Statistics and Probability Commons^™

Functional Car Models For Spatially Correlated Functional Datasets, Lin Zhang, Veerabhadran Baladandayuthapani, Hongxiao Zhu, Keith A. Baggerly, Tadeusz Majewski, Bogdan Czerniak, Jeffrey S. Morris

Jeffrey S. Morris

We develop a functional conditional autoregressive (CAR) model for spatially correlated data for which functions are collected on areal units of a lattice. Our model performs functional response regression while accounting for spatial correlations with potentially nonseparable and nonstationary covariance structure, in both the space and functional domains. We show theoretically that our construction leads to a CAR model at each functional location, with spatial covariance parameters varying and borrowing strength across the functional domain. Using basis transformation strategies, the nonseparable spatial-functional model is computationally scalable to enormous functional datasets, generalizable to different basis functions, and can be used on …

Hypothesis Testing For Functional Linear Models, Y-R Su, Cz Di, L Hsu

Chongzhi Di

Functional data arise frequently in many biomedical studies, where it is often of interest to investigate the dynamic association between functional predictors and a scalar response variable. While functional linear models (FLM) are widely used to address these questions, hypothesis testing for the functional association in the FLM framework remains challenging. A popular approach to testing the functional effects is through dimension reduction by functional principal component (PC) analysis. However, its power performance depends on the choice of the number of PCs, and is not systematically studied. In this paper, we first investigate the power performance of the Wald-type test …

An Efficient Basket Trial Design, Kristen Cunanan, Alexia Iasonos, Ronglai Shen, Colin B. Begg, Mithat Gonen

Memorial Sloan-Kettering Cancer Center, Dept. of Epidemiology & Biostatistics Working Paper Series

The landscape for early phase cancer clinical trials is changing dramatically due to the advent of targeted therapy. Increasingly, new drugs are designed to work against a target such as the presence of a specific tumor mutation. Since typically only a small proportion of cancer patients will possess the mutational target, but the mutation is present in many different cancers, a new class of basket trials is emerging, whereby the drug is tested simultaneously in different baskets, i.e., sub-groups of different tumor types. Investigators not only desire to test whether the drug works, but also to determine which types of …

Variable Selection For Case-Cohort Studies With Failure Time Outcome, Andy Ni, Jianwen Cai, Donglin Zeng

Memorial Sloan-Kettering Cancer Center, Dept. of Epidemiology & Biostatistics Working Paper Series

Case-cohort designs are widely used in large cohort studies to reduce the cost associated with covariate measurement. In many such studies the number of covariates is very large, so an efficient variable selection method is necessary. In this paper, we study the properties of variable selection using the smoothly clipped absolute deviation penalty in a case-cohort design with a diverging number of parameters. We establish the consistency and asymptotic normality of the maximum penalized pseudo-partial likelihood estimator, and show that the proposed variable selection procedure is consistent and has an asymptotic oracle property. Simulation studies compare the finite sample performance …

Leveraging Contact Network Structure In The Design Of Cluster Randomized Trials, Guy Harling, Rui Wang, Jukka-Pekka Onnela, Victor Degruttola

Harvard University Biostatistics Working Paper Series

Background: In settings like the Ebola epidemic, where proof-of-principle trials have succeeded but questions remain about the effectiveness of different possible modes of implementation, it may be useful to develop trials that not only generate information about intervention effects but also themselves provide public health benefit. Cluster randomized trials are of particular value for infectious disease prevention research by virtue of their ability to capture both direct and indirect effects of intervention; the latter of which depends heavily on the nature of contact networks within and across clusters. By leveraging information about these networks – in particular the degree …

Using Validation Data To Adjust The Inverse Probability Weighting Estimator For Misclassified Treatment, Danielle Braun, Corwin Zigler, Francesca Dominici, Malka Gorfine

Harvard University Biostatistics Working Paper Series

The inverse probability weighting (IPW) estimator is widely used to estimate the treatment effect in observational studies in which patient characteristics might not be balanced by treatment group. The estimator assumes that treatment assignment, is error-free, but in reality treatment assignment can be measured with error. This arises in the context of comparative effectiveness research, using administrative data sources in which accurate procedural or billing codes are not always available. We show the bias introduced to the estimator when using error-prone treatment assignment, and propose an adjusted estimator using a validation study to eliminate this bias. In simulations, we explore …

Estimation And Inference For The Mediation Proportion, Daniel Nevo, Xiaomei Liao, Donna Spiegelman

Harvard University Biostatistics Working Paper Series

In epidemiology, public health and social science, mediation analysis is often undertaken to investigate the extent to which the effect of a risk factor on an outcome of interest is mediated by other covariates. A pivotal quantity of interest in such an analysis is the mediation proportion. A common method for estimating it, termed the "difference method'', compares estimates from models with and without the hypothesized mediator. However, rigorous methodology for estimation and statistical inference for this quantity has not previously been available. We formulated the problem for the Cox model and generalized linear models, and utilize a data duplication …

A Cautionary Note On The Effect Of Treatment Misclassification On The Average Treatment Effect, Danielle Braun, Corwin Zigler, Malka Gorfine, Francesca Dominici

Harvard University Biostatistics Working Paper Series

Comparative effectiveness research often relies on large administrative data, such as claims data. Methods to estimate treatment effects assume that treatment assignment is error-free, but in reality the inaccuracy of procedural or billing codes frequently misclassifies patients into treatment groups. Propensity score methods are widely used to analyze observational studies in which patient characteristics might not be balanced by treatment group. We evaluate the impact of treatment misclassification on 1) propensity score estimation; 2) treatment effect estimation conditional on propensity score estimation and implementation. We focus on three common propensity score implementations: subclassification, matching, and inverse probability of treatment weighting …

The Myth Of Making Inferences For An Overall Treatment Efficacy With Data From Multiple Comparative Studies Via Meta-Analysis, Takahiro Hasegawa, Brian Claggett, Lu Tian, Scott D. Solomon, Marc A. Pfeffer, Lee-Jen Wei

Harvard University Biostatistics Working Paper Series

Meta analysis techniques, if applied appropriately, can provide a summary of the totality of evidence regarding an overall difference between a new treatment and a control group using data from multiple comparative clinical studies. The standard meta analysis procedures, however, may not give a meaningful between-group difference summary measure or identify a meaningful patient population of interest, especially when the fixed effect model assumption is not met. Moreover, a single between-group comparison measure without a reference value obtained from patients in the control arm would likely not be informative enough for clinical decision making. In this paper, we propose a …

Moving Beyond The Conventional Stratified Analysis To Estimate An Overall Treatment Efficacy With The Data From A Comparative Randomized Clinical Study, Lu Tian, Fei Jiang, Takahiro Hasegawa, Hajime Uno, Marc Alan Pfeffer, L.J. Wei

Harvard University Biostatistics Working Paper Series

No abstract provided.

Certain Characterizations Of Recently Introduced Distributions, Gholamhossein G. Hamedani, Seyed Morteza Najibi

Mathematics, Statistics and Computer Science Faculty Research and Publications

Various characterizations of twenty two recently introduced distributions are presented. These characterizations are based on: (I) ration of two truncated moments; (ii) the hazard function and (iii) conditional expectations.

A Hybrid Segmentation And D-Bar Method For Electrical Impedance Tomography, Sarah J. Hamilton, J. M. Reyes, Samuli Siltanen, X. Zhang

Mathematics, Statistics and Computer Science Faculty Research and Publications

The regularized D-bar method for electrical impedance tomography (EIT) provides a rigorous mathematical approach for solving the full nonlinear inverse problem directly, i.e., without iterations. It is based on a low-pass filtering in the (nonlinear) frequency domain. However, the resulting D-bar reconstructions are inherently smoothed, leading to a loss of edge distinction. In this paper, a novel method that combines a D-bar approach with the edge-preserving nature of total variation (TV) regularization is presented. The method also includes a data-driven contrast adjustment technique guided by the key functions (CGO solutions) of the D-bar method. The new TV-enhanced D-bar …

An Ensemble Model Of Qsar Tools For Regulatory Risk Assessment, Prachi Pradeep, Richard J. Povinelli, Shannon White, Stephen Merrill

Mathematics, Statistics and Computer Science Faculty Research and Publications

Quantitative structure activity relationships (QSARs) are theoretical models that relate a quantitative measure of chemical structure to a physical property or a biological effect. QSAR predictions can be used for chemical risk assessment for protection of human and environmental health, which makes them interesting to regulators, especially in the absence of experimental data. For compatibility with regulatory use, QSAR models should be transparent, reproducible and optimized to minimize the number of false negatives. In silico QSAR tools are gaining wide acceptance as a faster alternative to otherwise time-consuming clinical and animal testing methods. However, different QSAR tools often make conflicting …

A Generalization Of The Difference Of Slopes Test To Poisson Regression With Three-Way Interaction, Melinda Bierhals

Theses, Dissertations and Capstones

Linear regression models involving interaction can use the difference of slopes test to compare slopes for various situations. We will be generalizing this process to develop a procedure to compare rates in a Poisson regression model, allowing us to consider unbounded count data as opposed to continuous data. We will apply this process to an educational data set from a sample of students located in two different Los Angeles high schools. Our model will include a three-way interaction and address the following questions:

• Does language ability impact the relationship between math ability and attendance in the same way for …

Existence Of Periodic Solutions For A Quantum Volterra Equation, Muhammad Islam, Jeffrey T. Neugebauer

Mathematics Faculty Publications

The objective of this paper is to study the periodicity properties of functions that arise in quantum calculus, which has been emerging as an important branch of mathematics due to its various applications in physics and other related fields. The paper has two components. First, a relation between two existing periodicity notions is established. Second, the existence of periodic solutions of a q-Volterra integral equation, which is a general integral form of a first order q-difference equation, is obtained. At the end, some examples are provided. These examples show the effectiveness of the relation between the two periodicity notions that …

Stochastic Models Of Evidence Accumulation In Changing Environments, Alan Veliz-Cuba, Zachary P. Kilpatrick, Krešimir Josić

Mathematics Faculty Publications

Organisms and ecological groups accumulate evidence to make decisions. Classic experiments and theoretical studies have explored this process when the correct choice is fixed during each trial. However, we live in a constantly changing world. What effect does such impermanence have on classical results about decision making? To address this question we use sequential analysis to derive a tractable model of evidence accumulation when the correct option changes in time. Our analysis shows that ideal observers discount prior evidence at a rate determined by the volatility of the environment, and the dynamics of evidence accumulation is governed by the information …

Almost Automorphic Solutions Of Delayed Neutral Dynamic Systems On Hybrid Domains, Murat Adıvar, Halis Can Koyuncuoğlu, Youssef Raffoul

Mathematics Faculty Publications

We study the existence of almost automorphic solutions of the delayed neutral dynamic system on hybrid domains that are additively periodic. We use exponential dichotomy and prove uniqueness of projector of exponential dichotomy to obtain some limit results leading to sufficient conditions for existence of almost automorphic solutions to neutral system. Unlike the existing literature we prove our existence results without assuming boundedness of the coefficient matrices in the system. Hence, we significantly improve the results in the existing literature. Finally, we also provide an existence result for an almost periodic solutions of the system.

Positive Solutions For A Singular Fourth Order Nonlocal Boundary Value Problem, John M. Davis, Paul W. Eloe, John R. Graef, Johnny Henderson

Mathematics Faculty Publications

Positive solutions are obtained for the fourth order nonlocal boundary value problem, u⁽⁴⁾=f(x,u), 0 < x < 1, u(0) = u''(0) = u'(1) = u''(1) - u''(2/3)=0, where f(x,u) is singular at x = 0, x=1, y=0, and may be singular at y=∞. The solutions are shown to exist at fixed points for an operator that is decreasing with respect to a cone.

Salvage Brachytherapy For Biochemically Recurrent Prostate Cancer Following Primary Brachytherapy, John M. Lacy, William A. Wilson, Raevti Bole, Li Chen, Ali S. Meigooni, Randall G. Rowland, William H. St. Clair

Urology Faculty Publications

Purpose. In this study, we evaluated our experience with salvage brachytherapy after discovery of biochemical recurrence after a prior brachytherapy procedure. Methods and Materials. From 2001 through 2012 twenty-one patients treated by brachytherapy within University of Kentucky or from outside centers developed biochemical failure and had no evidence of metastases. Computed tomography (CT) scans were evaluated; patients who had an underseeded portion of their prostate were considered for reimplantation. Results. The majority of the patients in this study (61.9%) were low risk and median presalvage PSA was 3.49 (range 17.41–1.68). Mean follow-up was 61 months. At last follow-up after reseeding, …

Male Pattern Baldness In Relation To Prostate Cancer–Specific Mortality: A Prospective Analysis In The Nhanes I Epidemiologic Follow-Up Study, Cindy Ke Zhou, Paul H Levine, Sean D. Cleary, Heather J. Hoffman, Barry I Graubard, Michael B. Cook

Epidemiology Faculty Publications

We used male pattern baldness as a proxy for long-term androgen exposure and investigated the association of dermatologist-assessed hair loss with prostate cancer–specific mortality in the first National Health and Nutrition Examination Survey Epidemiologic Follow-up Study. From the baseline survey (1971–1974), we included 4,316 men who were 25–74 years of age and had no prior cancer diagnosis. We estimated hazard ratios and used Cox proportional hazards regressions with age as the time metric and baseline hazard stratified by baseline age. A hybrid framework was used to account for stratification and clustering of the sample design, with adjustment for the variables …