Statistics and Probability Commons^™

Dose Expansion Cohorts In Phase I Trials, Alexia Iasonos, John O'Quigley

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

A rapidly increasing number of Phase I dose-finding studies, and in particular those based on the standard 3+3 design, frequently prolong the study and include dose expansion cohorts (DEC) with the goal to better characterize the toxicity profiles of experimental agents and to study disease specific cohorts. These trials consist of two phases: the usual dose escalation phase that aims to establish the maximum tolerated dose (MTD) and the dose expansion phase that accrues additional patients, often with different eligibility criteria, and where additional information is being collected. Current protocols typically do not specify whether the MTD will be updated …

Variable Selection For Zero-Inflated And Overdispersed Data With Application To Health Care Demand In Germany, Zhu Wang, Shuangge Ma, Ching-Yun Wang

COBRA Preprint Series

In health services and outcome research, count outcomes are frequently encountered and often have a large proportion of zeros. The zero-inflated negative binomial (ZINB) regression model has important applications for this type of data. With many possible candidate risk factors, this paper proposes new variable selection methods for the ZINB model. We consider maximum likelihood function plus a penalty including the least absolute shrinkage and selection operator (LASSO), smoothly clipped absolute deviation (SCAD) and minimax concave penalty (MCP). An EM (expectation-maximization) algorithm is proposed for estimating the model parameters and conducting variable selection simultaneously. This algorithm consists of estimating penalized …

Targeted Covariate-Adjusted Response-Adaptive Lasso-Based Randomized Controlled Trials, Antoine Chambaz, Wenjing Zheng, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

We present a new covariate-adjusted response-adaptive randomized controlled trial design and inferential procedure built on top of it. The procedure is targeted in the sense that (i) the sequence of randomization schemes is group-sequentially determined by targeting a user-specified optimal randomization design based on accruing data and, (ii) our estimator of the user-specified parameter of interest, seen as the value of a functional evaluated at the true, unknown distribution of the data, is targeted toward it by following the paradigm of targeted minimum loss estimation. We focus for clarity on the case that the parameter of interest is the marginal …

Variable-Domain Functional Regression For Modeling Icu Data, Jonathan E. Gellar, Elizabeth Colantuoni, Dale M. Needham, Ciprian M. Crainiceanu

Johns Hopkins University, Dept. of Biostatistics Working Papers

We introduce a class of scalar-on-function regression models with subject-specific functional predictor domains. The fundamental idea is to consider a bivariate functional parameter that depends both on the functional argument and on the width of the functional predictor domain. Both parametric and nonparametric models are introduced to fit the functional coefficient. The nonparametric model is theoretically and practically invariant to functional support transformation, or support registration. Methods were motivated by and applied to a study of association between daily measures of the Intensive Care Unit (ICU) Sequential Organ Failure Assessment (SOFA) score and two outcomes: in-hospital mortality, and physical impairment …

Ranking World Class Chess Players Using Only Results From Head-To-Head Games, Sterling Swygert

Senior Theses

This honors thesis explores a method of ranking the world’s top ten chess grand- masters using only the outcomes of games containing only players in that very set. This method allows for players in a single era to be quickly ranked via algorithmic and numerical means, including very specific information, from a statistical stand- point. Furthermore, unlike the rating systems that are commonly used, the Elo and the Glicko systems, this method is Classicist in its statistical approach, rather than Bayesian. Finally, this ranking method also differs from others as it limits the infor- mation to games between the individuals …

Sieve Plateau Variance Estimators: A New Approach To Confidence Interval Estimation For Dependent Data, Molly M. Davies, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Suppose we have a data set of n-observations where the extent of dependence between them is poorly understood. We assume we have an estimator that is squareroot-consistent for a particular estimand, and the dependence structure is weak enough so that the standardized estimator is asymptotically normally distributed. Our goal is to estimate the asymptotic variance of the standardized estimator so that we can construct a Wald-type confidence interval for the estimate. In this paper we present an approach that allows us to learn this asymptotic variance from a sequence of influence function based candidate variance estimators. We focus on time …

Surface Reconstruction Using Differential Invariant Signatures, Sophors Khut

Mathematics, Statistics, and Computer Science Honors Projects

This thesis addresses the problem of reassembling a broken surface. Three di- mensional curve matching is used to determine shared edges of broken pieces. In practice, these pieces may have different orientation and position in space, so edges cannot be directly compared. Instead, a differential invariant signature is used to make the comparison. A similarity score between edge signatures determines if two pieces share an edge. The Procrustes algorithm is applied to find the translations and rotations that best fit shared edges. The method is implemented in Matlab, and tested on a broken spherical surface.

Hurdle Models And Age Effects In The Major League Baseball Draft, Justin Sims

Mathematics, Statistics, and Computer Science Honors Projects

Major League Baseball (MLB) franchises expend an abundance of resources on scouting in preparation for the June Amateur Draft. In addition to the classic "tools" assessed, another factor considered is age: younger players may get selected over older players of equal ability because of anticipated development, whereas college players may get selected over high school players due to a shortened latency before reaching the majors. Additionally, Little League rules in effect until 2006 operated on an August 1-July 31 year, meaning that, in their youth, players born on August 1 were the eldest relative to their cohort. We examine the …

Parallel Design Patterns And Program Performance, Yu Zhao

Mathematics, Statistics, and Computer Science Honors Projects

With the rapid advancement of parallel and distributed computing (PDC), three types of hardware and their corresponding software (hardware-software pairs) are becoming more and more popular: Distributed Memory Systems with the Message Passing Interface (MPI) library, Shared Memory Systems with the OpenMP library and Co-processor Systems with a general purpose parallel computing library. Alongside the development of both hardware and software aspects of PDC, the process of designing parallel programs has also improved significantly over the years. A consequence of this is that researchers have been able to describe many parallel design patterns, which are recurring solutions to well-known problems …

Bias And Precision Of The Squared Canonical Correlation Coefficient Under Nonnormal Data Condition, Lesley F. Leach, Robin K. Henson

Journal of Modern Applied Statistical Methods

Monte Carlo methods were employed to investigate the effect of nonnormality on the bias associated with the squared canonical correlation coefficient (R_c²). The majority of R_c² estimates were found to be extremely biased, but the magnitude of bias was impacted little by the degree of nonnormality.

Stochastic Randomized Response Model For A Quantitative Sensitive Random Variable, Sarjinder Singh, Stephen A. Sedory

Journal of Modern Applied Statistical Methods

A new stochastic randomized response model is introduced that is useful for estimating the population mean of a sensitive quantitative variable. The proposed stochastic randomized response model is an extension of the stochastic randomized response model from a qualitative sensitive variable to a quantitative variable found in Singh (2002). The stochastic nature of a randomized response device helps increase a respondent’s cooperation while collecting information on sensitive variables in a society. The Bar-Lev, Bobovitch, and Boukai (2004) model is shown to be a special case of the proposed model.

Ridge Regression In Calibration Models With Symmetric Padding Extension-Daubechies Wavelet Transform Preprocessing, Nurwiani, S Sunaryo, Setiawan, B W. Otok

Journal of Modern Applied Statistical Methods

Wavelet transformation is commonly used in calibration models as a preprocessing step. This preprocessing does not involve all results of a spectrum discretization; consequently, a lot of information can be missing. To avoid missing information, a symmetric padding extension (SPE) can be used to place all data points into dyadic scales, however, high dimensional discretization points need to be reduced. Dimension reduction can be performed with Daubechies wavelet transformation (DWT). Scale function and Daubechies wavelet are continuous functions, thus they perform a faster approximation. SPE-DWT preprocessing combines SPE and DWT. Multicollinearity often occurs in calibration models; the ridge regression (RR) …

Statistical Power Of Alternative Structural Models For Comparative Effectiveness Research: Advantages Of Modeling Unreliability, Emil N. Coman, Eugen Iordache, Lisa Dierker, Judith Fifield, Jean J. Schensul, Suzanne Suggs, Russell Barbour

Journal of Modern Applied Statistical Methods

The advantages of modeling the unreliability of outcomes when evaluating the comparative effectiveness of health interventions is illustrated. Adding an action-research intervention component to a regular summer job program for youth was expected to help in preventing risk behaviors. A series of simple two-group alternative structural equation models are compared to test the effect of the intervention on one key attitudinal outcome in terms of model fit and statistical power with Monte Carlo simulations. Some models presuming parameters equal across the intervention and comparison groups were under- powered to detect the intervention effect, yet modeling the unreliability of the outcome …

A Flexible Method For Conducting Power Analysis For Two- And Three-Level Hierarchical Linear Models In R, Yi Pan, Matthew T. Mcbee

Journal of Modern Applied Statistical Methods

A general approach for conducting power analysis in two- and three-level hierarchical linear models (HLMs) is described. The method can be used to perform power analysis to detect fixed effects at any level of a HLM with dichotomous or continuous covariates. It can easily be extended to perform power analysis for functions of parameters. Important steps in the derivation of this approach are illustrated and numerical examples are provided. Sample code implementing this approach is provided using the free program R.

Estimation Of Reliability In Multicomponent Stress-Strength Based On Generalized Rayleigh Distribution, Gadde Srinivasa Rao

Journal of Modern Applied Statistical Methods

A multicomponent system of k components having strengths following k- independently and identically distributed random variables x₁, x₂, ..., x_k and each component experiencing a random stress Y is considered. The system is regarded as alive only if at least s out of k (s < k) strengths exceed the stress. The reliability of such a system is obtained when strength and stress variates are given by a generalized Rayleigh distribution with different shape parameters. Reliability is estimated using the maximum likelihood (ML) method of estimation in samples drawn from strength and stress …

Specifying Asymmetric Star Models With Linear And Nonlinear Garch Innovations: Monte Carlo Approach, Olaoluwa S. Yaya, Olanrewaju I. Shittu

Journal of Modern Applied Statistical Methods

Economic and finance time series are typically asymmetric and are expected to be modeled using asymmetrical nonlinear time series models. Smooth Transition Autoregressive (STAR) models: Logistic (LSTAR) and Exponential (ESTAR) are known to be asymmetric and symmetric respectively. Under non-normal and heteroscedastic innovations, the residuals of these models are estimated using Generalized Autoregressive Conditionally Heteroscedastic (GARCH) models with variants which include linear and nonlinear forms. The small sample properties of STAR-GARCH variants are yet to be established but these properties are investigated using Monte Carlo (MC) simulation. An MC investigation was conducted to investigate the performance of selections of STAR-GARCH …

Robustness Of Several Estimators Of The Acf Of Ar(1) Process With Non-Gaussian Errors, A A. Smadi, J J. Jaber, A G. Al-Zu'bi

Journal of Modern Applied Statistical Methods

The autocorrelation function (ACF) plays an important role in the context of ARMA modeling, especially for their identification and estimation. This study considers the robust estimation of the ACF of the AR(1) model if the white noise (WN) process is non- Gaussian. Three estimators including the ordinary moment estimator and two other (robust) estimators are considered. The impacts of the deviation from normality of the WN process on those estimators in terms of bias, MSE and distribution via Monte-Carlo simulation are examined. The empirical distribution of those estimators when the errors are normal, t, Cauchy and exponential are studied. …

Two Parameter Modified Ratio Estimators With Two Auxiliary Variables For Estimation Of Finite Population Mean With Known Skewness, Kurtosis And Correlation Coefficient, Jambulingam Subramani, G Prabavathy

Journal of Modern Applied Statistical Methods

Consider the two parameter modified ratio estimators for the estimation of finite population mean using the skewness, kurtosis and correlation coefficient of two auxiliary variables. The efficiencies of the proposed modified ratio estimators are assessed with that of the simple random sampling without replacement (SRSWOR) sample mean and some of the existing ratio estimators in terms of mean squared errors. The entire above is explained with the help of certain natural populations available in the literature.

Change Point Estimation For Pareto Type-Ii Model, Gyan Prakash

Journal of Modern Applied Statistical Methods

Some Bayes estimators of the change point for the Pareto Type-II model under right item failure-censoring scheme are proposed. The Bayes estimators are obtained here in two cases, the first is when one parameter is known and second when both parameters are considered as the random variable. The performances of the procedures are illustrated by simulation technique.

Comparison Of Three Calculation Methods For A Bayesian Inference Of Two Poisson Parameters, Yohei Kawasaki, Etsuo Miyaoka

Journal of Modern Applied Statistical Methods

The statistical inference drawn from the difference between two independent Poisson parameters is often discussed in medical literature. Kawasaki and Miyaoka (2012) proposed an index θ = P(λ_1,post < λ_2,post), where λ_1,post and λ_2,post denote Poisson parameters following posterior density. A new calculation method is proposed using MCMC and an approximate expression and exact expression for θ are compared.