile error of 1.7-2.3 mm was found when the present approach was used to reconstruct surface models of the cadaver femurs from sparse-point data with noise added.

Correspondence establishment in statistical modeling of shapes with arbitrary topology

Correspondence establishment is a key step in statistical shape model building. There are several automated methods for solving this problem in 3D, but they usually can only handle objects with simple topology, like that of a sphere or a disc. We propose an extension to correspondence establishment over a population based on the optimization of the minimal description length function, allowing considering objects with arbitrary topology. Instead of using a fixed structure of kernel placement on a sphere for the systematic manipulation of point landmark positions, we rely on an adaptive, hierarchical organization of surface patches. This hierarchy can be built on surfaces of arbitrary topology and the resulting patches are used as a basis for a consistent, multi-scale modification of the surfaces' parameterization, based on point distribution models. The feasibility of the approach is demonstrated on synthetic models with different topologies.

Statistical evaluation of alternative models of human evolution

An appropriate model of recent human evolution is not only important to understand our own history, but it is necessary to disentangle the effects of demography and selection on genome diversity. Although most genetic data support the view that our species originated recently in Africa, it is still unclear if it completely replaced former members of the Homo genus, or if some interbreeding occurred during its range expansion. Several scenarios of modern human evolution have been proposed on the basis of molecular and paleontological data, but their likelihood has never been statistically assessed. Using DNA data from 50 nuclear loci sequenced in African, Asian and Native American samples, we show here by extensive simulations that a simple African replacement model with exponential growth has a higher probability (78%) as compared with alternative multiregional evolution or assimilation scenarios. A Bayesian analysis of the data under this best supported model points to an origin of our species approximately 141 thousand years ago (Kya), an exit out-of-Africa approximately 51 Kya, and a recent colonization of the Americas approximately 10.5 Kya. We also find that the African replacement model explains not only the shallow ancestry of mtDNA or Y-chromosomes but also the occurrence of deep lineages at some autosomal loci, which has been formerly interpreted as a sign of interbreeding with Homo erectus.

Shear band evolution in Zr/Hf-based bulk metallic glasses under static and dynamic indentations

Bulk metallic glasses (BMGs) exhibit superior mechanical properties as compared with other conventional materials and have been proposed for numerous engineering and technological applications. Zr/Hf-based BMGs or tungsten reinforced BMG composites are considered as a potential replacement for depleted uranium armor-piercing projectiles because of their ability to form localized shear bands during impact, which has been known to be the dominant plastic deformation mechanism in BMGs. However, in conventional tensile, compressive and bending tests, limited ductility has been observed because of fracture initiation immediately following the shear band formation. To fully investigate shear band characteristics, indentation tests that can confine the deformation in a limited region have been pursued. In this thesis, a detailed investigation of thermal stability and mechanical deformation behavior of Zr/Hf-based BMGs is conducted. First, systematic studies had been implemented to understand the influence of relative compositions of Zr and Hf on thermal stability and mechanical property evolution. Second, shear band evolution under indentations were investigated experimentally and theoretically. Three kinds of indentation studies were conducted on BMGs in the current study. (a) Nano-indentation to determine the mechanical properties as a function of Hf/Zr content. (b) Static Vickers indentation on bonded split specimens to investigate the shear band evolution characteristics beneath the indention. (c) Dynamic Vickers indentation on bonded split specimens to investigate the influence of strain rate. It was found in the present work that gradually replacing Zr by Hf remarkably increases the density and improves the mechanical properties. However, a slight decrease in glass forming ability with increasing Hf content has also been identified through thermodynamic analysis although all the materials in the current study were still found to be amorphous. Many indentation studies have revealed only a few shear bands surrounding the indent on the top surface of the specimen. This small number of shear bands cannot account for the large plastic deformation beneath the indentations. Therefore, a bonded interface technique has been used to observe the slip-steps due to shear band evolution. Vickers indentations were performed along the interface of the bonded split specimen at increasing loads. At small indentation loads, the plastic deformation was primarily accommodated by semi-circular primary shear bands surrounding the indentation. At higher loads, secondary and tertiary shear bands were formed inside this plastic zone. A modified expanding cavity model was then used to predict the plastic zone size characterized by the shear bands and to identify the stress components responsible for the evolution of the various types of shear bands. The applicability of various hardness—yield-strength ( H −σγ ) relationships currently available in the literature for bulk metallic glasses (BMGs) is also investigated. Experimental data generated on ZrHf-based BMGs in the current study and those available elsewhere on other BMG compositions were used to validate the models. A modified expanding-cavity model, employed in earlier work, was extended to propose a new H −σγ relationship. Unlike previous models, the proposed model takes into account not only the indenter geometry and the material properties, but also the pressure sensitivity index of the BMGs. The influence of various model parameters is systematically analyzed. It is shown that there is a good correlation between the model predictions and the experimental data for a wide range of BMG compositions. Under dynamic Vickers indentation, a decrease in indentation hardness at high loading rate was observed compared to static indentation hardness. It was observed that at equivalent loads, dynamic indentations produced more severe deformation features on the loading surface than static indentations. Different from static indentation, two sets of widely spaced semi-circular shear bands with two different curvatures were observed. The observed shear band pattern and the strain rate softening in indentation hardness were rationalized based on the variations in the normal stress on the slip plane, the strain rate of shear and the temperature rise associated with the indentation deformation. Finally, a coupled thermo-mechanical model is proposed that utilizes a momentum diffusion mechanism for the growth and evolution of the final spacing of shear bands. The influence of strain rate, confinement pressure and critical shear displacement on the shear band spacing, temperature rise within the shear band, and the associated variation in flow stress have been captured and analyzed. Consistent with the known pressure sensitive behavior of BMGs, the current model clearly captures the influence of the normal stress in the formation of shear bands. The normal stress not only reduces the time to reach critical shear displacement but also causes a significant temperature rise during the shear band formation. Based on this observation, the variation of shear band spacing in a typical dynamic indentation test has been rationalized. The temperature rise within a shear band can be in excess of 2000K at high strain rate and high confinement pressure conditions. The associated drop in viscosity and flow stress may explain the observed decrease in fracture strength and indentation hardness. The above investigations provide valuable insight into the deformation behavior of BMGs under static and dynamic loading conditions. The shear band patterns observed in the above indentation studies can be helpful to understand and model the deformation features under complex loading scenarios such as the interaction of a penetrator with armor. Future work encompasses (1) extending and modifying the coupled thermo-mechanical model to account for the temperature rise in quasistatic deformation; and (2) expanding this model to account for the microstructural variation-crystallization and free volume migration associated with the deformation.

Controlling electronic and magnetic properties of ultra narrow multilayered nanowires

Interest in the study of magnetic/non-magnetic multilayered structures took a giant leap since Grünberg and his group established that the interlayer exchange coupling (IEC) is a function of the non-magnetic spacer width. This interest was further fuelled by the discovery of the phenomenal Giant Magnetoresistance (GMR) effect. In fact, in 2007 Albert Fert and Peter Grünberg were awarded the Nobel Prize in Physics for their contribution to the discovery of GMR. GMR is the key property that is being used in the read-head of the present day computer hard drive as it requires a high sensitivity in the detection of magnetic field. The recent increase in demand for device miniaturization encouraged researchers to look for GMR in nanoscale multilayered structures. In this context, one dimensional(1-D) multilayerd nanowire structure has shown tremendous promise as a viable candidate for ultra sensitive read head sensors. In fact, the phenomenal giant magnetoresistance(GMR) effect, which is the novel feature of the currently used multilayered thin film, has already been observed in multilayered nanowire systems at ambient temperature. Geometrical confinement of the supper lattice along the 2-dimensions (2-D) to construct the 1-D multilayered nanowire prohibits the minimization of magnetic interaction- offering a rich variety of magnetic properties in nanowire that can be exploited for novel functionality. In addition, introduction of non-magnetic spacer between the magnetic layers presents additional advantage in controlling magnetic properties via tuning the interlayer magnetic interaction. Despite of a large volume of theoretical works devoted towards the understanding of GMR and IEC in super lattice structures, limited theoretical calculations are reported in 1-D multilayered systems. Thus to gauge their potential application in new generation magneto-electronic devices, in this thesis, I have discussed the usage of first principles density functional theory (DFT) in predicting the equilibrium structure, stability as well as electronic and magnetic properties of one dimensional multilayered nanowires. Particularly, I have focused on the electronic and magnetic properties of Fe/Pt multilayered nanowire structures and the role of non-magnetic Pt spacer in modulating the magnetic properties of the wire. It is found that the average magnetic moment per atom in the nanowire increases monotonically with an ~1/(N(Fe)) dependance, where N(Fe) is the number of iron layers in the nanowire. A simple model based upon the interfacial structure is given to explain the 1/(N(Fe)) trend in magnetic moment obtained from the first principle calculations. A new mechanism, based upon spin flip with in the layer and multistep electron transfer between the layers, is proposed to elucidate the enhancement of magnetic moment of Iron atom at the Platinum interface. The calculated IEC in the Fe/Pt multilayered nanowire is found to switch sign as the width of the non-magnetic spacer varies. The competition among short and long range direct exchange and the super exchange has been found to play a key role for the non-monotonous sign in IEC depending upon the width of the Platinum spacer layer. The calculated magnetoresistance from Julliere's model also exhibit similar switching behavior as that of IEC. The universality of the behavior of exchange coupling has also been looked into by introducing different non-magnetic spacers like Palladium, Copper, Silver, and Gold in between magnetic Iron layers. The nature of hybridization between Fe and other non-magnetic spacer is found to dictate the inter layer magnetic interaction. For example, in Fe/Pd nanowire the d-p hybridization in two spacer layer case favors anti-ferromagnetic (AFM) configuration over ferromagnetic (FM) configuration. However, the hybridization between half-filled Fe(d) and filled Cu(p) state in Fe/Cu nanowire favors FM coupling in the 2-spacer system.

Utilizing Gaussian-Schell model beams to mitigate atmospheric turbulence in free space optical communications / by Kyle R. Drexler.

Turbulence affects traditional free space optical communication by causing speckle to appear in the received beam profile. This occurs due to changes in the refractive index of the atmosphere that are caused by fluctuations in temperature and pressure, resulting in an inhomogeneous medium. The Gaussian-Schell model of partial coherence has been suggested as a means of mitigating these atmospheric inhomogeneities on the transmission side. This dissertation analyzed the Gaussian-Schell model of partial coherence by verifying the Gaussian-Schell model in the far-field, investigated the number of independent phase control screens necessary to approach the ideal Gaussian-Schell model, and showed experimentally that the Gaussian-Schell model of partial coherence is achievable in the far-field using a liquid crystal spatial light modulator. A method for optimizing the statistical properties of the Gaussian-Schell model was developed to maximize the coherence of the field while ensuring that it does not exhibit the same statistics as a fully coherent source. Finally a technique to estimate the minimum spatial resolution necessary in a spatial light modulator was developed to effectively propagate the Gaussian-Schell model through a range of atmospheric turbulence strengths. This work showed that regardless of turbulence strength or receiver aperture, transmitting the Gaussian-Schell model of partial coherence instead of a fully coherent source will yield a reduction in the intensity fluctuations of the received field. By measuring the variance of the intensity fluctuations and the received mean, it is shown through the scintillation index that using the Gaussian-Schell model of partial coherence is a simple and straight forward method to mitigate atmospheric turbulence instead of traditional adaptive optics in free space optical communications.