The Importance of Scale for Spatial-confounding Bias and Precision of Spatial Regression Estimators

Increasingly, regression models are used when residuals are spatially correlated. Prominent examples include studies in environmental epidemiology to understand the chronic health effects of pollutants. I consider the effects of residual spatial structure on the bias and precision of regression coefficients, developing a simple framework in which to understand the key issues and derive informative analytic results. When the spatial residual is induced by an unmeasured confounder, regression models with spatial random effects and closely-related models such as kriging and penalized splines are biased, even when the residual variance components are known. Analytic and simulation results show how the bias depends on the spatial scales of the covariate and the residual; bias is reduced only when there is variation in the covariate at a scale smaller than the scale of the unmeasured confounding. I also discuss how the scales of the residual and the covariate affect efficiency and uncertainty estimation when the residuals can be considered independent of the covariate. In an application on the association between black carbon particulate matter air pollution and birth weight, controlling for large-scale spatial variation appears to reduce bias from unmeasured confounders, while increasing uncertainty in the estimated pollution effect.

Survival Analysis with Large Dimensional Covariates: An Application in Microarray Studies

Use of microarray technology often leads to high-dimensional and low- sample size data settings. Over the past several years, a variety of novel approaches have been proposed for variable selection in this context. However, only a small number of these have been adapted for time-to-event data where censoring is present. Among standard variable selection methods shown both to have good predictive accuracy and to be computationally efficient is the elastic net penalization approach. In this paper, adaptation of the elastic net approach is presented for variable selection both under the Cox proportional hazards model and under an accelerated failure time (AFT) model. Assessment of the two methods is conducted through simulation studies and through analysis of microarray data obtained from a set of patients with diffuse large B-cell lymphoma where time to survival is of interest. The approaches are shown to match or exceed the predictive performance of a Cox-based and an AFT-based variable selection method. The methods are moreover shown to be much more computationally efficient than their respective Cox- and AFT- based counterparts.

On the Accelerated Failure Time Model for Current Status and Interval Censored Data

This paper introduces a novel approach to making inference about the regression parameters in the accelerated failure time (AFT) model for current status and interval censored data. The estimator is constructed by inverting a Wald type test for testing a null proportional hazards model. A numerically efficient Markov chain Monte Carlo (MCMC) based resampling method is proposed to simultaneously obtain the point estimator and a consistent estimator of its variance-covariance matrix. We illustrate our approach with interval censored data sets from two clinical studies. Extensive numerical studies are conducted to evaluate the finite sample performance of the new estimators.

Designed Extension of Survival Studies: Application to Clinical Trials with Unrecognized Heterogeneity

It is well known that unrecognized heterogeneity among patients, such as is conferred by genetic subtype, can undermine the power of randomized trial, designed under the assumption of homogeneity, to detect a truly beneficial treatment. We consider the conditional power approach to allow for recovery of power under unexplained heterogeneity. While Proschan and Hunsberger (1995) confined the application of conditional power design to normally distributed observations, we consider more general and difficult settings in which the data are in the framework of continuous time and are subject to censoring. In particular, we derive a procedure appropriate for the analysis of the weighted log rank test under the assumption of a proportional hazards frailty model. The proposed method is illustrated through application to a brain tumor trial.

A BAYESIAN SHRINKAGE MODEL FOR INCOMPLETE LONGITUDINAL BINARY DATA WITH APPLICATION TO THE BREAST CANCER PREVENTION TRIAL

We consider inference in randomized studies, in which repeatedly measured outcomes may be informatively missing due to drop out. In this setting, it is well known that full data estimands are not identified unless unverified assumptions are imposed. We assume a non-future dependence model for the drop-out mechanism and posit an exponential tilt model that links non-identifiable and identifiable distributions. This model is indexed by non-identified parameters, which are assumed to have an informative prior distribution, elicited from subject-matter experts. Under this model, full data estimands are shown to be expressed as functionals of the distribution of the observed data. To avoid the curse of dimensionality, we model the distribution of the observed data using a Bayesian shrinkage model. In a simulation study, we compare our approach to a fully parametric and a fully saturated model for the distribution of the observed data. Our methodology is motivated and applied to data from the Breast Cancer Prevention Trial.

Nonparametric Estimation of the Bivariate Recurrence Time Distribution

This paper considers statistical models in which two different types of events, such as the diagnosis of a disease and the remission of the disease, occur alternately over time and are observed subject to right censoring. We propose nonparametric estimators for the joint distribution of bivariate recurrence times and the marginal distribution of the first recurrence time. In general, the marginal distribution of the second recurrence time cannot be estimated due to an identifiability problem, but a conditional distribution of the second recurrence time can be estimated non-parametrically. In literature, statistical methods have been developed to estimate the joint distribution of bivariate recurrence times based on data of the first pair of censored bivariate recurrence times. These methods are efficient in the current model because recurrence times of higher orders are not used. Asymptotic properties of the estimators are established. Numerical studies demonstrate the estimator performs well with practical sample sizes. We apply the proposed method to a Denmark psychiatric case register data set for illustration of the methods and theory.

Kernel Estimation of Rate Function for Recurrent Event Data

Recurrent event data are largely characterized by the rate function but smoothing techniques for estimating the rate function have never been rigorously developed or studied in statistical literature. This paper considers the moment and least squares methods for estimating the rate function from recurrent event data. With an independent censoring assumption on the recurrent event process, we study statistical properties of the proposed estimators and propose bootstrap procedures for the bandwidth selection and for the approximation of confidence intervals in the estimation of the occurrence rate function. It is identified that the moment method without resmoothing via a smaller bandwidth will produce curve with nicks occurring at the censoring times, whereas there is no such problem with the least squares method. Furthermore, the asymptotic variance of the least squares estimator is shown to be smaller under regularity conditions. However, in the implementation of the bootstrap procedures, the moment method is computationally more efficient than the least squares method because the former approach uses condensed bootstrap data. The performance of the proposed procedures is studied through Monte Carlo simulations and an epidemiological example on intravenous drug users.

Analyzing Bivariate Survival Data with Interval Sampling and Application to Cancer Epidemiology

In medical follow-up studies, ordered bivariate survival data are frequently encountered when bivariate failure events are used as the outcomes to identify the progression of a disease. In cancer studies interest could be focused on bivariate failure times, for example, time from birth to cancer onset and time from cancer onset to death. This paper considers a sampling scheme where the first failure event (cancer onset) is identified within a calendar time interval, the time of the initiating event (birth) can be retrospectively confirmed, and the occurrence of the second event (death) is observed sub ject to right censoring. To analyze this type of bivariate failure time data, it is important to recognize the presence of bias arising due to interval sampling. In this paper, nonparametric and semiparametric methods are developed to analyze the bivariate survival data with interval sampling under stationary and semi-stationary conditions. Numerical studies demonstrate the proposed estimating approaches perform well with practical sample sizes in different simulated models. We apply the proposed methods to SEER ovarian cancer registry data for illustration of the methods and theory.

Statistical analysis of personal radiofrequency electromagnetic field measurements with nondetects

Exposimeters are increasingly applied in bioelectromagnetic research to determine personal radiofrequency electromagnetic field (RF-EMF) exposure. The main advantages of exposimeter measurements are their convenient handling for study participants and the large amount of personal exposure data, which can be obtained for several RF-EMF sources. However, the large proportion of measurements below the detection limit is a challenge for data analysis. With the robust ROS (regression on order statistics) method, summary statistics can be calculated by fitting an assumed distribution to the observed data. We used a preliminary sample of 109 weekly exposimeter measurements from the QUALIFEX study to compare summary statistics computed by robust ROS with a naïve approach, where values below the detection limit were replaced by the value of the detection limit. For the total RF-EMF exposure, differences between the naïve approach and the robust ROS were moderate for the 90th percentile and the arithmetic mean. However, exposure contributions from minor RF-EMF sources were considerably overestimated with the naïve approach. This results in an underestimation of the exposure range in the population, which may bias the evaluation of potential exposure-response associations. We conclude from our analyses that summary statistics of exposimeter data calculated by robust ROS are more reliable and more informative than estimates based on a naïve approach. Nevertheless, estimates of source-specific medians or even lower percentiles depend on the assumed data distribution and should be considered with caution.

Adaptive sensing for target tracking applications

In a statistical inference scenario, the estimation of target signal or its parameters is done by processing data from informative measurements. The estimation performance can be enhanced if we choose the measurements based on some criteria that help to direct our sensing resources such that the measurements are more informative about the parameter we intend to estimate. While taking multiple measurements, the measurements can be chosen online so that more information could be extracted from the data in each measurement process. This approach fits well in Bayesian inference model often used to produce successive posterior distributions of the associated parameter. We explore the sensor array processing scenario for adaptive sensing of a target parameter. The measurement choice is described by a measurement matrix that multiplies the data vector normally associated with the array signal processing. The adaptive sensing of both static and dynamic system models is done by the online selection of proper measurement matrix over time. For the dynamic system model, the target is assumed to move with some distribution and the prior distribution at each time step is changed. The information gained through adaptive sensing of the moving target is lost due to the relative shift of the target. The adaptive sensing paradigm has many similarities with compressive sensing. We have attempted to reconcile the two approaches by modifying the observation model of adaptive sensing to match the compressive sensing model for the estimation of a sparse vector.

Improved impurity fingerprinting of heparin by high resolution (1)H NMR spectroscopy

For improving the identification of potential heparin impurities such as oversulfated chondroitin sulfate (OSCS) the standard 2D (1)H-(1)H NMR NOESY was applied. Taking advantage of spin diffusion and adjusting the experimental parameters accordingly additional contaminant-specific signals of the corresponding sugar ring protons can easily be detected. These are usually hidden by the more intense heparin signals. Compared to the current 1D (1)H procedure proposed for screening commercial unfractionated heparin samples and focusing on the contaminants acetyl signals more informative and unique fingerprints may be obtained. Correspondingly measured (1)H fingerprints of a few potential impurities are given and their identification in two contaminated commercial heparin samples is demonstrated. The proposed 2D NOESY method is not intended to replace the current 1D method for detecting and quantifying heparin impurities but may be regarded as a valuable supplement for an improved and more reliable identification of these contaminants.

ALTERNATING CURRENT DIELECTROPHORETIC MANIPULATION OF ERYTHROCYTES IN MEDICAL MICRODEVICE TECHNOLOGY

Medical microdevices have gained popularity in the past few decades because they allow the medical laboratory to be taken out into the field and for disease diagnostics to happen with a smaller sample volume, at a lower cost and much faster. Blood is the human body's most readily available and informative diagnostic fluid because of the wealth of information it provides about the body's general health including enzymatic, proteomic and immunological states. The purpose of this project is to optimize operating conditions and study ABO-Rh erythrocytes dielectrophoretic responses to alternating current electric signals. The end goal of this project is the creation of a relatively inexpensive microfluidic device, which can be used for the ABO-Rh typing of a blood sample. This dissertation presents results showing how blood samples of a known ABO- Rh blood type exhibit differing behavior to the same electrical stimulus based on their blood type. The first panel of donors and experiments, presented in Chapter 4 occurred when a sample of known blood type was injected into a microdevice with a T-shaped electrode configuration and the erythorcytes were found to rupture at a rate specific to their ABO-Rh blood type. The second set of experiments, presented in Chapter 5, were originally published in Electrophoresis in 20111. Novel in this work was the discovery that treatment of human erythrocytes with β-galactosidase successfully removed ABO surface antigens such that native A and B blood no longer agglutinated with the proper antibodies. This work was performed in a medium of conductivity 0.9S/m which is close to the measured conductivity of pooled plasma (~1.1S/m). The ability to perform dielectrophoresis experiments at physiological conductivities conditions is advantageous for future portable devices because the device/instrument would not need to store dilution buffers. The final results of this project, presented in Chapter 6, explore the entire dielectrophoretic spectra of the ABO-Rh erythrocytes including the cross-over frequency and the magnitudes of the positive or negative dielectrophoretic response. These were completed at lower medium conductivities of 0.1S/m and 0.01-0.04S/m. These results show that by using the sweep function built into the Agilent alternating current generator it is possible to explore how a single group of blood cells will react to rapid changes in frequency and will provide the user with curve that can be matched the theoretical dielectrophoretic response curves. As a whole this project shows that it is possible to distinguish human erythrocytes by their ABO-Rh blood type via three different dielectrophoretic methods. This work builds on the foundation of that it is possible to distinguish healthy from infected cells2-7, similar cell types1,7-14 and other work regarding the dielectrophoresis of human erythrocytes1,10,11. This work has implications in both medical diagnostics and future dielectrophoretic work because it has shown that ABO-Rh blood type is now a factor, which must be identified when working with a human blood sample. It also shows that the creation of a microfluidic device that subjects human erythrocytes to a dielectrophoretic impulse and then exports an ABO-Rh blood type is a near future possibility.

On Graphically Checking Goodness-of-fit of Binary Logistic Regression Models

OBJECTIVES: This paper is concerned with checking goodness-of-fit of binary logistic regression models. For the practitioners of data analysis, the broad classes of procedures for checking goodness-of-fit available in the literature are described. The challenges of model checking in the context of binary logistic regression are reviewed. As a viable solution, a simple graphical procedure for checking goodness-of-fit is proposed. METHODS: The graphical procedure proposed relies on pieces of information available from any logistic analysis; the focus is on combining and presenting these in an informative way. RESULTS: The information gained using this approach is presented with three examples. In the discussion, the proposed method is put into context and compared with other graphical procedures for checking goodness-of-fit of binary logistic models available in the literature. CONCLUSION: A simple graphical method can significantly improve the understanding of any logistic regression analysis and help to prevent faulty conclusions.

VHL inactivation is an important pathway for the development of malignant sporadic pancreatic endocrine tumors

A small subset of familial pancreatic endocrine tumors (PET) arises in patients with von Hippel-Lindau syndrome and these tumors may have an adverse outcome compared to other familial PET. Sporadic PET rarely harbors somatic VHL mutations, but the chromosomal location of the VHL gene is frequently deleted in sporadic PET. A subset of sporadic PET shows active hypoxia signals on mRNA and protein level. To identify the frequency of functionally relevant VHL inactivation in sporadic PET and to examine a possible prognostic significance we correlated epigenetic and genetic VHL alterations with hypoxia signals. VHL mutations were absent in all 37 PETs examined. In 2 out of 35 informative PET (6%) methylation of the VHL promoter region was detected and VHL deletion by fluorescence in situ hybridization was found in 14 out of 79 PET (18%). Hypoxia inducible factor 1alpha (HIF1-alpha), carbonic anhydrase 9 (CA-9), and glucose transporter 1 (GLUT-1) protein was expressed in 19, 27, and 30% of the 152 PETs examined. Protein expression of the HIF1-alpha downstream target CA-9 correlated significantly with the expression of CA-9 RNA (P<0.001), VHL RNA (P<0.05), and VHL deletion (P<0.001) as well as with HIF1-alpha (P<0.005) and GLUT-1 immunohistochemistry (P<0.001). These PET with VHL alterations and signs of hypoxia signalling were characterized by a significantly shortened disease-free survival. We conclude that VHL gene impairment by promoter methylation and VHL deletion in nearly 25% of PET leads to the activation of the HIF-pathway. Our data suggest that VHL inactivation and consecutive hypoxia signals may be a mechanism for the development of sporadic PET with an adverse outcome.