Statistical Methodology Commons^™

Semiparametric Theory And Empirical Processes In Causal Inference, Edward Kennedy

Edward H. Kennedy

In this paper we review important aspects of semiparametric theory and empirical processes that arise in causal inference problems. We begin with a brief introduction to the general problem of causal inference, and go on to discuss estimation and inference for causal effects under semiparametric models, which allow parts of the data-generating process to be unrestricted if they are not of particular interest (i.e., nuisance functions). These models are very useful in causal problems because the outcome process is often complex and difficult to model, and there may only be information available about the treatment process (at best). Semiparametric theory …

A Review Of Frequentist Tests For The 2x2 Binomial Trial, Chris Lloyd

Chris J. Lloyd

The 2x2 binomial trial is the simplest of data structures yet its statistical analysis and the issues it raises have been debated and revisited for over 70 years. Which analysis should biomedical researchers use in applications? In this review, we consider frequentist tests only, specifically tests with control size either exactly or very close to exactly. These procedures can be classified as conditional and unconditional. Amongst tests motivated by a conditional model, Lancaster’s mid-p and Liebermeister’s test are less conservative than Fisher’s classical test, but do not control type 1 error. Within the conditional framework, only Fisher’s test can be …

Cross-Validation And Hypothesis Testing In Neuroimaging: An Irenic Comment On The Exchange Between Friston And Lindquist Et Al., Philip T. Reiss

Philip T. Reiss

The “ten ironic rules for statistical reviewers” presented by Friston (2012) prompted a rebuttal by Lindquist et al. (2013), which was followed by a rejoinder by Friston (2013). A key issue left unresolved in this discussion is the use of cross-validation to test the significance of predictive analyses. This note discusses the role that cross-validation-based and related hypothesis tests have come to play in modern data analyses, in neuroimaging and other fields. It is shown that such tests need not be suboptimal and can fill otherwise-unmet inferential needs.

欠測値補定の診断手法としての多重代入法(高橋将宜), Masayoshi Takahashi

Masayoshi Takahashi

No abstract provided.

Depicting Estimates Using The Intercept In Meta-Regression Models: The Moving Constant Technique, Blair T. Johnson Dr., Tania B. Huedo-Medina Dr.

Blair T. Johnson

In any scientific discipline, the ability to portray research patterns graphically often aids greatly in interpreting a phenomenon. In part to depict phenomena, the statistics and capabilities of meta-analytic models have grown increasingly sophisticated. Accordingly, this article details how to move the constant in weighted meta-analysis regression models (viz. “meta-regression”) to illuminate the patterns in such models across a range of complexities. Although it is commonly ignored in practice, the constant (or intercept) in such models can be indispensible when it is not relegated to its usual static role. The moving constant technique makes possible estimates and confidence intervals at …

An Outlier Robust Block Bootstrap For Small Area Estimation, Payam Mokhtarian, Ray Chambers

Payam Mokhtarian

Small area inference based on mixed models, i.e. models that contain both fixed and random effects, are the industry standard for this field, allowing between area heterogeneity to be represented by random area effects. Use of the linear mixed model is ubiquitous in this context, with maximum likelihood, or its close relative, REML, the standard method for estimating the parameters of this model. These parameter estimates, and in particular the resulting predicted values of the random area effects, are then used to construct empirical best linear unbiased predictors (EBLUPs) of the unknown small area means. It is now well known …

Adaptive Pair-Matching In The Search Trial And Estimation Of The Intervention Effect, Laura Balzer, Maya L. Petersen, Mark J. Van Der Laan

Laura B. Balzer

In randomized trials, pair-matching is an intuitive design strategy to protect study validity and to potentially increase study power. In a common design, candidate units are identified, and their baseline characteristics used to create the best n/2 matched pairs. Within the resulting pairs, the intervention is randomized, and the outcomes measured at the end of follow-up. We consider this design to be adaptive, because the construction of the matched pairs depends on the baseline covariates of all candidate units. As consequence, the observed data cannot be considered as n/2 independent, identically distributed (i.i.d.) pairs of units, as current practice assumes. …

A Model Averaging Approach For High-Dimensional Regression, Tomohiro Ando, Ker-Chau Li

Tomohiro Ando

No abstract provided.

Approximate Bayesian Computation In State Space Models, Gael Martin, Brendan Mccabe, Christian Robert, Worapree Ole Maneesoonthorn

Worapree Ole Maneesoonthorn

A new approach to inference in state space models is proposed, based on approximate Bayesian computation (ABC). ABC avoids evaluation of the likelihood function by matching observed summary statistics with statistics computed from data simulated from the true process; exact inference being feasible only if the statistics are sufficient. With finite sample sufficiency unattainable in the state space setting, we seek asymptotic sufficiency via the maximum likelihood estimator (MLE) of the parameters of an auxiliary model. We prove that this auxiliary model-based approach achieves Bayesian consistency, and that - in a precise limiting sense - the proximity to (asymptotic) sufficiency …

Comparison Of Methods For Estimating The Effect Of Salvage Therapy In Prostate Cancer When Treatment Is Given By Indication., Jeremy Taylor, Jincheng Shen, Edward Kennedy, Lu Wang, Douglas Schaubel

Edward H. Kennedy

For patients who were previously treated for prostate cancer, salvage hormone therapy is frequently given when the longitudinal marker prostate-specific antigen begins to rise during follow-up. Because the treatment is given by indication, estimating the effect of the hormone therapy is challenging. In a previous paper we described two methods for estimating the treatment effect, called two-stage and sequential stratification. The two-stage method involved modeling the longitudinal and survival data. The sequential stratification method involves contrasts within matched sets of people, where each matched set includes people who did and did not receive hormone therapy. In this paper, we evaluate …

Importance Accelerated Robbins-Monro Recursion With Applications To Parametric Confidence Limits, Zdravjko I. Botev, Chris Lloyd

Chris J. Lloyd

Monro (1951) to calculating confidence limits leads to poor efficiency and difficulties in estimating the appropriate governing constants as well as the standard error. We suggest sampling instead from an alternative importance distribu- tion and modifying the Robbins-Monro recursion accordingly. This can reduce the asymptotic variance by the usual importance sampling factor. It also allows the standard error and optimal step length to be estimated from the simulation. The methodology is applied to computing almost exact confidence limits in a generalised linear model.

R Codes For "Multilevel Sparse Functional Principal Component Analysis" (Stat), Chongzhi Di

Chongzhi Di

No abstract provided.

From Amazon To Apple: Modeling Online Retail Sales, Purchase Incidence And Visit Behavior, Anastasios Panagiotelis, Michael S. Smith, Peter Danaher

Michael Stanley Smith

In this study we propose a multivariate stochastic model for website visit duration, page views, purchase incidence and the sale amount for online retailers. The model is constructed by composition from carefully selected distributions, and involves copula components. It allows for the strong nonlinear relationships between the sales and visit variables to be explored in detail, and can be used to construct sales predictions. The model is readily estimated using maximum likelihood, making it an attractive choice in practice given the large sample sizes that are commonplace in online retail studies. We examine a number of top-ranked U.S. online retailers, …

Spectral Density Shrinkage For High-Dimensional Time Series, Mark Fiecas, Rainer Von Sachs

Mark Fiecas

Formulation And Derivation Of Simultaneous Band Scores Or Simbas, Mark J. Meyer, Jeffrey S. Morris

Mark J Meyer

The formulation and derivation of the Simultaneous Band Score or SimBaS procedure that is implemented and discussed in Bayesian Function-on-Function Regression for Multi-Level Functional Data.

Hierarchical Vector Auto-Regressive Models And Their Applications To Multi-Subject Effective Connectivity, Cristina Gorrostieta, Mark Fiecas, Hernando Ombao, Erin Burke, Steven Cramer

Mark Fiecas

Bayesian Hierarchical Modeling With 3pno Item Response Models, Yanyan Sheng, Todd Christopher Headrick

Todd Christopher Headrick

Fully Bayesian estimation has been developed for unidimensional IRT models. In this context, prior distributions can be specified in a hierarchical manner so that item hyperparameters are unknown and yet still have their own priors. This type of hierarchical modeling is useful in terms of the three-parameter IRT model as it reduces the difficulty of specifying model hyperparameters that lead to adequate prior distributions. Further, hierarchical modeling ameliorates the noncovergence problem associated with nonhierarchical models when appropriate prior information is not available. As such, a Fortran subroutine is provided to implement a hierarchical modeling procedure associated with the three-parameter normal …

On The Exact Size Of Multiple Comparison Tests, Chris Lloyd

Chris J. Lloyd

No abstract provided.

Instrumental Variable Analyses: Exploiting Natural Randomness To Understand Causal Mechanisms, Theodore Iwashyna, Edward Kennedy

Edward H. Kennedy

Instrumental variable analysis is a technique commonly used in the social sciences to provide evidence that a treatment causes an outcome, as contrasted with evidence that a treatment is merely associated with differences in an outcome. To extract such strong evidence from observational data, instrumental variable analysis exploits situations where some degree of randomness affects how patients are selected for a treatment. An instrumental variable is a characteristic of the world that leads some people to be more likely to get the specific treatment we want to study but does not otherwise change thosepatients’ outcomes. This seminar explains, in nonmathematical …

Theory And Methods For Gini Coefficients Partitioned By Quantile Range, Chaitra Nagaraja

Chaitra H Nagaraja

The Gini coefficient is frequently used to measure inequality in populations. However, it is possible that inequality levels may change over time differently for disparate subgroups which cannot be detected with population-level estimates only. Therefore, it may be informative to examine inequality separately for these segments. The case where the population is split into two segments based on non-overlapping quantile ranges is examined. Asymptotic theory is derived and practical methods to estimate standard errors and construct confidence intervals using resampling methods are developed. An application to per capita income across census tracts using American Community Survey data is considered.

A Comparison Of Periodic Autoregressive And Dynamic Factor Models In Intraday Energy Demand Forecasting, Thomas Mestekemper, Goeran Kauermann, Michael Smith

Michael Stanley Smith

We suggest a new approach for forecasting energy demand at an intraday resolution. Demand in each intraday period is modeled using semiparametric regression smoothing to account for calendar and weather components. Residual serial dependence is captured by one of two multivariate stationary time series models, with dimension equal to the number of intraday periods. These are a periodic autoregression and a dynamic factor model. We show the benefits of our approach in the forecasting of district heating demand in a steam network in Germany and aggregate electricity demand in the state of Victoria, Australia. In both studies, accounting for weather …

An Overview Of Targeted Maximum Likelihood Estimation, Susan Gruber

Susan Gruber

These slides provide an introduction to targeted maximum likelihood estimation in a point treatment setting.

Bayesian Approaches To Copula Modelling, Michael S. Smith

Michael Stanley Smith

Copula models have become one of the most widely used tools in the applied modelling of multivariate data. Similarly, Bayesian methods are increasingly used to obtain efficient likelihood-based inference. However, to date, there has been only limited use of Bayesian approaches in the formulation and estimation of copula models. This article aims to address this shortcoming in two ways. First, to introduce copula models and aspects of copula theory that are especially relevant for a Bayesian analysis. Second, to outline Bayesian approaches to formulating and estimating copula models, and their advantages over alternative methods. Copulas covered include Archimedean, copulas constructed …

Bayesian Methods For Expression-Based Integration, Elizabeth M. Jennings, Jeffrey S. Morris, Raymond J. Carroll, Ganiraju C. Manyam, Veera Baladandayuthapani

Jeffrey S. Morris

We propose methods to integrate data across several genomic platforms using a hierarchical Bayesian analysis framework that incorporates the biological relationships among the platforms to identify genes whose expression is related to clinical outcomes in cancer. This integrated approach combines information across all platforms, leading to increased statistical power in finding these predictive genes, and further provides mechanistic information about the manner in which the gene affects the outcome. We demonstrate the advantages of the shrinkage estimation used by this approach through a simulation, and finally, we apply our method to a Glioblastoma Multiforme dataset and identify several genes potentially …

Quantifying Temporal Correlations: A Test-Retest Evaluation Of Functional Connectivity In Resting-State Fmri, Mark Fiecas, Hernando Ombao, Dan Van Lunen, Richard Baumgartner, Alexandre Coimbra, Dai Feng

Mark Fiecas

There have been many interpretations of functional connectivity and proposed measures of temporal correlations between BOLD signals across different brain areas. These interpretations yield from many studies on functional connectivity using resting-state fMRI data that have emerged in recent years. However, not all of these studies used the same metrics for quantifying the temporal correlations between brain regions. In this paper, we use a public-domain test–retest resting-state fMRI data set to perform a systematic investigation of the stability of the metrics that are often used in resting-state functional connectivity (FC) studies. The fMRI data set was collected across three different …

Methods For Evaluating Prediction Performance Of Biomarkers And Tests, Margaret S. Pepe Phd, Holly Janes Phd

Margaret S Pepe PhD

This chapter describes and critiques methods for evaluating the performance of markers to predict risk of a current or future clinical outcome. We consider three criteria that are important for evaluating a risk model: calibration, benefit for decision making and accurate classification. We also describe and discuss a variety of summary measures in common use for quantifying predictive information such as the area under the ROC curve and R-squared. The roles and problems with recently proposed risk reclassification approaches are discussed in detail.

Obtaining Critical Values For Test Of Markov Regime Switching, Douglas G. Steigerwald, Valerie Bostwick

Douglas G. Steigerwald

For Markov regime-switching models, testing for the possible presence of more than one regime requires the use of a non-standard test statistic. Carter and Steigerwald (forthcoming, Journal of Econometric Methods) derive in detail the analytic steps needed to implement the test ofMarkov regime-switching proposed by Cho and White (2007, Econometrica). We summarize the implementation steps and address the computational issues that arise. A new command to compute regime-switching critical values, rscv, is introduced and presented in the context of empirical research.

Big Data And The Future, Sherri Rose

Sherri Rose

No abstract provided.

A Logistic L-Moment-Based Analog For The Tukey G-H, G, H, And H-H System Of Distributions, Todd C. Headrick, Mohan D. Pant

Mohan Dev Pant

This paper introduces a standard logistic L-moment-based system of distributions. The proposed system is an analog to the standard normal conventional moment-based Tukey g-h, g, h, and h-h system of distributions. The system also consists of four classes of distributions and is referred to as (i) asymmetric γ-κ, (ii) log-logistic γ, (iii) symmetric κ, and (iv) asymmetric κL-κR. The system can be used in a variety of settings such as simulation or modeling events—most notably when heavy-tailed distributions are of interest. A procedure is also described for simulating γ-κ, γ, κ, and κL-κR distributions with specified L-moments and L-correlations. The …

Variances For Maximum Penalized Likelihood Estimates Obtained Via The Em Algorithm, Mark Segal, Peter Bacchetti, Nicholas Jewell

Mark R Segal

We address the problem of providing variances for parameter estimates obtained under a penalized likelihood formulation through use of the EM algorithm. The proposed solution represents a synthesis of two existent techniques. Firstly, we exploit the supplemented EM algorithm developed in Meng and Rubin (1991) that provides variance estimates for maximum likelihood estimates obtained via the EM algorithm. Their procedure relies on evaluating the Jacobian of the mapping induced by the EM algorithm. Secondly, we utilize a result from Green (1990) that provides an expression for the Jacobian of the mapping induced by the EM algorithm applied to a penalized …