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Testing multiple hypotheses of conditional independence with provable error rate control is a fundamental problem with various applications. To infer conditional independence with family-wise error rate (FWER) control when only summary statistics of marginal dependence are accessible, we adopt GhostKnockoff to directly generate knockoff copies of summary statistics and propose a new filter to select features conditionally dependent on the response. In addition, we develop a computationally efficient algorithm to greatly reduce the computational cost of knockoff copies generation without sacrificing power and FWER control. Experiments on simulated data and a real dataset of Alzheimer's disease genetics demonstrate the advantage of the proposed method over existing alternatives in both statistical power and computational efficiency. [ABSTRACT FROM AUTHOR]

We consider the problem of testing multiple null hypotheses, where a decision to reject or retain must be made for each one and embedding incorrect decisions into a real‐life context may inflict different losses. We argue that traditional methods controlling the Type I error rate may be too restrictive in this situation and that the standard familywise error rate may not be appropriate. Using a decision‐theoretic approach, we define suitable loss functions for a given decision rule, where incorrect decisions can be treated unequally by assigning different loss values. Taking expectation with respect to the sampling distribution of the data allows us to control the familywise expected loss instead of the conventional familywise error rate. Different loss functions can be adopted, and we search for decision rules that satisfy certain optimality criteria within a broad class of decision rules for which the expected loss is bounded by a fixed threshold under any parameter configuration. We illustrate the methods with the problem of establishing efficacy of a new medicinal treatment in non‐overlapping subgroups of patients. [ABSTRACT FROM AUTHOR]

We discuss three issues. In the first part, we discuss the criteria emphasized by Maurer, Bretz, and Xun, warning that it modifies the per comparison error rate that does not address the concerns raised by multiple testing. In the second part, we strengthen the optimality results developed in the paper, based on our recent results. In the third part, we highlight the potentially important role that the use of weights may have in practice and discuss the difficulties in assigning weights that convey the importance in the gain and loss functions, especially as it pertains to multiple endpoints. [ABSTRACT FROM AUTHOR]

This document is a response to discussions on the topic of optimal test procedures for multiple hypotheses controlling the familywise expected loss. The authors appreciate the comments and acknowledge the importance of the debate on error rates in multiple testing. They agree with the comments and provide further discussion on common themes raised by the discussants. The document explores various error rates, such as familywise error rate (FWER), per comparison error rate (PCER), and per family error rate (PFER), and their relationship to the familywise expected loss (FWEL). The authors highlight the advantages of embedding these error rates within a general class of error rates to clarify the consequences of incorrect decisions for practitioners. They also discuss the populationwise error rate (PWER) and its connection to the FWEL in a specific application. The text delves into the use of weights in subgroup analyses and the challenges of determining costs and gains in different settings. It emphasizes the importance of considering the relative risks and losses associated with false decisions in clinical trials. The document also addresses the need for multiplicity adjustment in global clinical trials conducted across multiple regions and the different perspectives on loss functions. It mentions the use of Bayesian methods as an alternative approach to classical decision theory and discusses the simulation-based framework for Bayesian designs. The article explains that both frequentist and Bayesian approaches lead to the same optimal rule for minimizing expected loss but differ in how weights are incorporated into error rate control. It also mentions a simulation-based approach that weakly controls the familywise error [Extracted from the article]

This comment builds on the familywise expected loss (FWEL) framework suggested by Maurer, Bretz, and Xun in 2022. By representing the populationwise error rate (PWER) as FWEL, it is illustrated how the FWEL framework can be extended to clinical trials with multiple and overlapping populations and the PWER can be generalized to more general losses. The comment also addresses the question of how to deal with midtrial changes in the posttrial risks and related losses that are caused by data‐driven decisions. Focusing on multiarm trials with the possibility of dropping treatments midtrial, we suggest to switch from control of the unconditional expected loss to control of the conditional expected loss that is related to the actual risks and is conditional on the sample event that causes the change in the risks. The problem and here suggested solution is also motivated with a sequence of independent trials for a hitherto incurable disease which ends when an efficient treatment is found. No multiplicity adjustment is applied in this case and we show how this can be justified by the consideration of the changing out‐trial risks and with control of conditional type I error rates and losses. [ABSTRACT FROM AUTHOR]

Sample size and power determination are crucial design considerations for biomedical studies intending to formally test the effects of key variables on an outcome. Other known prognostic factors may exist, necessitating the use of techniques for covariate adjustment when conducting this evaluation. Moreover, the main interest often includes assessing the impact of more than one variable on an outcome, such as multiple treatments or risk factors. Regression models are frequently employed for these purposes, formalizing this assessment as a test of multiple regression parameters. But, the presence of multiple variables of primary interest and correlation between covariates can complicate sample size/power calculation. Given the paucity of available sample size formulas for this context, these calculations are often performed via simulation, which can be both time‐consuming as well as demanding extensive probability modeling. We propose a simpler, general approach to sample size and power determination that may be applied when testing multiple parameters in commonly used regression models, including generalized linear models as well as ordinary and stratified versions of the Cox and Fine–Gray models. Through both rigorous simulations and theoretical derivations, we demonstrate the formulas' accuracy in producing sample sizes that will meet the type I error rate and power specifications of the study design. [ABSTRACT FROM AUTHOR]

In data analysis using dimension reduction methods, the main goal is to summarize how the response is related to the covariates through a few linear combinations. One key issue is to determine the number of independent, relevant covariate combinations, which is the dimension of the sufficient dimension reduction (SDR) subspace. In this work, we propose an easily‐applied approach to conduct inference for the dimension of the SDR subspace, based on augmentation of the covariate set with simulated pseudo‐covariates. Applying the partitioning principal to the possible dimensions, we use rigorous sequential testing to select the dimensionality, by comparing the strength of the signal arising from the actual covariates to that appearing to arise from the pseudo‐covariates. We show that under a "uniform direction" condition, our approach can be used in conjunction with several popular SDR methods, including sliced inverse regression. In these settings, the test statistic asymptotically follows a beta distribution and therefore is easily calibrated. Moreover, the family‐wise type I error rate of our sequential testing is rigorously controlled. Simulation studies and an analysis of newborn anthropometric data demonstrate the robustness of the proposed approach, and indicate that the power is comparable to or greater than the alternatives. [ABSTRACT FROM AUTHOR]

Semi‐competing risks refer to the time‐to‐event analysis setting, where the occurrence of a non‐terminal event is subject to whether a terminal event has occurred, but not vice versa. Semi‐competing risks arise in a broad range of clinical contexts, including studies of preeclampsia, a condition that may arise during pregnancy and for which delivery is a terminal event. Models that acknowledge semi‐competing risks enable investigation of relationships between covariates and the joint timing of the outcomes, but methods for model selection and prediction of semi‐competing risks in high dimensions are lacking. Moreover, in such settings researchers commonly analyze only a single or composite outcome, losing valuable information and limiting clinical utility—in the obstetric setting, this means ignoring valuable insight into timing of delivery after preeclampsia has onset. To address this gap, we propose a novel penalized estimation framework for frailty‐based illness–death multi‐state modeling of semi‐competing risks. Our approach combines non‐convex and structured fusion penalization, inducing global sparsity as well as parsimony across submodels. We perform estimation and model selection via a pathwise routine for non‐convex optimization, and prove statistical error rate results in this setting. We present a simulation study investigating estimation error and model selection performance, and a comprehensive application of the method to joint risk modeling of preeclampsia and timing of delivery using pregnancy data from an electronic health record. [ABSTRACT FROM AUTHOR]

Recent Hi‐C technology enables more comprehensive chromosomal conformation research, including the detection of structural variations, especially translocations. In this paper, we formulate the interchromosomal translocation detection as a problem of scan clustering in a spatial point process. We then develop TranScan, a new translocation detection method through scan statistics with the control of false discovery. The simulation shows that TranScan is more powerful than an existing sophisticated scan clustering method, especially under strong signal situations. Evaluation of TranScan against current translocation detection methods on realistic breakpoint simulations generated from real data suggests better discriminative power under the receiver‐operating characteristic curve. Power analysis also highlights TranScan's consistent outperformance when sequencing depth and heterozygosity rate is varied. Comparatively, Type I error rate is lowest when evaluated using a karyotypically normal cell line. Both the simulation and real data analysis indicate that TranScan has great potentials in interchromosomal translocation detection using Hi‐C data. [ABSTRACT FROM AUTHOR]

The Globaltest is a powerful test for the global null hypothesis that there is no association between a group of features and a response of interest, which is popular in pathway testing in metabolomics. Evaluating multiple feature sets, however, requires multiple testing correction. In this paper, we propose a multiple testing method, based on closed testing, specifically designed for the Globaltest. The proposed method controls the familywise error rate simultaneously over all possible feature sets, and therefore allows post hoc inference, that is, the researcher may choose feature sets of interest after seeing the data without jeopardizing error control. To circumvent the exponential computation time of closed testing, we derive a novel shortcut that allows exact closed testing to be performed on the scale of metabolomics data. An R package ctgt is available on comprehensive R archive network for the implementation of the shortcut procedure, with applications on several real metabolomics data examples. [ABSTRACT FROM AUTHOR]

Hung et al. (2007) considered the problem of controlling the type I error rate for a primary and secondary endpoint in a clinical trial using a gatekeeping approach in which the secondary endpoint is tested only if the primary endpoint crosses its monitoring boundary. They considered a two‐look trial and showed by simulation that the naive method of testing the secondary endpoint at full level α at the time the primary endpoint reaches statistical significance does not control the familywise error rate at level α. Tamhane et al. (2010) derived analytic expressions for familywise error rate and power and confirmed the inflated error rate of the naive approach. Nonetheless, many people mistakenly believe that the closure principle can be used to prove that the naive procedure controls the familywise error rate. The purpose of this note is to explain in greater detail why there is a problem with the naive approach and show that the degree of alpha inflation can be as high as that of unadjusted monitoring of a single endpoint. [ABSTRACT FROM AUTHOR]

When planning a two‐arm group sequential clinical trial with a binary primary outcome that has severe implications for quality of life (e.g., mortality), investigators may strive to find the design that maximizes in‐trial patient benefit. In such cases, Bayesian response‐adaptive randomization (BRAR) is often considered because it can alter the allocation ratio throughout the trial in favor of the treatment that is currently performing better. Although previous studies have recommended using fixed randomization over BRAR based on patient benefit metrics calculated from the realized trial sample size, these previous comparisons have been limited by failures to hold type I and II error rates constant across designs or consider the impacts on all individuals directly affected by the design choice. In this paper, we propose a metric for comparing designs with the same type I and II error rates that reflects expected outcomes among individuals who would participate in the trial if enrollment is open when they become eligible. We demonstrate how to use the proposed metric to guide the choice of design in the context of two recent trials in persons suffering out of hospital cardiac arrest. Using computer simulation, we demonstrate that various implementations of group sequential BRAR offer modest improvements with respect to the proposed metric relative to conventional group sequential monitoring alone. [ABSTRACT FROM AUTHOR]

Functional data are smooth, often continuous, random curves, which can be seen as an extreme case of multivariate data with infinite dimensionality. Just as componentwise inference for multivariate data naturally performs feature selection, subsetwise inference for functional data performs domain selection. In this paper, we present a unified testing framework for domain selection on populations of functional data. In detail, p‐values of hypothesis tests performed on pointwise evaluations of functional data are suitably adjusted for providing control of the familywise error rate (FWER) over a family of subsets of the domain. We show that several state‐of‐the‐art domain selection methods fit within this framework and differ from each other by the choice of the family over which the control of the FWER is provided. In the existing literature, these families are always defined a priori. In this work, we also propose a novel approach, coined thresholdwise testing, in which the family of subsets is instead built in a data‐driven fashion. The method seamlessly generalizes to multidimensional domains in contrast to methods based on a priori defined families. We provide theoretical results with respect to consistency and control of the FWER for the methods within the unified framework. We illustrate the performance of the methods within the unified framework on simulated and real data examples and compare their performance with other existing methods. [ABSTRACT FROM AUTHOR]

High‐dimensional clustering analysis is a challenging problem in statistics and machine learning, with broad applications such as the analysis of microarray data and RNA‐seq data. In this paper, we propose a new clustering procedure called spectral clustering with feature selection (SC‐FS), where we first obtain an initial estimate of labels via spectral clustering, then select a small fraction of features with the largest R‐squared with these labels, that is, the proportion of variation explained by group labels, and conduct clustering again using selected features. Under mild conditions, we prove that the proposed method identifies all informative features with high probability and achieves the minimax optimal clustering error rate for the sparse Gaussian mixture model. Applications of SC‐FS to four real‐world datasets demonstrate its usefulness in clustering high‐dimensional data. [ABSTRACT FROM AUTHOR]

The rapid acceleration of genetic data collection in biomedical settings has recently resulted in the rise of genetic compendiums filled with rich longitudinal disease data. One common feature of these data sets is their plethora of interval‐censored outcomes. However, very few tools are available for the analysis of genetic data sets with interval‐censored outcomes, and in particular, there is a lack of methodology available for set‐based inference. Set‐based inference is used to associate a gene, biological pathway, or other genetic construct with outcomes and is one of the most popular strategies in genetics research. This work develops three such tests for interval‐censored settings beginning with a variance components test for interval‐censored outcomes, the interval‐censored sequence kernel association test (ICSKAT). We also provide the interval‐censored version of the Burden test, and then we integrate ICSKAT and Burden to construct the interval censored sequence kernel association test—optimal (ICSKATO) combination. These tests unlock set‐based analysis of interval‐censored data sets with analogs of three highly popular set‐based tools commonly applied to continuous and binary outcomes. Simulation studies illustrate the advantages of the developed methods over ad hoc alternatives, including protection of the type I error rate at very low levels and increased power. The proposed approaches are applied to the investigation that motivated this study, an examination of the genes associated with bone mineral density deficiency and fracture risk. [ABSTRACT FROM AUTHOR]

A popular design for clinical trials assessing targeted therapies is the two‐stage adaptive enrichment design with recruitment in stage 2 limited to a biomarker‐defined subgroup chosen based on data from stage 1. The data‐dependent selection leads to statistical challenges if data from both stages are used to draw inference on treatment effects in the selected subgroup. If subgroups considered are nested, as when defined by a continuous biomarker, treatment effect estimates in different subgroups follow the same distribution as estimates in a group‐sequential trial. This result is used to obtain tests controlling the familywise type I error rate (FWER) for six simple subgroup selection rules, one of which also controls the FWER for any selection rule. Two approaches are proposed: one based on multivariate normal distributions suitable if the number of possible subgroups, k, is small, and one based on Brownian motion approximations suitable for large k. The methods, applicable in the wide range of settings with asymptotically normal test statistics, are illustrated using survival data from a breast cancer trial. [ABSTRACT FROM AUTHOR]

A common assumption of data analysis in clinical trials is that the patient population, as well as treatment effects, do not vary during the course of the study. However, when trials enroll patients over several years, this hypothesis may be violated. Ignoring variations of the outcome distributions over time, under the control and experimental treatments, can lead to biased treatment effect estimates and poor control of false positive results. We propose and compare two procedures that account for possible variations of the outcome distributions over time, to correct treatment effect estimates, and to control type‐I error rates. The first procedure models trends of patient outcomes with splines. The second leverages conditional inference principles, which have been introduced to analyze randomized trials when patient prognostic profiles are unbalanced across arms. These two procedures are applicable in response‐adaptive clinical trials. We illustrate the consequences of trends in the outcome distributions in response‐adaptive designs and in platform trials, and investigate the proposed methods in the analysis of a glioblastoma study. [ABSTRACT FROM AUTHOR]

This paper addresses patient heterogeneity associated with prediction problems in biomedical applications. We propose a systematic hypothesis testing approach to determine the existence of patient subgroup structure and the number of subgroups in patient population if subgroups exist. A mixture of generalized linear models is considered to model the relationship between the disease outcome and patient characteristics and clinical factors, including targeted biomarker profiles. We construct a test statistic based on expectation maximization (EM) algorithm and derive its asymptotic distribution under the null hypothesis. An important computational advantage of the test is that the involved parameter estimates under the complex alternative hypothesis can be obtained through a small number of EM iterations, rather than optimizing the objective function. We demonstrate the finite sample performance of the proposed test in terms of type‐I error rate and power, using extensive simulation studies. The applicability of the proposed method is illustrated through an application to a multicenter prostate cancer study. [ABSTRACT FROM AUTHOR]

High‐dimensional biomarkers such as genomics are increasingly being measured in randomized clinical trials. Consequently, there is a growing interest in developing methods that improve the power to detect biomarker–treatment interactions. We adapt recently proposed two‐stage interaction detecting procedures in the setting of randomized clinical trials. We also propose a new stage 1 multivariate screening strategy using ridge regression to account for correlations among biomarkers. For this multivariate screening, we prove the asymptotic between‐stage independence, required for familywise error rate control, under biomarker–treatment independence. Simulation results show that in various scenarios, the ridge regression screening procedure can provide substantially greater power than the traditional one‐biomarker‐at‐a‐time screening procedure in highly correlated data. We also exemplify our approach in two real clinical trial data applications. [ABSTRACT FROM AUTHOR]

Finally, denote the probability that a random test HT ht is positive by HT ht . Thus, HT ht , that is, Sp is greater for the combination than the test alone. The PLR line for I T i is HT ht , which passes through HT ht and (0,0) and has slope I l i SB 1 sb . Denote the absence or presence of the condition being diagnosed by HT ht , HT ht . [Extracted from the article]

Small study effects occur when smaller studies show different, often larger, treatment effects than large ones, which may threaten the validity of systematic reviews and meta‐analyses. The most well‐known reasons for small study effects include publication bias, outcome reporting bias, and clinical heterogeneity. Methods to account for small study effects in univariate meta‐analysis have been extensively studied. However, detecting small study effects in a multivariate meta‐analysis setting remains an untouched research area. One of the complications is that different types of selection processes can be involved in the reporting of multivariate outcomes. For example, some studies may be completely unpublished while others may selectively report multiple outcomes. In this paper, we propose a score test as an overall test of small study effects in multivariate meta‐analysis. Two detailed case studies are given to demonstrate the advantage of the proposed test over various naive applications of univariate tests in practice. Through simulation studies, the proposed test is found to retain nominal Type I error rates with considerable power in moderate sample size settings. Finally, we also evaluate the concordance between the proposed tests with the naive application of univariate tests by evaluating 44 systematic reviews with multiple outcomes from the Cochrane Database. [ABSTRACT FROM AUTHOR]

Quantitative traits analyzed in Genome‐Wide Association Studies (GWAS) are often nonnormally distributed. For such traits, association tests based on standard linear regression are subject to reduced power and inflated type I error in finite samples. Applying the rank‐based inverse normal transformation (INT) to nonnormally distributed traits has become common practice in GWAS. However, the different variations on INT‐based association testing have not been formally defined, and guidance is lacking on when to use which approach. In this paper, we formally define and systematically compare the direct (D‐INT) and indirect (I‐INT) INT‐based association tests. We discuss their assumptions, underlying generative models, and connections. We demonstrate that the relative powers of D‐INT and I‐INT depend on the underlying data generating process. Since neither approach is uniformly most powerful, we combine them into an adaptive omnibus test (O‐INT). O‐INT is robust to model misspecification, protects the type I error, and is well powered against a wide range of nonnormally distributed traits. Extensive simulations were conducted to examine the finite sample operating characteristics of these tests. Our results demonstrate that, for nonnormally distributed traits, INT‐based tests outperform the standard untransformed association test, both in terms of power and type I error rate control. We apply the proposed methods to GWAS of spirometry traits in the UK Biobank. O‐INT has been implemented in the R package RNOmni, which is available on CRAN. [ABSTRACT FROM AUTHOR]

In this paper, we propose a Bayesian design framework for a biosimilars clinical program that entails conducting concurrent trials in multiple therapeutic indications to establish equivalent efficacy for a proposed biologic compared to a reference biologic in each indication to support approval of the proposed biologic as a biosimilar. Our method facilitates information borrowing across indications through the use of a multivariate normal correlated parameter prior (CPP), which is constructed from easily interpretable hyperparameters that represent direct statements about the equivalence hypotheses to be tested. The CPP accommodates different endpoints and data types across indications (eg, binary and continuous) and can, therefore, be used in a wide context of models without having to modify the data (eg, rescaling) to provide reasonable information‐borrowing properties. We illustrate how one can evaluate the design using Bayesian versions of the type I error rate and power with the objective of determining the sample size required for each indication such that the design has high power to demonstrate equivalent efficacy in each indication, reasonably high power to demonstrate equivalent efficacy simultaneously in all indications (ie, globally), and reasonable type I error control from a Bayesian perspective. We illustrate the method with several examples, including designing biosimilars trials for follicular lymphoma and rheumatoid arthritis using binary and continuous endpoints, respectively. [ABSTRACT FROM AUTHOR]

Spatial extent inference (SEI) is widely used across neuroimaging modalities to adjust for multiple comparisons when studying brain‐phenotype associations that inform our understanding of disease. Recent studies have shown that Gaussian random field (GRF)‐based tools can have inflated family‐wise error rates (FWERs). This has led to substantial controversy as to which processing choices are necessary to control the FWER using GRF‐based SEI. The failure of GRF‐based methods is due to unrealistic assumptions about the spatial covariance function of the imaging data. A permutation procedure is the most robust SEI tool because it estimates the spatial covariance function from the imaging data. However, the permutation procedure can fail because its assumption of exchangeability is violated in many imaging modalities. Here, we propose the (semi‐) parametric bootstrap joint (PBJ; sPBJ) testing procedures that are designed for SEI of multilevel imaging data. The sPBJ procedure uses a robust estimate of the spatial covariance function, which yields consistent estimates of standard errors, even if the covariance model is misspecified. We use the methods to study the association between performance and executive functioning in a working memory functional magnetic resonance imaging study. The sPBJ has similar or greater power to the PBJ and permutation procedures while maintaining the nominal type 1 error rate in reasonable sample sizes. We provide an R package to perform inference using the PBJ and sPBJ procedures. [ABSTRACT FROM AUTHOR]

It is known that the one‐sided Simes' test controls the error rate if the underlying distribution is multivariate totally positive of order 2 (MTP2), but not in general. The two‐sided test also controls the error rate when the coordinate absolute value has an MTP2 distribution, which holds more generally. We prove mathematically that when the coordinate absolute value controls the error rate at level 2α, then certain kinds of truncated Simes' tests also control the one‐sided error rate at level α. We also compare the closure of the truncated tests with the Holms, Hochberg, and Hommel procedures in many scenarios when the test statistics are multivariate normal. [ABSTRACT FROM AUTHOR]

Despite major methodological developments, Bayesian inference in Gaussian graphical models remains challenging in high dimension due to the tremendous size of the model space. This article proposes a method to infer the marginal and conditional independence structures between variables by multiple testing, which bypasses the exploration of the model space. Specifically, we introduce closed‐form Bayes factors under the Gaussian conjugate model to evaluate the null hypotheses of marginal and conditional independence between variables. Their computation for all pairs of variables is shown to be extremely efficient, thereby allowing us to address large problems with thousands of nodes as required by modern applications. Moreover, we derive exact tail probabilities from the null distributions of the Bayes factors. These allow the use of any multiplicity correction procedure to control error rates for incorrect edge inclusion. We demonstrate the proposed approach on various simulated examples as well as on a large gene expression data set from The Cancer Genome Atlas. [ABSTRACT FROM AUTHOR]

It is an important and yet challenging task to identify true signals from many adverse events that may be reported during the course of a clinical trial. One unique feature of drug safety data from clinical trials, unlike data from post‐marketing spontaneous reporting, is that many types of adverse events are reported by only very few patients leading to rare events. Due to the limited study size, the p‐values of testing whether the rate is higher in the treatment group across all types of adverse events are in general not uniformly distributed under the null hypothesis that there is no difference between the treatment group and the placebo group. A consequence is that typically fewer than 100α percent of the hypotheses are rejected under the null at the nominal significance level of α. The other challenge is multiplicity control. Adverse events from the same body system may be correlated. There may also be correlations between adverse events from different body systems. To tackle these challenging issues, we develop Monte‐Carlo‐based methods for the signal identification from patient‐reported adverse events in clinical trials. The proposed methodologies account for the rare events and arbitrary correlation structures among adverse events within and/or between body systems. Extensive simulation studies demonstrate that the proposed method can accurately control the family‐wise error rate and is more powerful than existing methods under many practical situations. Application to two real examples is provided. [ABSTRACT FROM AUTHOR]

Response‐adaptive designs allow the randomization probabilities to change during the course of a trial based on cumulated response data so that a greater proportion of patients can be allocated to the better performing treatments. A major concern over the use of response‐adaptive designs in practice, particularly from a regulatory viewpoint, is controlling the type I error rate. In particular, we show that the naïve z‐test can have an inflated type I error rate even after applying a Bonferroni correction. Simulation studies have often been used to demonstrate error control but do not provide a guarantee. In this article, we present adaptive testing procedures for normally distributed outcomes that ensure strong familywise error control by iteratively applying the conditional invariance principle. Our approach can be used for fully sequential and block randomized trials and for a large class of adaptive randomization rules found in the literature. We show there is a high price to pay in terms of power to guarantee familywise error control for randomization schemes with extreme allocation probabilities. However, for proposed Bayesian adaptive randomization schemes in the literature, our adaptive tests maintain or increase the power of the trial compared to the z‐test. We illustrate our method using a three‐armed trial in primary hypercholesterolemia. [ABSTRACT FROM AUTHOR]

Lot Quality Assurance Sampling (LQAS) plans are widely used for health monitoring purposes. We propose a systematic approach to design multiple‐objective LQAS plans that meet user‐specified type 1 and 2 error rates and targets for selected diagnostic accuracy metrics. These metrics may include sensitivity, specificity, positive predictive value, and negative predictive value in high or low anticipated prevalence rate populations. We use Mixed Integer Nonlinear Programming (MINLP) tools to implement our design methodology. Our approach is flexible in that it can directly generate classic LQAS plans that control error rates only and find optimal LQAS plans that meet multiple objectives in terms of diagnostic metrics. We give examples, compare results with the classic LQAS and provide an application using a malaria outcome indicator survey in Mozambique. [ABSTRACT FROM AUTHOR]

Summary: Assessing the statistical significance of risk factors when screening large numbers of 2×2 tables that cross‐classify disease status with each type of exposure poses a challenging multiple testing problem. The problem is especially acute in large‐scale genomic case‐control studies. We develop a potentially more powerful and computationally efficient approach (compared with existing methods, including Bonferroni and permutation testing) by taking into account the presence of complex dependencies between the 2×2 tables. Our approach gains its power by exploiting Monte Carlo simulation from the estimated null distribution of a maximally selected log‐odds ratio. We apply the method to case‐control data from a study of a large collection of genetic variants related to the risk of early onset stroke. [ABSTRACT FROM AUTHOR]

Considerable interest has recently been focused on studying multiple phenotypes simultaneously in both epidemiological and genomic studies, either to capture the multidimensionality of complex disorders or to understand shared etiology of related disorders. We seek to identify multiple regulators or predictors that are associated with multiple outcomes when these outcomes may be measured on very different scales or composed of a mixture of continuous, binary, and not-fully observed elements. We first propose an estimation technique to put all effects on similar scales, and we induce sparsity on the estimated effects. We provide standard asymptotic results for this estimator and show that resampling can be used to quantify uncertainty in finite samples. We finally provide a multiple testing procedure which can be geared specifically to the types of multiple regulators of interest, and we establish that, under standard regularity conditions, the familywise error rate will approach 0 as sample size diverges. Simulation results indicate that our approach can improve over unregularized methods both in reducing bias in estimation and improving power for testing. [ABSTRACT FROM AUTHOR]

We introduce in this work the Interval Testing Procedure (ITP), a novel inferential technique for functional data. The procedure can be used to test different functional hypotheses, e.g., distributional equality between two or more functional populations, equality of mean function of a functional population to a reference. ITP involves three steps: (i) the representation of data on a (possibly high-dimensional) functional basis; (ii) the test of each possible set of consecutive basis coefficients; (iii) the computation of the adjusted p-values associated to each basis component, by means of a new strategy here proposed. We define a new type of error control, the interval-wise control of the family wise error rate, particularly suited for functional data. We show that ITP is provided with such a control. A simulation study comparing ITP with other testing procedures is reported. ITP is then applied to the analysis of hemodynamical features involved with cerebral aneurysm pathology. ITP is implemented in the fdatest R package. [ABSTRACT FROM AUTHOR]

We consider in this article testing rare variants by environment interactions in sequencing association studies. Current methods for studying the association of rare variants with traits cannot be readily applied for testing for rare variants by environment interactions, as these methods do not effectively control for the main effects of rare variants, leading to unstable results and/or inflated Type 1 error rates. We will first analytically study the bias of the use of conventional burdenbased tests for rare variants by environment interactions, and show the tests can often be invalid and result in inflated Type 1 error rates. To overcome these difficulties, we develop the interaction sequence kernel association test (iSKAT) for assessing rare variants by environment interactions. The proposed test iSKAT is optimal in a class of variance component tests and is powerful and robust to the proportion of variants in a gene that interact with environment and the signs of the effects. This test properly controls for the main effects of the rare variants using weighted ridge regression while adjusting for covariates. We demonstrate the performance of iSKAT using simulation studies and illustrate its application by analysis of a candidate gene sequencing study of plasma adiponectin levels. [ABSTRACT FROM AUTHOR]

High-dimensional binary classification tasks, for example, the classification of microarray samples into normal and cancer tissues, usually involve a tuning parameter. By reporting the performance of the best tuning parameter value only, over-optimistic prediction errors are obtained. For correcting this tuning bias, we develop a new method which is based on a decomposition of the unconditional error rate involving the tuning procedure, that is, we estimate the error rate of wrapper algorithms as introduced in the context of internal cross-validation (ICV) by Varma and Simon (2006, BMC Bioinformatics 7, 91). Our subsampling-based estimator can be written as a weighted mean of the errors obtained using the different tuning parameter values, and thus can be interpreted as a smooth version of ICV, which is the standard approach for avoiding tuning bias. In contrast to ICV, our method guarantees intuitive bounds for the corrected error. Additionally, we suggest to use bias correction methods also to address the conceptually similar method selection bias that results from the optimal choice of the classification method itself when evaluating several methods successively. We demonstrate the performance of our method on microarray and simulated data and compare it to ICV. This study suggests that our approach yields competitive estimates at a much lower computational price. [ABSTRACT FROM AUTHOR]

Genetic imprinting and in utero maternal effects are causes of parent-of-origin effect but they are confounded with each other. Tests attempting to detect only one of these effects would have a severely inflated type I error rate if the assumption of the absence of the other effect is violated. Some existing methods avoid the potential confounding by modeling imprinting and in utero maternal effect simultaneously. However, these methods are not amendable to extended families, which are commonly recruited in family-based studies. In this article, we propose a likelihood approach for detecting imprinting and maternal effects (LIME) using general pedigrees from prospective family-based association studies. LIME formulates the probability of familial genotypes without the Hardy-Weinberg equilibrium assumption by introducing a novel concept called conditional mating type between marry-in founders and their nonfounder spouses. Further, a logit link is used to model the penetrance. To deal with the issue of incomplete pedigree genotypic data, LIME imputes the unobserved genotypes implicitly by considering all compatible ones conditional on the observed genotypes. We carried out a simulation study to evaluate the relative power and type I error of LIME and two existing methods. The results show that the use of extended pedigree data, even with incomplete information, can achieve much greater power than using nuclear families for detecting imprinting and in utero maternal effects without leading to inflated type I error rates. [ABSTRACT FROM AUTHOR]

Latent class models are increasingly used to assess the accuracy of medical diagnostic tests and other classifications when no gold standard is available and the true state is unknown. When the latent class is treated as the true class, the latent class models provide measures of components of accuracy including specificity and sensitivity and their complements, type I and type II error rates. The error rates according to the latent class model differ from the true error rates, however, and empirical comparisons with a gold standard suggest the true error rates often are larger. We investigate conditions under which the true type I and type II error rates are larger than those provided by the latent class models. Results from Uebersax (1988, Psychological Bulletin 104, 405-416) are extended to accommodate random effects and covariates affecting the responses. The results are important for interpreting the results of latent class analyses. An error decomposition is presented that incorporates an error component from invalidity of the latent class model. [ABSTRACT FROM AUTHOR]

Summary In the presence of nuisance parameters, the conditional error rate principle is difficult to apply because of the dependency of the conditional error function of the preplanned test on nuisance parameters. To use the conditional error rate principle with nuisance parameters, we propose to search among tests that guarantee overall error control for the test that maximizes a weighted combination of the conditional error rates over possible values of the nuisance parameters. We show that the optimization problem that defines such a test can be solved efficiently by existing algorithms. [ABSTRACT FROM AUTHOR]

We consider a clinical trial with a primary and a secondary endpoint where the secondary endpoint is tested only if the primary endpoint is significant. The trial uses a group sequential procedure with two stages. The familywise error rate (FWER) of falsely concluding significance on either endpoint is to be controlled at a nominal level α. The type I error rate for the primary endpoint is controlled by choosing any α-level stopping boundary, e.g., the standard O'Brien-Fleming or the Pocock boundary. Given any particular α-level boundary for the primary endpoint, we study the problem of determining the boundary for the secondary endpoint to control the FWER. We study this FWER analytically and numerically and find that it is maximized when the correlation coefficient ρ between the two endpoints equals 1. For the four combinations consisting of O'Brien-Fleming and Pocock boundaries for the primary and secondary endpoints, the critical constants required to control the FWER are computed for different values of ρ. An ad hoc boundary is proposed for the secondary endpoint to address a practical concern that may be at issue in some applications. Numerical studies indicate that the O'Brien-Fleming boundary for the primary endpoint and the Pocock boundary for the secondary endpoint generally gives the best primary as well as secondary power performance. The Pocock boundary may be replaced by the ad hoc boundary for the secondary endpoint with a very little loss of secondary power if the practical concern is at issue. A clinical trial example is given to illustrate the methods. [ABSTRACT FROM AUTHOR]

Methods for performing multiple tests of paired proportions are described. A broadly applicable method using McNemar's exact test and the exact distributions of all test statistics is developed; the method controls the familywise error rate in the strong sense under minimal assumptions. A closed form (not simulation-based) algorithm for carrying out the method is provided. A bootstrap alternative is developed to account for correlation structures. Operating characteristics of these and other methods are evaluated via a simulation study. Applications to multiple comparisons of predictive models for disease classification and to postmarket surveillance of adverse events are given. [ABSTRACT FROM AUTHOR]

A challenging and crucial issue in clinical studies in cancer involving gene microarray experiments is the discovery, among a large number of genes, of a relatively small panel of genes whose elements are associated with a relevant clinical outcome variable such as time-to-death or time-to-recurrence of disease. A semiparametric approach, using dependence functions known as copulas, is considered to quantify and estimate the pairwise association between the outcome and each gene expression. These time-to-event type endpoints are typically subject to censoring as not all events are realized at the time of the analysis. Furthermore, given that the total number of genes is typically large, it is imperative to control a relevant error rate in any gene discovery procedure. The proposed method addresses the two aforementioned issues by direct incorporation of the censoring mechanism and by appropriate statistical adjustment for multiplicity. The performance of the proposed method is studied through simulation and illustrated with an application using a case study in lung cancer. [ABSTRACT FROM AUTHOR]

We derive and compare the operating characteristics of hierarchical and square array-based testing algorithms for case identification in the presence of testing error. The operating characteristics investigated include efficiency (i.e., expected number of tests per specimen) and error rates (i.e., sensitivity, specificity, positive and negative predictive values, per-family error rate, and per-comparison error rate). The methodology is illustrated by comparing different pooling algorithms for the detection of individuals recently infected with HIV in North Carolina and Malawi. [ABSTRACT FROM AUTHOR]