Large-Scale Multiple Testing of Composite Null Hypotheses Under Heteroskedasticity

Heteroskedasticity poses several methodological challenges in designing valid and powerful procedures for simultaneous testing of composite null hypotheses. In particular, the conventional practice of standardizing or re-scaling heteroskedastic test statistics in this setting may severely affect the power of the underlying multiple testing procedure. Additionally, when the inferential parameter of interest is correlated with the variance of the test statistic, methods that ignore this dependence may fail to control the type I error at the desired level. We propose a new Heteroskedasticity Adjusted Multiple Testing (HAMT) procedure that avoids data reduction by standardization, and directly incorporates the side information from the variances into the testing procedure. Our approach relies on an improved nonparametric empirical Bayes deconvolution estimator that offers a practical strategy for capturing the dependence between the inferential parameter of interest and the variance of the test statistic. We develop theory to show that HAMT is asymptotically valid and optimal for FDR control. Simulation results demonstrate that HAMT outperforms existing procedures with substantial power gain across many settings at the same FDR level. The method is illustrated on an application involving the detection of engaged users on a mobile game app

Harnessing The Collective Wisdom: Fusion Learning Using Decision Sequences From Diverse Sources

Learning from the collective wisdom of crowds enhances the transparency of scientific findings by incorporating diverse perspectives into the decision-making process. Synthesizing such collective wisdom is related to the statistical notion of fusion learning from multiple data sources or studies. However, fusing inferences from diverse sources is challenging since cross-source heterogeneity and potential data-sharing complicate statistical inference. Moreover, studies may rely on disparate designs, employ widely different modeling techniques for inferences, and prevailing data privacy norms may forbid sharing even summary statistics across the studies for an overall analysis. In this paper, we propose an Integrative Ranking and Thresholding (IRT) framework for fusion learning in multiple testing. IRT operates under the setting where from each study a triplet is available: the vector of binary accept-reject decisions on the tested hypotheses, the study-specific False Discovery Rate (FDR) level and the hypotheses tested by the study. Under this setting, IRT constructs an aggregated, nonparametric, and discriminatory measure of evidence against each null hypotheses, which facilitates ranking the hypotheses in the order of their likelihood of being rejected. We show that IRT guarantees an overall FDR control under arbitrary dependence between the evidence measures as long as the studies control their respective FDR at the desired levels. Furthermore, IRT synthesizes inferences from diverse studies irrespective of the underlying multiple testing algorithms employed by them. While the proofs of our theoretical statements are elementary, IRT is extremely flexible, and a comprehensive numerical study demonstrates that it is a powerful framework for pooling inferences.Comment: 29 pages and 10 figures. Under review at a journa

Nonparametric Empirical Bayes Estimation on Heterogeneous Data

The simultaneous estimation of many parameters based on data collected from corresponding studies is a key research problem that has received renewed attention in the high-dimensional setting. Many practical situations involve heterogeneous data where heterogeneity is captured by a nuisance parameter. Effectively pooling information across samples while correctly accounting for heterogeneity presents a significant challenge in large-scale estimation problems. We address this issue by introducing the "Nonparametric Empirical Bayes Structural Tweedie" (NEST) estimator, which efficiently estimates the unknown effect sizes and properly adjusts for heterogeneity via a generalized version of Tweedie's formula. For the normal means problem, NEST simultaneously handles the two main selection biases introduced by heterogeneity: one, the selection bias in the mean, which cannot be effectively corrected without also correcting for, two, selection bias in the variance. Our theoretical results show that NEST has strong asymptotic properties without requiring explicit assumptions about the prior. Extensions to other two-parameter members of the exponential family are discussed. Simulation studies show that NEST outperforms competing methods, with much efficiency gains in many settings. The proposed method is demonstrated on estimating the batting averages of baseball players and Sharpe ratios of mutual fund returns.Comment: 66 pages including 33 pages of main text, 5 pages of bibliography, and 29 pages of supplementary tex

Mass Cytometric Analysis of HIV Entry, Replication, and Remodeling in Tissue CD4+ T Cells

To characterize susceptibility to HIV infection, we phenotyped infected tonsillar T cells by single-cell mass cytometry and created comprehensive maps to identify which subsets of CD4+ T cells support HIV fusion and productive infection. By comparing HIV-fused and HIV-infected cells through dimensionality reduction, clustering, and statistical approaches to account for viral perturbations, we identified a subset of memory CD4+ T cells that support HIV entry but not viral gene expression. These cells express high levels of CD127, the IL-7 receptor, and are believed to be long-lived lymphocytes. In HIV-infected patients, CD127-expressing cells preferentially localize to extrafollicular lymphoid regions with limited viral replication. Thus, CyTOF-based phenotyping, combined with analytical approaches to distinguish between selective infection and receptor modulation by viruses, can be used as a discovery tool