Statistical Theory Commons^™

On Two-Stage Hypothesis Testing Procedures Via Asymptotically Independent Statistics, James Dai, Charles Kooperberg, Michael L. Leblanc, Ross Prentice

UW Biostatistics Working Paper Series

Kooperberg and LeBlanc (2008) proposed a two-stage testing procedure to screen for significant interactions in genome-wide association (GWA) studies by a soft threshold on marginal associations (MA), though its theoretical properties and generalization have not been elaborated. In this article, we discuss conditions that are required to achieve strong control of the Family-Wise Error Rate (FWER) by such procedures for low or high-dimensional hypothesis testing. We provide proof of asymptotic independence of marginal association statistics and interaction statistics in linear regression, logistic regression, and Cox proportional hazard models in a randomized clinical trial (RCT) with a rare event. In case-control …

Stratifying Subjects For Treatment Selection With Censored Event Time Data From A Comparative Study, Lihui Zhao, Tianxi Cai, Lu Tian, Hajime Uno, Scott D. Solomon, L. J. Wei

Harvard University Biostatistics Working Paper Series

No abstract provided.

On Two-Stage Hypothesis Testing Procedures Via Asymptotically Independent Statistics, James Y. Dai, Charles Kooperberg, Michael Leblanc, Ross L. Prentice

UW Biostatistics Working Paper Series

Kooperberg08 proposed a two-stage testing procedure to screen for significant interactions in genome-wide association (GWA) studies by a soft threshold on marginal associations (MA), though its theoretical properties and generalization have not been elaborated. In this article, we discuss conditions that are required to achieve strong control of the Family-Wise Error Rate (FWER) by such procedures for low or high-dimensional hypothesis testing. We provide proof of asymptotic independence of marginal association statistics and interaction statistics in linear regression, logistic regression, and Cox proportional hazard models in a randomized clinical trial (RCT) with a rare event. In case-control studies nested within …

A Perturbation Method For Inference On Regularized Regression Estimates, Jessica Minnier, Lu Tian, Tianxi Cai

Harvard University Biostatistics Working Paper Series

No abstract provided.

Principled Sure Independence Screening For Cox Models With Ultra-High-Dimensional Covariates, Sihai Dave Zhao, Yi Li

Harvard University Biostatistics Working Paper Series

No abstract provided.

Optimizing Randomized Trial Designs To Distinguish Which Subpopulations Benefit From Treatment, Michael Rosenblum, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

It is a challenge to evaluate experimental treatments where it is suspected that the treatment effect may only be strong for certain subpopulations, such as those having a high initial severity of disease, or those having a particular gene variant. Standard randomized controlled trials can have low power in such situations. They also are not optimized to distinguish which subpopulations benefit from a treatment. With the goal of overcoming these limitations, we consider randomized trial designs in which the criteria for patient enrollment may be changed, in a preplanned manner, based on interim analyses. Since such designs allow data-dependent changes …

The Strength Of Statistical Evidence For Composite Hypotheses: Inference To The Best Explanation, David R. Bickel

COBRA Preprint Series

A general function to quantify the weight of evidence in a sample of data for one hypothesis over another is derived from the law of likelihood and from a statistical formalization of inference to the best explanation. For a fixed parameter of interest, the resulting weight of evidence that favors one composite hypothesis over another is the likelihood ratio using the parameter value consistent with each hypothesis that maximizes the likelihood function over the parameter of interest. Since the weight of evidence is generally only known up to a nuisance parameter, it is approximated by replacing the likelihood function with …

Model-Robust Regression And A Bayesian `Sandwich' Estimator, Adam A. Szpiro, Kenneth M. Rice, Thomas Lumley

UW Biostatistics Working Paper Series

The published version of this paper in Annals of Applied Statistics (Vol. 4, No. 4 (2010), 2099–2113) is available from the journal web site at http://dx.doi.org/10.1214/10-AOAS362.

We present a new Bayesian approach to model-robust linear regression that leads to uncertainty estimates with the same robustness properties as the Huber-White sandwich estimator. The sandwich estimator is known to provide asymptotically correct frequentist inference, even when standard modeling assumptions such as linearity and homoscedasticity in the data-generating mechanism are violated. Our derivation provides a compelling Bayesian justification for using this simple and popular tool, and it also clarifies what is being estimated …

Asymptotic Properties Of The Sequential Empirical Roc And Ppv Curves, Joseph S. Koopmeiners, Ziding Feng

UW Biostatistics Working Paper Series

The receiver operating characteristic (ROC) curve, the positive predictive value (PPV) curve and the negative predictive value (NPV) curve are three common measures of performance for a diagnostic biomarker. The independent increments covariance structure assumption is common in the group sequential study design literature. Showing that summary measures of the ROC, PPV and NPV curves have an independent increments covariance structure will provide the theoretical foundation for designing group sequential diagnostic biomarker studies. The ROC, PPV and NPV curves are often estimated empirically to avoid assumptions about the distributional form of the biomarkers. In this paper we derive asymptotic theory …

Estimating Causal Effects In Trials Involving Multi-Treatment Arms Subject To Non-Compliance: A Bayesian Frame-Work, Qi Long, Roderick J. Little, Xihong Lin

Harvard University Biostatistics Working Paper Series

No abstract provided.

Super Learner In Prediction, Eric C. Polley, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Super learning is a general loss based learning method that has been proposed and analyzed theoretically in van der Laan et al. (2007). In this article we consider super learning for prediction. The super learner is a prediction method designed to find the optimal combination of a collection of prediction algorithms. The super learner algorithm finds the combination of algorithms minimizing the cross-validated risk. The super learner framework is built on the theory of cross-validation and allows for a general class of prediction algorithms to be considered for the ensemble. Due to the previously established oracle results for the cross-validation …

Assessing Noninferiority In A Three-Arm Trial Using The Bayesian Approach, Pulak Ghosh, Farouk S. Nathoo, Mithat Gonen, Ram C. Tiwari

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

Non-inferiority trials, which aim to demonstrate that a test product is not worse than a competitor by more than a pre-specified small amount, are of great importance to the pharmaceutical community. As a result, methodology for designing and analyzing such trials is required, and developing new methods for such analysis is an important area of statistical research. The three-arm clinical trial is usually recommended for non-inferiority trials by the Food and Drug Administration (FDA). The three-arm trial consists of a placebo, a reference, and an experimental treatment, and simultaneously tests the superiority of the reference over the placebo along with …

Derivation Of Mass Independent Quantum Treatment Of Phenomenon, David Parker

Journal of Modern Applied Statistical Methods

The derivation and applications is presented of a spatial variable or spatial radius which is related to the inertia or mass-energy of any quantum body by a Lorentz invariant relation. Mass independent DeBroglie and Schroedinger equations are derived and applied to the resolution of the linguistic incompatibility between quantum theory and the geometrical weak equivalence principle. The equivalence principle is restated in terms of the spatial radius. The gravitational attraction between bodies and the relativistic energy are both presented in terms of the spatial radius follows. The ratio of the gravitational force to the Coulomb force at the Planck scale …

Ranked Set Sampling Using Auxiliary Variables Of A Randomized Response Procedure For Estimating The Mean Of A Sensitive Quantitative Character, Carlos N. Bouza

Journal of Modern Applied Statistical Methods

The analysis of the behavior of estimators of the mean of a sensitive variable is considered when a randomized response procedure is used. The results deal with the inference based on simple random sampling with replacement study design. A study of the behavior of the procedures for a ranked set sampling design is developed. A gain in accuracy is generally associated with the proposed alternative model.

An Equivalence Test Based On N And P, Markus Neuhäeuser

Journal of Modern Applied Statistical Methods

An equivalence test is proposed which is based on the P-value of a test for a difference and the sample size. This test may be especially appropriate for an exploratory re-analysis if only a non-significant test for a difference was reported. Thus, neither a confidence interval is available, nor is there access to the raw data. The test is illustrated using two examples; for both applications the smallest equivalence range for which equivalence could be demonstrated is calculated.

The Effectiveness Of Stepwise Discriminant Analysis As A Post Hoc Procedure To A Significant Manova, Erik L. Heiny, Daniel J. Mundform

Journal of Modern Applied Statistical Methods

The effectiveness of SWDA as a post hoc procedure in a two-way MANOVA was examined using various numbers of dependent variables, sample sizes, effect sizes, correlation structures, and significance levels. The procedure did not work well in general except with small numbers of variables, larger samples and low correlations between variables.

Model Based Vs. Model Independent Tests For Cross-Correlation, H.E.T. Holgersson, Peter S. Karlsson

Journal of Modern Applied Statistical Methods

This article discusses the issue of whether cross correlation should be tested by model dependent or model independent methods. Several different tests are proposed and their main properties are investigated analytically and with simulations. It is argued that model independent tests should be used in applied work.

On Exact 100(1-Α)% Confidence Interval Of Autocorrelation Coefficient In Multivariate Data When The Errors Are Autocorrelated, Madhusudan Bhandary

Journal of Modern Applied Statistical Methods

An exact 100(1−α)% confidence interval for the autocorrelation coefficient ρ is derived based on a single multinormal sample. The confidence interval is the interval between the two roots of a quadratic equation in ρ . A real life example is also presented.

The Performance Of Multiple Imputation For Likert-Type Items With Missing Data, Walter Leite, S. Natasha Beretvas

Journal of Modern Applied Statistical Methods

The performance of multiple imputation (MI) for missing data in Likert-type items assuming multivariate normality was assessed using simulation methods. MI was robust to violations of continuity and normality. With 30% of missing data, MAR conditions resulted in negatively biased correlations. With 50% missingness, all results were negatively biased.

Median-Unbiased Optimal Smoothing And Trend Extraction, Dimitrios D. Thomakos

Journal of Modern Applied Statistical Methods

The problem of smoothing a time series for extracting its low frequency characteristics, collectively called its trend, is considered. A competitive approach is proposed and compared with existing methods in choosing the optimal degree of smoothing based on the distribution of the residuals from the smooth trend.

On A Comparison Between Two Measures Of Spatial Association, Faisal G. Khamis, Abdul Aziz Jemain, Kamarulzaman Ibrahim

Journal of Modern Applied Statistical Methods

Two measures of spatial association between two variables were used by many researchers. These are the Wartenberg (1985) and Lee (2001) measures. Based on simulation for lattice data, the sensitivity of both measures was studied and compared with different choices of spatial structures, spatial weights and sample sizes using bias and mean square error. Different scenarios are used in terms of assumed numbers and sample sizes. Moran’s I is used to examine the spatial autocorrelation of such a variable with itself. Both the Wartenberg and Lee measures are found to be sensitive, however, Wartenberg’s measure is found to be somewhat …

An Evaluation Of Multiple Imputation For Meta-Analytic Structural Equation Modeling, Carolyn F. Furlow, S. Natasha Beretvas

Journal of Modern Applied Statistical Methods

A simulation study was used to evaluate multiple imputation (MI) to handle MCAR correlations in the first step of meta-analytic structural equation modeling: the synthesis of the correlation matrix and the test of homogeneity. No substantial parameter bias resulted from using MI. Although some SE bias was found for meta-analyses involving smaller numbers of studies, the homogeneity test was never rejected when using MI.

Impact Of Measurement Model Modification On Structural Parameter Integrity When Measurement Model Is Misspecified, Weihua Fan

Journal of Modern Applied Statistical Methods

In the process of model modification, parameters of residual covariances are often treated as free parameters to improve model fit. However, the effect of such measurement model modifications on the important structural parameter estimates under various measurement model misspecifications has not been systematically studied. Monte Carlo simulation was conducted to compare structural estimates before and after measurement model modifications of adding residual covariances under varying sample sizes and model misspecifications. Results showed that researchers should pay attention when such measurement model modifications are made to initially misspecified model with missing path(s).

Can Specification Searches Be Useful For Hypothesis Generation?, Samuel B. Green, Marilyn S. Thompson

Journal of Modern Applied Statistical Methods

Previous studies suggest that results from specification searches, as typically employed in structural equation modeling, should not be used to reach strong research conclusions due to their poor reliability. Analyses of computer generated data indicate that search results can be sufficiently reliable for exploratory purposes with properly designed and analyzed studies.

Measuring Openness, Gaetano Ferrieri

Journal of Modern Applied Statistical Methods

A method for measuring international openness is elaborated. This synthetic indicator measures the capacity of countries for a given phenomenon adjusted for their weight in the same phenomenon. The method implemented and applied to international trade and illustrated here as a case study in merchandise exports, has a wide range of applications in the socio-economic field.

On The Appropriate Transformation Technique And Model Selection In Forecasting Economic Time Series: An Application To Botswana Gdp Data, D. K. Shangodoyin, K. Setlhare, K. K. Moseki, K. Sediakgotla

Journal of Modern Applied Statistical Methods

Selected data transformation techniques in time series modeling are evaluated using real-life data on Botswana Gross Domestic Product (GDP). The transformation techniques considered were modified, although reasonable estimates of the original with no significant difference at α = 0.05 level were obtained: minimizing square of first difference (MFD) and minimizing square of second difference (MSD) provided the best transformation for GDP, whereas the Goldstein and Khan (GKM) method had a deficiency of losing data points. The Box-Jenkins procedure was adapted to fit suitable ARIMA (p, d, q) models to both the original and transformed series, with AIC and SIC as …

A New Biased Estimator Derived From Principal Component Regression Estimator, Set Foong Ng, Heng Chin Low, Soon Hoe Quah

Journal of Modern Applied Statistical Methods

A new biased estimator obtained by combining the Principal Component Regression Estimator and the special case of Liu-type estimator is proposed. The properties of the new estimator are derived and comparisons between the new estimator and other estimators in terms of mean squared error are presented.

Optimal Meter Placement By Reconciliation Conventional Measurements And Phasor Measurement Units (Pmus), Reza Kaihani, Ali Reza Seifi

Journal of Modern Applied Statistical Methods

The success of state estimation depends on the number, type and location of the established meters and RTUs on the system. A new method by incorporating conventional measurements and New Technology of Phasor Measurement Units (PMU) is proposed. Conventional meters (power injection and power flow measurements) are allocated in order to reduce the number of meters, RTUs, critical measurements, critical sets and leverage points, and also to improve the numerical stability of equations; a genetic algorithm is used for optimization. A second step involves adding PMUs in areas in which it is expected that the accuracy of state estimation will …

Fisher Was Right, Ronald C. Serlin

Journal of Modern Applied Statistical Methods

Invited address presented to the Educational Statistician’s Special Interest Group at the annual meeting of the American Educational Research Association, Denver, May 1, 2010.

Inferences About The Population Mean: Empirical Likelihood Versus Bootstrap-T, Rand R. Wilcox

Journal of Modern Applied Statistical Methods

The problem of making inferences about the population mean, μ, is considered. Known theoretical results suggest that a Bartlett corrected empirical likelihood method is preferable to two basic bootstrap techniques: a symmetric two-sided bootstrap-t and an equal-tailed bootstrap-t. However, simulations in this study indicate that, when the sample size is small, these two bootstrap methods are generally better in terms of Type I errors and probability coverage. As the sample size increases, situations are found where the Bartlett corrected empirical likelihood method performs better than the equal-tailed bootstrap-t, but the symmetric bootstrap-t gives the best results. None of the four …