Identifying the causal relationship between genotype and phenotype is essential to expanding our understanding of the gene regulatory network spanning the molecular level to perceptible traits. A pleiotropic gene can act as a central hub in the network, influencing multiple outcomes. Identifying such a gene involves testing under a composite null hypothesis where the gene is associated with, at most, one trait. Traditional methods such as meta-analyses of top-hit $P$-values and sequential testing of multiple traits have been proposed, but these methods fail to consider the background of genome-wide signals. Since Huang\'s composite test produces uniformly distributed $P$-values for genome-wide variants under the composite null, we propose a gene-level pleiotropy test that entails combining the aforementioned method with the aggregated Cauchy association test. A polygenic trait involves multiple genes with different functions to co-regulate mechanisms. We show that polygenicity should be considered when identifying pleiotropic genes; otherwise, the associations polygenic traits initiate will give rise to false positives. In this study, we constructed gene-trait functional modules using the results of the proposed pleiotropy tests. Our analysis suite was implemented as an R package PGCtest. We demonstrated the proposed method with an application study of the Taiwan Biobank database and identified functional modules comprising specific genes and their co-regulated traits.

In immunology studies, flow cytometry is a commonly used multivariate single-cell assay. One key goal in flow cytometry analysis is to detect the immune cells responsive to certain stimuli. Statistically, this problem can be translated into comparing two protein expression probability density functions (pdfs) before and after the stimulus; the goal is to pinpoint the regions where these two pdfs differ. Further screening of these differential regions can be performed to identify enriched sets of responsive cells. In this paper, we model identifying differential density regions as a multiple testing problem. First, we partition the sample space into small bins. In each bin, we form a hypothesis to test the existence of differential pdfs. Second, we develop a novel multiple testing method, called TEAM (Testing on the Aggregation tree Method), to identify those bins that harbor differential pdfs while controlling the false discovery rate (FDR) under the desired level. TEAM embeds the testing procedure into an aggregation tree to test from fine- to coarse-resolution. The procedure achieves the statistical goal of pinpointing density differences to the smallest possible regions. TEAM is computationally efficient, capable of analyzing large flow cytometry data sets in much shorter time compared with competing methods. We applied TEAM and competing methods on a flow cytometry data set to identify T cells responsive to the cytomegalovirus (CMV)-pp65 antigen stimulation. With additional downstream screening, TEAM successfully identified enriched sets containing monofunctional, bifunctional, and polyfunctional T cells. Competing methods either did not finish in a reasonable time frame or provided less interpretable results. Numerical simulations and theoretical justifications demonstrate that TEAM has asymptotically valid, powerful, and robust performance. Overall, TEAM is a computationally efficient and statistically powerful algorithm that can yield meaningful biological insights in flow cytometry studies.

We consider the problem of multiple hypothesis testing when there is a logical nested structure to the hypotheses. When one hypothesis is nested inside another, the outer hypothesis must be false if the inner hypothesis is false. We model the nested structure as a directed acyclic graph, including chain and tree graphs as special cases. Each node in the graph is a hypothesis and rejecting a node requires also rejecting all of its ancestors. We propose a general framework for adjusting node-level test statistics using the known logical constraints. Within this framework, we study a smoothing procedure that combines each node with all of its descendants to form a more powerful statistic. We prove a broad class of smoothing strategies can be used with existing selection procedures to control the familywise error rate, false discovery exceedance rate, or false discovery rate, so long as the original test statistics are independent under the null. When the null statistics are not independent but are derived from positively-correlated normal observations, we prove control for all three error rates when the smoothing method is arithmetic averaging of the observations. Simulations and an application to a real biology dataset demonstrate that smoothing leads to substantial power gains.

The false discovery rate (FDR) is a widely used metric of statistical significance for genomic data analyses that involve multiple hypothesis testing. Power and sample size considerations are important in planning studies that perform these types of genomic data analyses. Here, we propose a three-rectangle approximation of a p-value histogram to derive a formula to compute the statistical power and sample size for analyses that involve the FDR. We also introduce the R package FDRsamplesize2, which incorporates these and other power calculation formulas to compute power for a broad variety of studies not covered by other FDR power calculation software. A few illustrative examples are provided. The FDRsamplesize2 package is available on CRAN.

Multiple testing has been a prominent topic in statistical research. Despite extensive work in this area, controlling false discoveries remains a challenging task, especially when the test statistics exhibit dependence. Various methods have been proposed to estimate the false discovery proportion (FDP) under arbitrary dependencies among the test statistics. One key approach is to transform arbitrary dependence into weak dependence and subsequently establish the strong consistency of FDP and false discovery rate under weak dependence. As a result, FDPs converge to the same asymptotic limit within the framework of weak dependence. However, we have observed that the asymptotic variance of FDP can be significantly influenced by the dependence structure of the test statistics, even when they exhibit only weak dependence. Quantifying this variability is of great practical importance, as it serves as an indicator of the quality of FDP estimation from the data. To the best of our knowledge, there is limited research on this aspect in the literature. In this paper, we aim to fill in this gap by quantifying the variation of FDP, assuming that the test statistics exhibit weak dependence and follow normal distributions. We begin by deriving the asymptotic expansion of the FDP and subsequently investigate how the asymptotic variance of the FDP is influenced by different dependence structures. Based on the insights gained from this study, we recommend that in multiple testing procedures utilizing FDP, reporting both the mean and variance estimates of FDP can provide a more comprehensive assessment of the study\'s outcomes.

Diagnostic accuracy studies assess the sensitivity and specificity of a new index test in relation to an established comparator or the reference standard. The development and selection of the index test are usually assumed to be conducted prior to the accuracy study. In practice, this is often violated, for instance, if the choice of the (apparently) best biomarker, model or cutpoint is based on the same data that is used later for validation purposes. In this work, we investigate several multiple comparison procedures which provide family-wise error rate control for the emerging multiple testing problem. Due to the nature of the co-primary hypothesis problem, conventional approaches for multiplicity adjustment are too conservative for the specific problem and thus need to be adapted. In an extensive simulation study, five multiple comparison procedures are compared with regard to statistical error rates in least-favourable and realistic scenarios. This covers parametric and non-parametric methods and one Bayesian approach. All methods have been implemented in the new open-source R package cases which allows us to reproduce all simulation results. Based on our numerical results, we conclude that the parametric approaches (maxT and Bonferroni) are easy to apply but can have inflated type I error rates for small sample sizes. The two investigated Bootstrap procedures, in particular the so-called pairs Bootstrap, allow for a family-wise error rate control in finite samples and in addition have a competitive statistical power.

Survival time is the primary endpoint of many randomized controlled trials, and a treatment effect is typically quantified by the hazard ratio under the assumption of proportional hazards. Awareness is increasing that in many settings this assumption is a priori violated, for example, due to delayed onset of drug effect. In these cases, interpretation of the hazard ratio estimate is ambiguous and statistical inference for alternative parameters to quantify a treatment effect is warranted. We consider differences or ratios of milestone survival probabilities or quantiles, differences in restricted mean survival times, and an average hazard ratio to be of interest. Typically, more than one such parameter needs to be reported to assess possible treatment benefits, and in confirmatory trials, the according inferential procedures need to be adjusted for multiplicity. A simple Bonferroni adjustment may be too conservative because the different parameters of interest typically show considerable correlation. Hence simultaneous inference procedures that take into account the correlation are warranted. By using the counting process representation of the mentioned parameters, we show that their estimates are asymptotically multivariate normal and we provide an estimate for their covariance matrix. We propose according to the parametric multiple testing procedures and simultaneous confidence intervals. Also, the logrank test may be included in the framework. Finite sample type I error rate and power are studied by simulation. The methods are illustrated with an example from oncology. A software implementation is provided in the R package nph.

In problems such as variable selection and graph estimation, models are characterized by Boolean logical structure such as the presence or absence of a variable or an edge. Consequently, false-positive error or false-negative error can be specified as the number of variables/edges that are incorrectly included or excluded in an estimated model. However, there are several other problems such as ranking, clustering, and causal inference in which the associated model classes do not admit transparent notions of false-positive and false-negative errors due to the lack of an underlying Boolean logical structure. In this paper, we present a generic approach to endow a collection of models with partial order structure, which leads to a hierarchical organization of model classes as well as natural analogs of false-positive and false-negative errors. We describe model selection procedures that provide false-positive error control in our general setting, and we illustrate their utility with numerical experiments.

Expression quantitative trait locus (eQTL) analysis is a useful tool to identify genetic loci that are associated with gene expression levels. Large collaborative efforts such as the Genotype-Tissue Expression (GTEx) project provide valuable resources for eQTL analysis in different tissues. Most existing methods, however, either focus on one tissue at a time, or analyze multiple tissues to identify eQTLs jointly present in multiple tissues. There is a lack of powerful methods to identify eQTLs in a target tissue while effectively borrowing strength from auxiliary tissues. In this paper, we propose a novel statistical framework to improve the eQTL detection efficacy in the tissue of interest with auxiliary information from other tissues. This framework can enhance the power of the hypothesis test for eQTL effects by incorporating shared and specific effects from multiple tissues into the test statistics. We also devise data-driven and distributed computing approaches for efficient implementation of eQTL detection when the number of tissues is large. Numerical studies in simulation demonstrate the efficacy of the proposed method, and the real data analysis of the GTEx example provides novel insights into eQTL findings in different tissues.

Transfer learning for high-dimensional Gaussian graphical models (GGMs) is studied. The target GGM is estimated by incorporating the data from similar and related auxiliary studies, where the similarity between the target graph and each auxiliary graph is characterized by the sparsity of a divergence matrix. An estimation algorithm, Trans-CLIME, is proposed and shown to attain a faster convergence rate than the minimax rate in the single-task setting. Furthermore, we introduce a universal debiasing method that can be coupled with a range of initial graph estimators and can be analytically computed in one step. A debiased Trans-CLIME estimator is then constructed and is shown to be element-wise asymptotically normal. This fact is used to construct a multiple testing procedure for edge detection with false discovery rate control. The proposed estimation and multiple testing procedures demonstrate superior numerical performance in simulations and are applied to infer the gene networks in a target brain tissue by leveraging the gene expressions from multiple other brain tissues. A significant decrease in prediction errors and a significant increase in power for link detection are observed.