Applied Statistics Commons^™

Strengthening Instrumental Variables Through Weighting, Douglas Lehmann, Yun Li, Rajiv Saran, Yi Li

The University of Michigan Department of Biostatistics Working Paper Series

Instrumental variable (IV) methods are widely used to deal with the issue of unmeasured confounding and are becoming popular in health and medical research. IV models are able to obtain consistent estimates in the presence of unmeasured confounding, but rely on assumptions that are hard to verify and often criticized. An instrument is a variable that influences or encourages individuals toward a particular treatment without directly affecting the outcome. Estimates obtained using instruments with a weak influence over the treatment are known to have larger small-sample bias and to be less robust to the critical IV assumption that the instrument …

Evaluating The Impact Of A Hiv Low-Risk Express Care Task-Shifting Program: A Case Study Of The Targeted Learning Roadmap, Linh Tran, Constantin T. Yiannoutsos, Beverly S. Musick, Kara K. Wools-Kaloustian, Abraham Siika, Sylvester Kimaiyo, Mark J. Van Der Laan, Maya L. Petersen

U.C. Berkeley Division of Biostatistics Working Paper Series

In conducting studies on an exposure of interest, a systematic roadmap should be applied for translating causal questions into statistical analyses and interpreting the results. In this paper we describe an application of one such roadmap applied to estimating the joint effect of both time to availability of a nurse-based triage system (low risk express care (LREC)) and individual enrollment in the program among HIV patients in East Africa. Our study population is comprised of 16;513 subjects found eligible for this task-shifting program within 15 clinics in Kenya between 2006 and 2009, with each clinic starting the LREC program between …

Modeled And Measured Image-Plane Polychromatic Speckle Contrast, Noah R. Van Zandt, Jack E. Mccrae, Steven T. Fiorino

Faculty Publications

The statistical properties of speckle relevant to short- to medium-range (tactical) active tracking involving polychromatic illumination are investigated. A numerical model is developed to allow rapid simulation of speckled images including the speckle contrast reduction effects of illuminator bandwidth, surface slope, and roughness, and the polarization properties of both the source and the reflection. Regarding surface slope (relative orientation of the surface normal and illumination/observation directions), Huntley’s theory for speckle contrast, which employs geometrical approximations to decrease computation time, is modified to increase accuracy by incorporation of a geometrical correction factor and better treatment of roughness and polarization. The resulting …

Models For Hsv Shedding Must Account For Two Levels Of Overdispersion, Amalia Magaret

UW Biostatistics Working Paper Series

We have frequently implemented crossover studies to evaluate new therapeutic interventions for genital herpes simplex virus infection. The outcome measured to assess the efficacy of interventions on herpes disease severity is the viral shedding rate, defined as the frequency of detection of HSV on the genital skin and mucosa. We performed a simulation study to ascertain whether our standard model, which we have used previously, was appropriately considering all the necessary features of the shedding data to provide correct inference. We simulated shedding data under our standard, validated assumptions and assessed the ability of 5 different models to reproduce the …

Thermally Induced Aggregation Of Rigid Spheres On A Liquid Surface, Eric Forgoston, Leo Hentschker, Siobhan Soltau, Patrick Truitt, Ashuwin Vaidya

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Fluids provide the optimal setting to explore natural patterns far from thermodynamic equilibrium. Experiments suggest that randomly dispersed particles on a liquid surface tend to aggregate on the surface of liquid over time, and the process is enhanced by an increase in the temperature of the liquid. We show that the agglomeration radii increases monotonically with temperature up until the point where all particles in the system form a single, large aggregate. The aggregation dynamics is related to changes in the material properties of the liquid including its viscosity and surface tension as well as the convection driven flow generated …

Modelling Subject-Specific Childhood Growth Using Linear Mixed-Effect Models With Cubic Regression Splines, Laura M. Grajeda, Andrada Ivanescu, Mayuko Saito, Ciprian Crainiceanu, Devan Jaganath, Robert H. Gilman, Jean E. Crabtree, Dermott Kelleher, Lilia Cabrera, Vitaliano Cama, William Checkley

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Background: Childhood growth is a cornerstone of pediatric research. Statistical models need to consider individual trajectories to adequately describe growth outcomes. Specifically, well-defined longitudinal models are essential to characterize both population and subject-specific growth. Linear mixed-effect models with cubic regression splines can account for the nonlinearity of growth curves and provide reasonable estimators of population and subject-specific growth, velocity and acceleration. Methods: We provide a stepwise approach that builds from simple to complex models, and account for the intrinsic complexity of the data. We start with standard cubic splines regression models and build up to a model that includes subject-specific …

Spatiotemporal Meta-Analysis: Reviewing Health Psychology Phenomena Over Space And Time., Blair T. Johnson

CHIP Documents

This supplemental material is meant to support this article:

Johnson, B. T., Crowley, E., & Marrouch, N. Spatiotemporal meta-analysis: Reviewing health psychology phenomena over space and time. Health Psychology Review.

Specifically, it is a database of GDPs per capita for nations in the world between 1800 and 2015. It is archived here to support an online supplement to this article.

GDP per capita

Is The Time Allocated To Review Patent Applications Inducing Examiners To Grant Invalid Patents?: Evidence From Micro-Level Application Data, Michael D. Frakes, Melissa F. Wasserman

Faculty Scholarship

We explore how examiner behavior is altered by the time allocated for reviewing patent applications. Insufficient examination time may hamper examiner search and rejection efforts, leaving examiners more inclined to grant invalid applications. To test this prediction, we use application-level data to trace the behavior of individual examiners over the course of a series of promotions that carry with them reductions in examination-time allocations. We find evidence demonstrating that such promotions are associated with reductions in examination scrutiny and increases in granting tendencies, as well as evidence that those additional patents being issued on the margin are of below-average quality.

Design & Analysis Of A Computer Experiment For An Aerospace Conformance Simulation Study, Ryan W. Gryder

Theses and Dissertations

Within NASA's Air Traffic Management Technology Demonstration # 1 (ATD-1), Interval Management (IM) is a flight deck tool that enables pilots to achieve or maintain a precise in-trail spacing behind a target aircraft. Previous research has shown that violations of aircraft spacing requirements can occur between an IM aircraft and its surrounding non-IM aircraft when it is following a target on a separate route. This research focused on the experimental design and analysis of a deterministic computer simulation which models our airspace configuration of interest. Using an original space-filling design and Gaussian process modeling, we found that aircraft delay assignments …

Extending The Latent Multinomial Model With Complex Error Processes And Dynamic Markov Bases, Simon J. Bonner, Matthew R. Schofield, Patrik Noren, Steven J. Price

Forestry and Natural Resources Faculty Publications

The latent multinomial model (LMM) of Link et al. [Biometrics 66 (2010) 178–185] provides a framework for modelling mark-recapture data with potential identification errors. Key is a Markov chain Monte Carlo (MCMC) scheme for sampling configurations of the latent counts of the true capture histories that could have generated the observed data. Assuming a linear map between the observed and latent counts, the MCMC algorithm uses vectors from a basis of the kernel to move between configurations of the latent data. Schofield and Bonner [Biometrics 71 (2015) 1070–1080] shows that this is sufficient for some models within the …

Multi-State Models With Missing Covariates, Wenjie Lou

Theses and Dissertations--Statistics

Multi-state models have been widely used to analyze longitudinal event history data obtained in medical studies. The tools and methods developed recently in this area require the complete observed datasets. While, in many applications measurements on certain components of the covariate vector are missing on some study subjects. In this dissertation, several likelihood-based methodologies were proposed to deal with datasets with different types of missing covariates efficiently when applying multi-state models.

Firstly, a maximum observed data likelihood method was proposed when the data has a univariate missing pattern and the missing covariate is a categorical variable. The construction of the …

Statistical Methods For Handling Intentional Inaccurate Responders, Kristen J. Mcquerry

Theses and Dissertations--Statistics

In self-report data, participants who provide incorrect responses are known as intentional inaccurate responders. This dissertation provides statistical analyses for address intentional inaccurate responses in the data.

Previous work with adolescent self-report, labeled survey participants who intentionally provide inaccurate answers as mischievous responders. This phenomenon also occurs in clinical research. For example, pregnant women who smoke may report that they are nonsmokers. Our advantage is that we do not solely have self-report answers and can verify responses with lab values. Currently, there is no clear method for handling these intentional inaccurate respondents when it comes to making statistical inferences.

We …

Empirical Likelihood And Differentiable Functionals, Zhiyuan Shen

Theses and Dissertations--Statistics

Empirical likelihood (EL) is a recently developed nonparametric method of statistical inference. It has been shown by Owen (1988,1990) and many others that empirical likelihood ratio (ELR) method can be used to produce nice confidence intervals or regions. Owen (1988) shows that -2logELR converges to a chi-square distribution with one degree of freedom subject to a linear statistical functional in terms of distribution functions. However, a generalization of Owen's result to the right censored data setting is difficult since no explicit maximization can be obtained under constraint in terms of distribution functions. Pan and Zhou (2002), instead, study the …

Improved Parameter Estimation Of The Log-Logistic Distribution With Applications, Joseph Reath

Dissertations, Master's Theses and Master's Reports

In this report, we work with parameter estimation of the log-logistic distribution. We first consider one of the most common methods encountered in the literature, the maximum likelihood (ML) method. However, it is widely known that the maximum likelihood estimators (MLEs) are usually biased with a finite sample size. This motivates a study of obtaining unbiased or nearly unbiased estimators for this distribution. Specifically, we consider a certain `corrective' approach and Efron's bootstrap resampling method, which both can reduce the biases of the MLEs to the second order of magnitude. As a comparison, we also consider the generalized moments (GM) …

Comparison Of Option Price From Black-Scholes Model To Actual Values, Matthew J. Krznaric

Williams Honors College, Honors Research Projects

The Black-Scholes model is a widely used method for pricing European-style options in a straightforward way, through the use of calculations and ideal market assumptions. Due to certain unrealistic ideal conditions exercised by the model, The Black-Scholes technique of pricing options may not be entirely accurate in implementation. This paper addresses these problems due to the model limitations, determining how The Black-Scholes method compares to the results when using the actual data. Using a mix of historical S&P500 data and generated normal distributions, we first calculated and graphed option prices through the Black-Scholes formulas. With the help of R, we …

Diversification And Market Neutral Portfolios In S&P500, Alan S. Agnew

Williams Honors College, Honors Research Projects

Our goal is to investigate strategies to deal with the risks associated with holding asset in the stock market. We first deal with risk of holding a specific stock, by the use of diversification. Later, we’ll attempt to deal with the market risk, which is the risk of entire market going up and down. Data used in this project comes from daily adjusted closing price of stocks listed in the S&P500 index ranging from January 3^rd, 2000 to December 31^st, 2015 and the data is processed using statistical software R.

Sections 2 through 4 of this …

Black Cloud Randomization Test, Nicholas S. Vanni

Williams Honors College, Honors Research Projects

The Black Cloud Randomization Test looks at a nontraditional question and attempts to answer the question using unique statistics. The purpose of this paper is to apply what has been learned throughout the years and apply this knowledge to a final project. Data for this project follows an emergency room’s on call schedule, as well as the number of traumas that came in during each day shift. The project builds on what has been already learned and helps to open a different way of working with statistics. The project was coded in the R software. With different restrictions, there are …

Dimension Reduction And Variable Selection, Hossein Moradi Rekabdarkolaee

Theses and Dissertations

High-dimensional data are becoming increasingly available as data collection technology advances. Over the last decade, significant developments have been taking place in high-dimensional data analysis, driven primarily by a wide range of applications in many fields such as genomics, signal processing, and environmental studies. Statistical techniques such as dimension reduction and variable selection play important roles in high dimensional data analysis. Sufficient dimension reduction provides a way to find the reduced space of the original space without a parametric model. This method has been widely applied in many scientific fields such as genetics, brain imaging analysis, econometrics, environmental sciences, etc. …

A New Right Tailed Test Of The Ratio Of Variances, Elizabeth Rochelle Lesser

UNF Graduate Theses and Dissertations

It is important to be able to compare variances efficiently and accurately regardless of the parent populations. This study proposes a new right tailed test for the ratio of two variances using the Edgeworth’s expansion. To study the Type I error rate and Power performance, simulation was performed on the new test with various combinations of symmetric and skewed distributions. It is found to have more controlled Type I error rates than the existing tests. Additionally, it also has sufficient power. Therefore, the newly derived test provides a good robust alternative to the already existing methods.

A Saddlepoint Approximation To Left-Tailed Hypothesis Tests Of Variance For Non-Normal Populations, Tyler L. Grimes

UNF Graduate Theses and Dissertations

When the variance of a single population needs to be assessed, the well-known chi-squared test of variance is often used but relies heavily on its normality assumption. For non-normal populations, few alternative tests have been developed to conduct left tailed hypothesis tests of variance. This thesis outlines a method for generating new test statistics using a saddlepoint approximation. Several novel test statistics are proposed. The type-I error rates and power of each test are evaluated using a Monte Carlo simulation study. One of the proposed test statistics, R_gamma2, controls type-I error rates better than existing tests, while having comparable power. …