Statistics and Probability Commons^™

Estimating Effects On Rare Outcomes: Knowledge Is Power, Laura B. Balzer, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Many of the secondary outcomes in observational studies and randomized trials are rare. Methods for estimating causal effects and associations with rare outcomes, however, are limited, and this represents a missed opportunity for investigation. In this article, we construct a new targeted minimum loss-based estimator (TMLE) for the effect of an exposure or treatment on a rare outcome. We focus on the causal risk difference and statistical models incorporating bounds on the conditional risk of the outcome, given the exposure and covariates. By construction, the proposed estimator constrains the predicted outcomes to respect this model knowledge. Theoretically, this bounding provides …

Time Scales Integral Inequalities For Superquadratic Functions, Josipa Barić, Rabia Bibi, Martin Bohner, Josip Pečarić

Mathematics and Statistics Faculty Research & Creative Works

In this paper, two different methods of proving Jensen's inequality on time scales for superquadratic functions are demonstrated. Some refinements of classical inequalities on time scales are obtained using properties of superquadratic functions and some known results for isotonic linear functionals. © 2013 The Korean Mathematical Society.

Linking And Retaining Hiv Patients In Care: The Importance Of Provider Attitudes And Behaviors, Manya Magnus, Jane Herwehe, Michelli Murtaza-Rossini, Petera Reine, Damien Cuffie, Deann Gruber, Michael Kaiser

Epidemiology Faculty Publications

Retention in HIV treatment may reduce morbidity and mortality, as well as slow the epidemic. Myriad barriers to retention include stigma, homophobia, structural barriers, transportation, and insurance. The purpose of this study was to evaluate patient perceptions of provider attitudes among HIV-infected persons within a state-wide public hospital system in Louisiana. A convenience sample of patients attending HIV clinics throughout the state participated in an anonymous interview. Factors associated with negative perceptions of care were evaluated in conjunction with a validated stigma measure. Factors associated with having a delayed entry into or break in care were evaluated in conjunction with …

Más-O-Menos: A Simple Sign Averaging Method For Discrimination In Genomic Data Analysis, Sihai Dave Zhao, Giovanni Parmigiani, Curtis Huttenhower, Levi Waldron

Harvard University Biostatistics Working Paper Series

No abstract provided.

An Alternative Approach To Reduce Dimensionality In Data Envelopment Analysis, Grace Lee Ching Yap, Wan Rosmanira Ismail, Zaidi Isa

Journal of Modern Applied Statistical Methods

Principal component analysis reduces dimensionality; however, uncorrelated components imply the existence of variables with weights of opposite signs. This complicates the application in data envelopment analysis. To overcome problems due to signs, a modification to the component axes is proposed and was verified using Monte Carlo simulations.

Robustness Of Dewma Versus Ewma Control Charts To Non-Normal Processes, Saad Saeed Alkahtani

Journal of Modern Applied Statistical Methods

Exponentially weighted moving average (EWMA) and double EWMA (DEWMA) control charts were designed under the normality assumption. This study considers various skewed (Gamma) and symmetric non-normal (t) distributions to examine the effect of non-normality on the average run length (ARL) performance of EWMA and DEWMA. ARL performances were investigated and compared using Monte Carlo simulations. Results show that DEWMA charts can be designed to be robust to non-normality, that the ARL performances of EWMA and DEWMA charts were more robust to t distributions and DEWMA was more robust to non-normality for larger values of the smoothing parameter.

An Approximate Approach To The Economic Design Of X̅ Charts By Considering The Cost Of Quality, M. A. A. Cox

Journal of Modern Applied Statistical Methods

The selection of three parameters {h,k,n} is necessary to design a x̅ control chart. A cost model employing a Burr distribution is examined. Previously employed methods are refined and extended. A series of approximations are proposed that enable a rapid parameter selection. It is hoped that reducing the computational complexity of previous approaches will lead to wider utilization of x̅ control charts.

Modeling And Handling Overdispersion Health Science Data With Zero-Inflated Poisson Model, Nur Syabiha Binti Zafakali, Wan Muhamad Amir Bin W Ahmad

Journal of Modern Applied Statistical Methods

Health sciences research often involves analyses of repeated measurement or longitudinal count data analyses that exhibit excess zeros. Overdispersion occurs when count data measurements have greater variability than allowed. This phenomenon can be carried over to zero-inflated count data modeling. Referred to as zero-inflation, the Zero-Inflated Poisson (ZIP) model can be used to model such data. The Zero-Inflated Negative Binomial (ZINB) model is used to account for overdispersion detected in count data. The ZINB model is considered as an alternative for the Zero-Inflated Generalized Poisson (ZIGP) model for zero-inflated overdispersed count data. Consequently, zero-inflated models have been proposed for the …

A Note On Α-Curvature Of The Manifolds Of The Length-Biased Lognormal And Gamma Distributions In View Of Related Applications In Data Analysis, Makarand V. Ratnaparkhi, Uttara V. Naik-Nimbalkar

Journal of Modern Applied Statistical Methods

The α-curvature tensors of the statistical manifolds of the length-biased versions of the log-normal and gamma distributions are derived and discussed. This study was designed to investigate observations related to the parameter estimation for the length-biased lognormal distribution as a model for the lengthbiased data from oil field exploration.

The Probit Link Function In Generalized Linear Models For Data Mining Applications, Mehdi Razzaghi

Journal of Modern Applied Statistical Methods

The use of logistic regression for outcome classification of dichotomous variables is well known in data mining applications. The estimated probability of the logit transformation belongs to the class of canonical link functions that follow from particular probability distribution functions. A closely related model is the probit link which can be used for binary responses. Although the probit link is not canonical, in some cases the overall fit of the model can be improved by using non-canonical link functions. This article reviews the properties of the probit link function and discusses its applications in data mining problems. Contrasts and comparisons …

Parameter Estimation Of A Class Of Hidden Markov Model With Diagnostics, E. B. Nkemnole, O. Abass, R. A. Kasumu

Journal of Modern Applied Statistical Methods

A stochastic volatility (SV) problem is formulated as a state space form of a Hidden Markov model (HMM). The SV model assumes that the distribution of asset returns conditional on the latent volatility is normal. This article analyzes the SV model with the student-t distribution and the generalized error distribution (GED) and compares these distributions with a mixture of normal distributions from Kim and Stoffer (2008). A Sequential Monte Carlo with Expectation Maximization (SMCEM) algorithm technique was used to estimate parameters for the extended volatility model; the Akaike Information Criteria (AIC) and forecast statistics were calculated to compare distribution fit. …

Estimation And Testing In Type I Generalized Half Logistic Distribution, R. R. L. Kantam, V. Ramakrishna, M. S. Ravikumar

Journal of Modern Applied Statistical Methods

A generalization of the half logistic distribution is developed through exponentiation of its cumulative distribution function and termed the Type I Generalized Half Logistic Distribution (GHLD). GHLD’s distributional characteristics and parameter estimation using maximum likelihood and modified maximum likelihood methods are presented with comparisons. Comparison of Type I GHLD and the exponential distribution is conducted via likelihood ratio criterion.

P-Values Versus Significance Levels, Phillip I. Good

Journal of Modern Applied Statistical Methods

In this article Phillip Good responds to Richard Anderson's article Conceptual Distinction between the Critical p Value and the Type I Error Rate in Permutation Testing.

Randomization Test P-Values Versus Significance Levels, Bryan Manly

Journal of Modern Applied Statistical Methods

Bryan Manly responds to Richard Anderson's article Conceptual Distinction between the Critical p Value and the Type I Error Rate in Permutation Testing.

Conceptual Distinction Between The Critical P Value And The Type I Error Rate In Permutation Testing: Author Response To Peer Comments, Richard B. Anderson

Journal of Modern Applied Statistical Methods

Richard Anderson responds to comments regarding his target article Conceptual Distinction between the Critical p Value and the Type I Error Rate in Permutation Testing.

Estimation Of Variance Using Known Coefficient Of Variation And Median Of An Auxiliary Variable, J. Subramani, G. Kumarapandiyan

Journal of Modern Applied Statistical Methods

A modified ratio type variance estimator for estimating population variance of a study variable when the population median and coefficient of variation of an auxiliary variable are known is proposed. The bias and mean squared error of the proposed estimator are derived and conditions under which the proposed estimator performs better than the traditional ratio type variance estimators and modified ratio type variance estimators are obtained. Using a numerical study results show that the proposed estimator performs better than the traditional ratio type variance estimator and existing modified ratio type variance estimators.

Priorities In Thurstone Scaling And Steady-State Probabilities In Markov Stochastic Modeling, Stan Lipovetsky

Journal of Modern Applied Statistical Methods

Thurstone scaling is widely used in marketing and advertising research where various methods of applied psychology are utilized. This article considers several analytical tools useful for positioning a set of items on a Thurstone scale via regression modeling and Markov stochastic processing in the form of Chapman-Kolmogorov equations. These approaches produce interval and ratio scales of preferences and enrich the possibilities of paired comparison estimation applied for solving practical problems of prioritization and probability of choice modeling.

On The Gamma-Half Normal Distribution And Its Applications, Ayman Alzaatreh, Kristen Knight

Journal of Modern Applied Statistical Methods

A new distribution, the gamma-half normal distribution, is proposed and studied. Various structural properties of the gamma-half normal distribution are derived. The shape of the distribution may be unimodal or bimodal. Results for moments, limit behavior, mean deviations and Shannon entropy are provided. To estimate the model parameters, the method of maximum likelihood estimation is proposed. Three real-life data sets are used to illustrate the applicability of the gamma-half normal distribution.

The Length-Biased Versus Random Sampling For The Binomial And Poisson Events, Makarand V. Ratnaparkhi, Uttara V. Naik-Nimbalkar

Journal of Modern Applied Statistical Methods

The equivalence between the length-biased and the random sampling on a non-negative, discrete random variable is established. The length-biased versions of the binomial and Poisson distributions are discussed.

Improved Estimators In Finite Population Surveys: Theory And Applications, Sunil Kumar

Journal of Modern Applied Statistical Methods

Improved estimators are proposed for estimating the population mean Y̅ of the study variable y using auxiliary variable x in simple random sampling. Explicit expression for the bias and MSE of the proposed family are derived to the first order of approximation. The proposed estimators are compared with other estimators and theoretical findings are illustrated by two numerical examples.