Closed testing has recently been shown to be optimal for simultaneous true discovery proportion control. It is, however, challenging to construct true discovery guarantee procedures in such a way that it focuses power on some feature sets chosen by users based on their specific interest or expertise. We propose a procedure that allows users to target power on prespecified feature sets, that is, \"focus sets.\" Still, the method also allows inference for feature sets chosen post hoc, that is, \"nonfocus sets,\" for which we deduce a true discovery lower confidence bound by interpolation. Our procedure is built from partial true discovery guarantee procedures combined with Holm\'s procedure and is a conservative shortcut to the closed testing procedure. A simulation study confirms that the statistical power of our method is relatively high for focus sets, at the cost of power for nonfocus sets, as desired. In addition, we investigate its power property for sets with specific structures, for example, trees and directed acyclic graphs. We also compare our method with AdaFilter in the context of replicability analysis. The application of our method is illustrated with a gene ontology analysis in gene expression data.

In precision medicine, there is much interest in estimating the expected-to-benefit (EB) subset, i.e. the subset of patients who are expected to benefit from a new treatment based on a collection of baseline characteristics. There are many statistical methods for estimating the EB subset, most of which produce a \'point estimate\' without a confidence statement to address uncertainty. Confidence intervals for the EB subset have been defined only recently, and their construction is a new area for methodological research. This article proposes a pseudo-response approach to EB subset estimation and confidence interval construction. Compared to existing methods, the pseudo-response approach allows us to focus on modelling a conditional treatment effect function (as opposed to the conditional mean outcome given treatment and baseline covariates) and is able to incorporate information from baseline covariates that are not involved in defining the EB subset. Simulation results show that incorporating such covariates can improve estimation efficiency and reduce the size of the confidence interval for the EB subset. The methodology is applied to a randomized clinical trial comparing two drugs for treating HIV infection.

Brain-effective connectivity analysis quantifies directed influence of one neural element or region over another, and it is of great scientific interest to understand how effective connectivity pattern is affected by variations of subject conditions. Vector autoregression (VAR) is a useful tool for this type of problems. However, there is a paucity of solutions when there is measurement error, when there are multiple subjects, and when the focus is the inference of the transition matrix. In this article, we study the problem of transition matrix inference under the high-dimensional VAR model with measurement error and multiple subjects. We propose a simultaneous testing procedure, with three key components: a modified expectation-maximization (EM) algorithm, a test statistic based on the tensor regression of a bias-corrected estimator of the lagged auto-covariance given the covariates, and a properly thresholded simultaneous test. We establish the uniform consistency for the estimators of our modified EM, and show that the subsequent test achieves both a consistent false discovery control, and its power approaches one asymptotically. We demonstrate the efficacy of our method through both simulations and a brain connectivity study of task-evoked functional magnetic resonance imaging.

A growing number of modern scientific problems in areas such as genomics, neurobiology, and spatial epidemiology involve the measurement and analysis of thousands of related features that may be stochastically dependent at arbitrarily strong levels. In this work, we consider the scenario where the features follow a multivariate Normal distribution. We demonstrate that dependence is manifested as random variation shared among features, and that standard methods may yield highly unstable inference due to dependence, even when the dependence is fully parameterized and utilized in the procedure. We propose a \"cross-dimensional inference\" framework that alleviates the problems due to dependence by modeling and removing the variation shared among features, while also properly regularizing estimation across features. We demonstrate the framework on both simultaneous point estimation and multiple hypothesis testing in scenarios derived from the scientific applications of interest.

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.

Multivariate interval-censored data arise when there are multiple types of events or clusters of study subjects, such that the event times are potentially correlated and when each event is only known to occur over a particular time interval. We formulate the effects of potentially time-varying covariates on the multivariate event times through marginal proportional hazards models while leaving the dependence structures of the related event times unspecified. We construct the nonparametric pseudolikelihood under the working assumption that all event times are independent, and we provide a simple and stable EM-type algorithm. The resulting nonparametric maximum pseudolikelihood estimators for the regression parameters are shown to be consistent and asymptotically normal, with a limiting covariance matrix that can be consistently estimated by a sandwich estimator under arbitrary dependence structures for the related event times. We evaluate the performance of the proposed methods through extensive simulation studies and present an application to data from the Atherosclerosis Risk in Communities Study.

Morphometric (i.e., shape and size) differences in the anatomy of cortical structures are associated with neurodevelopmental and neuropsychiatric disorders. Such differences can be quantized and detected by a powerful tool called Labeled Cortical Distance Map (LCDM). The LCDM method provides distances of labeled gray matter (GM) voxels from the GM/white matter (WM) surface for specific cortical structures (or tissues). Here we describe a method to analyze morphometric variability in the particular tissue using LCDM distances. To extract more of the information provided by LCDM distances, we perform pooling and censoring of LCDM distances. In particular, we employ Brown-Forsythe (BF) test of homogeneity of variance (HOV) on the LCDM distances. HOV analysis of pooled distances provides an overall analysis of morphometric variability of the LCDMs due to the disease in question, while the HOV analysis of censored distances suggests the location(s) of significant variation in these differences (i.e., at which distance from the GM/WM surface the morphometric variability starts to be significant). We also check for the influence of assumption violations on the HOV analysis of LCDM distances. In particular, we demonstrate that BF HOV test is robust to assumption violations such as the non-normality and within sample dependence of the residuals from the median for pooled and censored distances and are robust to data aggregation which occurs in analysis of censored distances. We recommend HOV analysis as a complementary tool to the analysis of distribution/location differences. We also apply the methodology on simulated normal and exponential data sets and assess the performance of the methods when more of the underlying assumptions are satisfied. We illustrate the methodology on a real data example, namely, LCDM distances of GM voxels in ventral medial prefrontal cortices (VMPFCs) to see the effects of depression or being of high risk to depression on the morphometry of VMPFCs. The methodology used here is also valid for morphometric analysis of other cortical structures.

We propose a construction of simultaneous confidence bands (SCBs) for functional parameters over arbitrary dimensional compact domains using the Gaussian Kinematic formula of t-processes (tGKF). Although the tGKF relies on Gaussianity, we show that a central limit theorem (CLT) for the parameter of interest is enough to obtain asymptotically precise covering even if the observations are non-Gaussian processes. As a proof of concept we study the functional signal-plus-noise model and derive a CLT for an estimator of the Lipshitz-Killing curvatures, the only data-dependent quantities in the tGKF. We further discuss extensions to discrete sampling with additive observation noise using scale space ideas from regression analysis. Our theoretical work is accompanied by a simulation study comparing different methods to construct SCBs for the population mean. We show that the tGKF outperforms state-of-the-art methods with precise covering for small sample sizes, and only a Rademacher multiplier-t bootstrap performs similarly well. A further benefit is that our SCBs are computational fast even for domains of dimension greater than one. Applications of SCBs to diffusion tensor imaging (DTI) fibers (1D) and spatio-temporal temperature data (2D) are discussed.

Much of the research on multiple comparison and simultaneous inference in the past 60 years or so has been for the comparisons of several population means. Spurrier seems to have been the first to investigate multiple comparisons of several simple linear regression lines using simultaneous confidence bands. In this paper, we extend the work of Liu et al. for finite comparisons of several univariate linear regression models using simultaneous confidence bands to finite comparisons of several multivariate linear regression models using simultaneous confidence tubes. We show how simultaneous confidence tubes can be constructed to allow more informative inferences for the comparison of several multivariate linear regression models than the current approach of hypotheses testing. The methods are illustrated with examples.

This paper studies simultaneous inference for factor loadings in the approximate factor model. We propose a test statistic based on the maximum discrepancy measure. Taking advantage of the fact that the test statistic can be approximated by the sum of the independent random variables, we develop a multiplier bootstrap procedure to calculate the critical value, and demonstrate the asymptotic size and power of the test. Finally, we apply our result to multiple testing problems by controlling the family-wise error rate (FWER). The conclusions are confirmed by simulations and real data analysis.