Physical Sciences and Mathematics Commons^™

Estimating Controlled Direct Effects Of Restrictive Feeding Practices In The `Early Dieting In Girls' Study, Yeying Zhu, Debashis Ghosh, Donna L. Coffman, Jennifer S. Williams

Debashis Ghosh

In this article, we examine the causal effect of parental restrictive feeding practices on children’s weight status. An important mediator we are interested in is children’s self-regulation status. Traditional mediation analysis (Baron and Kenny, 1986) applies a structural equation modelling (SEM) approach and decomposes the intent-to-treat (ITT) effect into direct and indirect effects. More recent approaches interpret the mediation effects based on the potential outcomes framework. In practice, there often exist confounders that jointly influence the mediator and the outcome. Inverse probability weighting based on propensity scores are used to adjust for confounding and reduce the dimensionality of confounders simultaneously. …

Equivalence Of Kernel Machine Regression And Kernel Distance Covariance For Multidimensional Trait Association Studies, Wen-Yu Hua, Debashis Ghosh

Debashis Ghosh

Associating genetic markers with a multidimensional phenotype is an important yet challenging problem. In this work, we establish the equivalence between two popular methods: kernel-machine regression (KMR), and kernel distance covariance (KDC). KMR is a semiparametric regression framework that models covariate effects parametrically and genetic markers non-parametrically, while KDC represents a class of methods that include distance covariance (DC) and Hilbert-Schmidt independence criterion (HSIC), which are nonparametric tests of independence. We show that the equivalence between the score test of KMR and the KDC statistic under certain conditions can lead to a novel generalization of the KDC test that incorporates …

A General Approach To Goodness Of Fit For U Processes, Debashis Ghosh, Youngjoo Cho

Debashis Ghosh

Goodness of fit procedures are essential tools for assessing model adequacy in statistics. In this work, we present a general theory and approach to goodness of fit techniques based on U-processes for the accelerated failure time (AFT) model. Many of the examples will focus on U-statistics of order 2. While many authors have proposed goodness of fit tests for U-statistics of order one, less has been developed for higher order U-statistics. In this paper, we propose goodness of fit tests for U-statistics of order 2 by using theoretical results from Nolan and Pollard (1987) and Nolan and Pollard (1988). We …

A Boosting Algorithm For Estimating Generalized Propensity Scores With Continuous Treatments, Yeying Zhu, Donna L. Coffman, Debashis Ghosh

Debashis Ghosh

In this article, we study the causal inference problem with a continuous treatment variable using propensity score-based methods. For a continuous treatment, the generalized propensity score is defined as the conditional density of the treatment-level given covariates (confounders). The dose–response function is then estimated by inverse probability weighting, where the weights are calculated from the estimated propensity scores. When the dimension of the covariates is large, the traditional nonparametric density estimation suffers from the curse of dimensionality. Some researchers have suggested a two-step estimation procedure by first modeling the mean function. In this study, we suggest a boosting algorithm to …

An Asymptotically Minimax Kernel Machine, Debashis Ghosh

Debashis Ghosh

Recently, a class of machine learning-inspired procedures, termed kernel machine methods, has been extensively developed in the statistical literature. It has been shown to have large power for a wide class of problems and applications in genomics and brain imaging. Many authors have exploited an equivalence between kernel machines and mixed eects models and used attendant estimation and inferential procedures. In this note, we construct a so-called `adaptively minimax' kernel machine. Such a construction highlights the role of thresholding in the observation space and limits on the interpretability of such kernel machines.

Multiple Comparison Procedures For Neuroimaging Genomewide Association Studies, Wen-Yu Hua, Thomas E. Nichols, Debashis Ghosh

Debashis Ghosh

Recent research in neuroimaging has been focusing on assessing associations between genetic variants measured on a genomewide scale and brain imaging phenotypes. Many publications in the area use massively univariate analyses on a genomewide basis for finding single nucleotide polymorphisms that influence brain structure. In this work, we propose using various dimensionalityreduction methods on both brain MRI scans and genomic data, motivated by the Alzheimer’s Disease Neuroimaging Initiative (ADNI) study. We also consider a new multiple testing adjustments inspired from the idea of local false discovery rate of Efron and others (2001). Our proposed procedure is able to find associations …

Penalized Regression Procedures For Variable Selection In The Potential Outcomes Framework, Debashis Ghosh, Yeying Zhu, Donna L. Coffman

Debashis Ghosh

A recent topic of much interest in causal inference is model selection. In this article, we describe a framework in which to consider penalized regression approaches to variable selection for causal effects. The framework leads to a simple `impute, then select' class of procedures that is agnostic to the type of imputation algorithm as well as penalized regression used. It also clarifies how model selection involves a multivariate regression model, and that these methods can be applied for identifying subgroups in which treatment effects are homogeneous. Analogies and links with the literature on machine learning methods, missing data and imputation …

A Data-Adaptive Strategy For Inverse Weighted Estimation Of Causal Effects, Yeying Zhu, Debashis Ghosh, Bhramar Mukherjee, Nandita Mitra

Debashis Ghosh

In most nonrandomized observational studies, differences between treatment groups may arise not only due to the treatment but also because of the effect of confounders. Therefore, causal inference regarding the treatment effect is not as straightforward as in a randomized trial. To adjust for confounding due to measured covariates, the average treatment effect is often estimated by using propensity scores. In this article, we focus on the use of inverse probability weighted (IPW) estimation methods. Typically, propensity scores are estimated by logistic regression. More recent suggestions have been to employ nonparametric classification algorithms from machine learning. In this article, we …

James-Stein Estimation And The Benjamini-Hochberg Procedure, Debashis Ghosh

Debashis Ghosh

For the problem of multiple testing, the Benjamini-Hochberg (B-H) procedure has become a very popular method in applications. Based on a spacings theory representation of the B-H procedure, we are able to motivate the use of shrinkage estimators for modifying the B-H procedure. Several generalizations in the paper are discussed, and the methodology is applied to real and simulated datasets.

Shrinkage In Adaptive Procedures For False Discovery Rate Estimation In Multiple Testing: Structure And Synthesis, Debashis Ghosh

Debashis Ghosh

There has been much interest in the study of adaptive estimation procedures for controlling the false discovery rate (FDR). In this article, we take the direct approach to estimation of FDR of Storey (2002) and show how it can reexpressed as a particular type of shrinkage estimator. This representation leads to natural conditions on finite-sample FDR control for a general class of shrinkage estimators. In addition, many previous proposals from the literature can be unified under this framework for which finite-sample FDR results can be developed. Some asymptotic results are also provided.

Generalized Benjamini-Hochberg Procedures Using Spacings, Debashis Ghosh

Debashis Ghosh

For the problem of multiple testing, the Benjamini-Hochberg (B-H) procedure has become a very popular method in applications. We show how the B-H procedure can be interpreted as a test based on the spacings corresponding to the p-value distributions. Using this equivalence, we develop a class of generalized B-H procedures that maintain control of the false discovery rate in finite-samples. We also consider the effect of correlation on the procedure; simulation studies are used to illustrate the methodology.

Software For Assumption Weighting For Meta-Analysis Of Genomic Data, Debashis Ghosh, Yihan Li

Debashis Ghosh

This is the software that accompanies Li and Ghosh, "Assumption weighting for incorporating heterogeneity into meta-analysis of genomic data."

A Causal Framework For Surrogate Endpoints With Semi-Competing Risks Data, Debashis Ghosh

Debashis Ghosh

In this note, we address the problem of surrogacy using a causal modelling framework that differs substantially from the potential outcomes model that pervades the biostatistical literature. The framework comes from econometrics and conceptualizes direct effects of the surrogate endpoint on the true endpoint. While this framework can incorporate the so-called semi-competing risks data structure, we also derive a fundamental non-identifiability result. Relationships to existing causal modelling frameworks are also discussed.

Propensity Score Modelling In Observational Studies Using Dimension Reduction Methods, Debashis Ghosh

Debashis Ghosh

Conditional independence assumptions are very important in causal inference modelling as well as in dimension reduction methodologies. These are two very strikingly different statistical literatures, and we study links between the two in this article. The concept of covariate sufficiency plays an important role, and we provide theoretical justication when dimension reduction and partial least squares methods will allow for valid causal inference to be performed. The methods are illustrated with application to a medical study and to simulated data.

Discrete Nonparametric Algorithms For Outlier Detection With Genomic Data, Debashis Ghosh

Debashis Ghosh

In high-throughput studies involving genetic data such as from gene expression mi- croarrays, dierential expression analysis between two or more experimental conditions has been a very common analytical task. Much of the resulting literature on multiple comparisons has paid relatively little attention to the choice of test statistic. In this article, we focus on the issue of choice of test statistic based on a special pattern of dierential expression. The approach here is based on recasting multiple comparisons procedures for assessing outlying expression values. A major complication is that the resulting p-values are discrete; some theoretical properties of sequential testing …

Detecting Outlier Genes From High-Dimensional Data: A Fuzzy Approach, Debashis Ghosh

Debashis Ghosh

A recent nding in cancer research has been the characterization of previously undis- covered chromosomal abnormalities in several types of solid tumors. This was found based on analyses of high-throughput data from gene expression microarrays and motivated the development of so-called `outlier' tests for dierential expression. One statistical issue was the potential discreteness of the test statistics. Using ideas from fuzzy set theory, we develop fuzzy outlier detection algorithms that have links to ideas in multiple comparisons. Two- and K-sample extensions are considered. The methodology is illustrated by application to two microarray studies.

Links Between Analysis Of Surrogate Endpoints And Endogeneity, Debashis Ghosh, Jeremy M. Taylor, Michael R. Elliott

Debashis Ghosh

There has been substantive interest in the assessment of surrogate endpoints in medical research. These are measures which could potentially replace \true" endpoints in clinical trials and lead to studies that require less follow-up. Recent research in the area has focused on assessments using causal inference frameworks. Beginning with a simple model for associating the surrogate and true endpoints in the population, we approach the problem as one of endogenous covariates. An instrumental variables estimator and general two-stage algorithm is proposed. Existing surrogacy frameworks are then evaluated in the context of the model. A numerical example is used to illustrate …

Meta-Analysis For Surrogacy: Accelerated Failure Time Models And Semicompeting Risks Modelling, Debashis Ghosh, Jeremy M. Taylor, Daniel J. Sargent

Debashis Ghosh

There has been great recent interest in the medical and statistical literature in the assessment and validation of surrogate endpoints as proxies for clinical endpoints in medical studies. More recently, authors have focused on using meta-analytical methods for quanti cation of surrogacy. In this article, we extend existing procedures for analysis based on the accelerated failure time model to this setting. An advantage of this approach relative to proportional hazards model is that it allows for analysis in the semi-competing risks setting, where we constrain the surrogate endpoint to occur before the true endpoint. A novel principal components procedure is …

Spline-Based Models For Predictiveness Curves, Debashis Ghosh, Michael Sabel

Debashis Ghosh

A biomarker is dened to be a biological characteristic that is objectively measured and evaluated as an indicator of normal biologic processes, pathogenic processes, or pharmacologic responses to a therapeutic intervention. The use of biomarkers in cancer has been advocated for a variety of purposes, which include use as surrogate endpoints, early detection of disease, proxies for environmental exposure and risk prediction. We deal with the latter issue in this paper. Several authors have proposed use of the predictiveness curve for assessing the capacity of a biomarker for risk prediction. For most situations, it is reasonable to assume monotonicity of …

Combining Multiple Models With Survival Data: The Phase Algorithm, Debashis Ghosh, Zheng Yuan

Debashis Ghosh

In many scientic studies, one common goal is to develop good prediction rules based on a set of available measurements. This paper proposes a model averaging methodology using proportional hazards regression models to construct new estimators of predicted survival probabilities. A screening step based on an adaptive searching algorithm is used to handle large numbers of covariates. The nite-sample properties of the proposed methodology is assessed using simulation studies. Application of the method to a cancer biomarker study is also given.

Hierarchical Hidden Markov Model With Application To Joint Analysis Of Chip-Chip And Chip-Seq Data, Hyungwon Choi, Debashis Ghosh, Zhaohui S. Qin

Debashis Ghosh

Motivation: Identication of transcription factor binding sites (TFBS) is a fundamental problem in understanding the mechanism of gene regulation. The ChIP-chip technology has accelerated this eort by providing a simultaneous genome-wide map of TFBS in a high-throughput fashion. Recently, a sequencing-based ChIP-seq has appeared as a promising alternative that can identify targets with an improved sensitivity/specicity in high resolution. However, studies have suggested that distinct experimental platforms can be complementary in TFBS identication. The availability of data obtained from multiple platforms motivates a meta-analysis for improved identication of candidate motifs.

Results: In this work, we propose a hierarchical hidden Markov …

A Double-Layered Mixture Model For The Joint Analysis Of Dna Copy Number And Gene Expression Data, Debashis Ghosh

Debashis Ghosh

Copy number aberration is a common form of genomic instability in cancer. Gene expression is closely tied to cytogenetic events by the central dogma of molecular biology, and serves as a mediator of copy number changes in disease phenotypes. Accordingly, it is of interest to develop proper statistical methods for jointly analyzing copy number and gene expression data. This work describes a novel Bayesian inferential approach for a double-layered mixture model (DLMM) which directly models the stochastic nature of copy number data and identifies abnormally expressed genes due to aberrant copy number. Simulation studies were conducted to illustrate the robustness …

Discrete Nonparametric Algorithms For Outlier Detection With Genomic Data, Debashis Ghosh

Debashis Ghosh

In high-throughput studies involving genetic data such as from gene expression microarrays, differential expression analysis between two or more experimental conditions has been a very common analytical task. Much of the resulting literature on multiple comparisons has paid relatively little attention to the choice of test statistic. In this article, we focus on the issue of choice of test statistic based on a special pattern of differential expression. The approach here is based on recasting multiple comparisons procedures for assessing outlying expression values. A major complication is that the resulting p-values are discrete; some theoretical properties of sequential testing procedures …

A Double-Layered Mixture Model For The Joint Analysis Of Dna Copy Number And Gene Expression Data, Debashis Ghosh

Debashis Ghosh

Copy number aberration is a common form of genomic instability in cancer. Gene expression is closely tied to cytogenetic events by the central dogma of molecular biology, and serves as a mediator of copy number changes in disease phenotypes. Accordingly, it is of interest to develop proper statistical methods for jointly analyzing copy number and gene expression data. This work describes a novel Bayesian inferential approach for a double-layered mixture model (DLMM) which directly models the stochastic nature of copy number data and identifies abnormally expressed genes due to aberrant copy number. Simulation studies were conducted to illustrate the robustness …

Discrete Nonparametric Algorithms For Outlier Detection With Genomic Data, Debashis Ghosh

Debashis Ghosh

In high-throughput studies involving genetic data such as from gene expression microarrays, differential expression analysis between two or more experimental conditions has been a very common analytical task. Much of the resulting literature on multiple comparisons has paid relatively little attention to the choice of test statistic. In this article, we focus on the issue of choice of test statistic based on a special pattern of differential expression. The approach here is based on recasting multiple comparisons procedures for assessing outlying expression values. A major complication is that the resulting p-values are discrete; some theoretical properties of sequential testing procedures …

Composite Endpoint Analysis For Assessing Surrogacy With Censored Data, Debashis Ghosh

Debashis Ghosh

Background: There is great interest in the development of surrogate endpoints using new technologies in medical research. The promise of such endpoints is that they would allow for faster completion of clinical trials and would be potentially cost-effective.

Purpose: In determining surrogacy, it is important to distinguish the roles of surrogate from the true endpoint. The latter should be thought of as the gold standard. We discuss a framework in which the utility of a surrogate endpoint is based on whether or not as part of a composite endpoint, it yields treatment effects that associate with that on the true …

Multiple Testing Procedures Under Confounding, Debashis Ghosh

Debashis Ghosh

While multiple testing procedures have been the focus of much statistical research, an important facet of the problem is how to deal with possible confounding. Procedures have been developed by authors in genetics and statistics. In this chapter, we relate these proposals. We propose two new multiple testing approaches within this framework. The first combines sensitivity analysis methods with false discovery rate estimation procedures. The second involves construction of shrinkage estimators that utilize the mixture model for multiple testing. The procedures are illustrated with applications to a gene expression profiling experiment in prostate cancer.

Joint Variable Selection And Classification With Immunohistochemical Data, Debashis Ghosh, Ratna Chakrabarti

Debashis Ghosh

To determine if candidate cancer biomarkers have utility in a clinical setting, validation using immunohistochemical methods is typically done. Most analyses of such data have not incorporated the multivariate nature of the staining profiles. In this article, we consider modelling such data using recently developed ideas from the machine learning community. In particular, we consider the joint goals of feature selection and classification. We develop esti- mation procedures for the analysis of immunohistochemical profiles using the least absolute selection and shrinkage operator. These lead to novel and flexible models and algorithms for the analysis of compositional data. The techniques are …

An Improved Model Averaging Scheme For Logistic Regression, Debashis Ghosh, Zheng Yuan

Debashis Ghosh

Recently, penalized regression methods have attracted much attention in the statistical literature. In this article, we argue that such methods can be improved for the purposes of prediction by utilizing model averaging ideas. We propose a new algorithm that combines penalized regression with model averaging for improved prediction. We also discuss the issue of model selection versus model averaging and propose a diagnostic based on the notion of generalized degrees of freedom. The proposed methods are studied using both simulated and real data.