Estimating heritability explained by local ancestry and evaluating stratification bias in admixture mapping from summary statistics.

The heritability explained by local ancestry markers in an admixed population (hγ2) provides crucial insight into the genetic architecture of a complex disease or trait. Estimation of hγ2 can be susceptible to biases due to population structure in ancestral populations. Here, we present heritability estimation from admixture mapping summary statistics (HAMSTA), an approach that uses summary statistics from admixture mapping to infer heritability explained by local ancestry while adjusting for biases due to ancestral stratification. Through extensive simulations, we demonstrate that HAMSTA hγ2 estimates are approximately unbiased and are robust to ancestral stratification compared to existing approaches. In the presence of ancestral stratification, we show a HAMSTA-derived sampling scheme provides a calibrated family-wise error rate (FWER) of ∼5% for admixture mapping, unlike existing FWER estimation approaches. We apply HAMSTA to 20 quantitative phenotypes of up to 15,988 self-reported African American individuals in the Population Architecture using Genomics and Epidemiology (PAGE) study. We observe hˆγ2 in the 20 phenotypes range from 0.0025 to 0.033 (mean hˆγ2 = 0.012 ± 9.2 × 10-4), which translates to hˆ2 ranging from 0.062 to 0.85 (mean hˆ2 = 0.30 ± 0.023). Across these phenotypes we find little evidence of inflation due to ancestral population stratification in current admixture mapping studies (mean inflation factor of 0.99 ± 0.001). Overall, HAMSTA provides a fast and powerful approach to estimate genome-wide heritability and evaluate biases in test statistics of admixture mapping studies.

Summary statistics knockoffs inference with family-wise error rate control.

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.

Optimal weighted Bonferroni tests and their graphical extensions.

Regulatory guidelines mandate the strong control of the familywise error rate in confirmatory clinical trials with primary and secondary objectives. Bonferroni tests are one of the popular choices for multiple comparison procedures and are building blocks of more advanced procedures. It is usually of interest to find the optimal weighted Bonferroni split for multiple hypotheses. We consider two popular quantities as the optimization objectives, which are the disjunctive power and the conjunctive power. The former is the probability to reject at least one false hypothesis and the latter is the probability to reject all false hypotheses. We investigate the behavior of each of them as a function of different Bonferroni splits, given assumptions about the alternative hypotheses and correlations between test statistics. Under independent tests, unique optimal Bonferroni weights exist; under dependence, optimal Bonferroni weights may not be unique based on a fine grid search. In general, we propose an optimization algorithm based on constrained nonlinear optimization and multiple starting points. The proposed algorithm efficiently identifies optimal Bonferroni weights to maximize the disjunctive or conjunctive power. In addition, we apply the proposed algorithm to graphical approaches, which include many Bonferroni-based multiple comparison procedures. Utilizing the closed testing principle, we adopt a two-step approach to find optimal graphs using the disjunctive power. We also identify a class of closed test procedures that optimize the conjunctive power. We apply the proposed algorithm to a case study to illustrate the utility of optimal graphical approaches that reflect study objectives.

The impact of allocation bias on test decisions in clinical trials with multiple endpoints using multiple testing strategies.

BACKGROUND: Considering multiple endpoints in clinical trials provide a more comprehensive understanding of treatment effects and may lead to increased power or reduced sample size, which may be beneficial in rare diseases. Besides the small sample sizes, allocation bias is an issue that affects the validity of these trials. We investigate the impact of allocation bias on testing decisions in clinical trials with multiple endpoints and offer a tool for selecting an appropriate randomization procedure (RP). METHODS: We derive a model for quantifying the effect of allocation bias depending on the RP in the case of two-arm parallel group trials with continuous multiple endpoints. We focus on two approaches to analyze multiple endpoints, either the Sidák procedure to show efficacy in at least one endpoint and the all-or-none procedure to show efficacy in all endpoints. RESULTS: To evaluate the impact of allocation bias on the test decision we propose a biasing policy for multiple endpoints. The impact of allocation on the test decision is measured by the family-wise error rate of the Sidák procedure and the type I error rate of the all-or-none procedure. Using the biasing policy we derive formulas to calculate these error rates. In simulations we show that, for the Sidák procedure as well as for the all-or-none procedure, allocation bias leads to inflation of the mean family-wise error and mean type I error, respectively. The strength of this inflation is affected by the choice of the RP. CONCLUSION: Allocation bias should be considered during the design phase of a trial to increase validity. The developed methodology is useful for selecting an appropriate RP for a clinical trial with multiple endpoints to minimize allocation bias effects.

Simultaneous Inference of Multiple Binary Endpoints in Biomedical Research: Small Sample Properties of Multiple Marginal Models and a Resampling Approach.

In biomedical research, the simultaneous inference of multiple binary endpoints may be of interest. In such cases, an appropriate multiplicity adjustment is required that controls the family-wise error rate, which represents the probability of making incorrect test decisions. In this paper, we investigate two approaches that perform single-step p $p$ -value adjustments that also take into account the possible correlation between endpoints. A rather novel and flexible approach known as multiple marginal models is considered, which is based on stacking of the parameter estimates of the marginal models and deriving their joint asymptotic distribution. We also investigate a nonparametric vector-based resampling approach, and we compare both approaches with the Bonferroni method by examining the family-wise error rate and power for different parameter settings, including low proportions and small sample sizes. The results show that the resampling-based approach consistently outperforms the other methods in terms of power, while still controlling the family-wise error rate. The multiple marginal models approach, on the other hand, shows a more conservative behavior. However, it offers more versatility in application, allowing for more complex models or straightforward computation of simultaneous confidence intervals. The practical application of the methods is demonstrated using a toxicological dataset from the National Toxicology Program.

Secondary analyses for genome-wide association studies using expression quantitative trait loci.

Genome-wide association studies (GWAS) have successfully identified thousands of single nucleotide polymorphisms (SNPs) associated with complex traits; however, the identified SNPs account for a fraction of trait heritability, and identifying the functional elements through which genetic variants exert their effects remains a challenge. Recent evidence suggests that SNPs associated with complex traits are more likely to be expression quantitative trait loci (eQTL). Thus, incorporating eQTL information can potentially improve power to detect causal variants missed by traditional GWAS approaches. Using genomic, transcriptomic, and platelet phenotype data from the Genetic Study of Atherosclerosis Risk family-based study, we investigated the potential to detect novel genomic risk loci by incorporating information from eQTL in the relevant target tissues (i.e., platelets and megakaryocytes) using established statistical principles in a novel way. Permutation analyses were performed to obtain family-wise error rates for eQTL associations, substantially lowering the genome-wide significance threshold for SNP-phenotype associations. In addition to confirming the well known association between PEAR1 and platelet aggregation, our eQTL-focused approach identified a novel locus (rs1354034) and gene (ARHGEF3) not previously identified in a GWAS of platelet aggregation phenotypes. A colocalization analysis showed strong evidence for a functional role of this eQTL.

Dynamic impairment classification through arrayed comparisons.

The multivariate normative comparison (MNC) method has been used for identifying cognitive impairment. When participants' cognitive brain domains are evaluated regularly, the longitudinal MNC (LMNC) has been introduced to correct for the intercorrelation among repeated assessments of multiple cognitive domains in the same participant. However, it may not be practical to wait until the end of study for diagnosis. For example, in participants of the Multicenter AIDS Cohort Study (MACS), cognitive functioning has been evaluated repeatedly for more than 35 years. Therefore, it is optimal to identify cognitive impairment at each assessment, while the family-wise error rate (FWER) is controlled with unknown number of assessments in future. In this work, we propose to use the difference of consecutive LMNC test statistics to construct independent tests. Frequency modeling can help predict how many assessments each participant will have, so Bonferroni-type correction can be easily adapted. A chi-squared test is used under the assumption of multivariate normality, and permutation test is proposed where this assumption is violated. We showed through simulation and the MACS data that our method controlled FWER below a predetermined level.

Practical basket design for binary outcomes with control of family-wise error rate.

BACKGROUND: A basket trial is a type of clinical trial in which eligibility is based on the presence of specific molecular characteristics across subpopulations with different cancer types. The existing basket designs with Bayesian hierarchical models often improve the efficiency of evaluating therapeutic effects; however, these models calibrate the type I error rate based on the results of simulation studies under various selected scenarios. The theoretical control of family-wise error rate (FWER) is important for decision-making regarding drug approval. METHODS: In this study, we propose a new Bayesian two-stage design with one interim analysis for controlling FWER at the target level, along with the formulations of type I and II error rates. Since the difficulty lies in the complexity of the theoretical formulation of the type I error rate, we devised the simulation-based method to approximate the type I error rate. RESULTS: The proposed design enabled adjustment of the cutoff value to control the FWER at the target value in the final analysis. The simulation studies demonstrated that the proposed design can be used to control the well-approximated FWER below the target value even in situations where the number of enrolled patients differed among subpopulations. CONCLUSIONS: The accrual number of patients is sometimes unable to reach the pre-defined value; therefore, existing basket designs may not ensure defined operating characteristics before beginning the trial. The proposed design that enables adjustment of the cutoff value to control FWER at the target value based on the results in the final analysis would be a better alternative.

Mediation Analysis for High-Dimensional Mediators and Outcomes with an Application to Multimodal Imaging Data.

Multimodal neuroimaging data have attracted increasing attention for brain research. An integrated analysis of multimodal neuroimaging data and behavioral or clinical measurements provides a promising approach for comprehensively and systematically investigating the underlying neural mechanisms of different phenotypes. However, such an integrated data analysis is intrinsically challenging due to the complex interactive relationships between the multimodal multivariate imaging variables. To address this challenge, a novel multivariate-mediator and multivariate-outcome mediation model (MMO) is proposed to simultaneously extract the latent systematic mediation patterns and estimate the mediation effects based on a dense bi-cluster graph approach. A computationally efficient algorithm is developed for dense bicluster structure estimation and inference to identify the mediation patterns with multiple testing correction. The performance of the proposed method is evaluated by an extensive simulation analysis with comparison to the existing methods. The results show that MMO performs better in terms of both the false discovery rate and sensitivity compared to existing models. The MMO is applied to a multimodal imaging dataset from the Human Connectome Project to investigate the effect of systolic blood pressure on whole-brain imaging measures for the regional homogeneity of the blood oxygenation level-dependent signal through the cerebral blood flow.

Genome-wide Significance Thresholds for Admixture Mapping Studies.

Admixture mapping studies have become more common in recent years, due in part to technological advances and growing international efforts to increase the diversity of genetic studies. However, many open questions remain about appropriate implementation of admixture mapping studies, including how best to control for multiple testing, particularly in the presence of population structure. In this study, we develop a theoretical framework to characterize the correlation of local ancestry and admixture mapping test statistics in admixed populations with contributions from any number of ancestral populations and arbitrary population structure. Based on this framework, we develop an analytical approach for obtaining genome-wide significance thresholds for admixture mapping studies. We validate our approach via analysis of simulated traits with real genotype data for 8,064 unrelated African American and 3,425 Hispanic/Latina women from the Women's Health Initiative SNP Health Association Resource (WHI SHARe). In an application to these WHI SHARe data, our approach yields genome-wide significant p value thresholds of 2.1 × 10-5 and 4.5 × 10-6 for admixture mapping studies in the African American and Hispanic/Latina cohorts, respectively. Compared to other commonly used multiple testing correction procedures, our method is fast, easy to implement (using our publicly available R package), and controls the family-wise error rate even in structured populations. Importantly, we note that the appropriate admixture mapping significance threshold depends on the number of ancestral populations, generations since admixture, and population structure of the sample; as a result, significance thresholds are not, in general, transferable across studies.

Dynamic Scan Procedure for Detecting Rare-Variant Association Regions in Whole-Genome Sequencing Studies.

Whole-genome sequencing (WGS) studies are being widely conducted in order to identify rare variants associated with human diseases and disease-related traits. Classical single-marker association analyses for rare variants have limited power, and variant-set-based analyses are commonly used by researchers for analyzing rare variants. However, existing variant-set-based approaches need to pre-specify genetic regions for analysis; hence, they are not directly applicable to WGS data because of the large number of intergenic and intron regions that consist of a massive number of non-coding variants. The commonly used sliding-window method requires the pre-specification of fixed window sizes, which are often unknown as a priori, are difficult to specify in practice, and are subject to limitations given that the sizes of genetic-association regions are likely to vary across the genome and phenotypes. We propose a computationally efficient and dynamic scan-statistic method (Scan the Genome [SCANG]) for analyzing WGS data; this method flexibly detects the sizes and the locations of rare-variant association regions without the need to specify a prior, fixed window size. The proposed method controls for the genome-wise type I error rate and accounts for the linkage disequilibrium among genetic variants. It allows the detected sizes of rare-variant association regions to vary across the genome. Through extensive simulated studies that consider a wide variety of scenarios, we show that SCANG substantially outperforms several alternative methods for detecting rare-variant-associations while controlling for the genome-wise type I error rates. We illustrate SCANG by analyzing the WGS lipids data from the Atherosclerosis Risk in Communities (ARIC) study.

Deep historical borrowing framework to prospectively and simultaneously synthesize control information in confirmatory clinical trials with multiple endpoints.

In current clinical trial development, historical information is receiving more attention as it provides utility beyond sample size calculation. Meta-analytic-predictive (MAP) priors and robust MAP priors have been proposed for prospectively borrowing historical data on a single endpoint. To simultaneously synthesize control information from multiple endpoints in confirmatory clinical trials, we propose to approximate posterior probabilities from a Bayesian hierarchical model and estimate critical values by deep learning to construct pre-specified strategies for hypothesis testing. This feature is important to ensure study integrity by establishing prospective decision functions before the trial conduct. Simulations are performed to show that our method properly controls family-wise error rate and preserves power as compared with a typical practice of choosing constant critical values given a subset of null space. Satisfactory performance under prior-data conflict is also demonstrated. We further illustrate our method using a case study in Immunology.

Gaining power in multiple testing of interval hypotheses via conditionalization.

In this article, we introduce a novel procedure for improving power of multiple testing procedures (MTPs) of interval hypotheses. When testing interval hypotheses the null hypothesis $P$-values tend to be stochastically larger than standard uniform if the true parameter is in the interior of the null hypothesis. The new procedure starts with a set of $P$-values and discards those with values above a certain pre-selected threshold, while the rest are corrected (scaled-up) by the value of the threshold. Subsequently, a chosen family-wise error rate (FWER) or false discovery rate MTP is applied to the set of corrected $P$-values only. We prove the general validity of this procedure under independence of $P$-values, and for the special case of the Bonferroni method, we formulate several sufficient conditions for the control of the FWER. It is demonstrated that this "filtering" of $P$-values can yield considerable gains of power.

Longitudinal multivariate normative comparisons.

Motivated by the Multicenter AIDS Cohort Study (MACS), we develop classification procedures for cognitive impairment based on longitudinal measures. To control family-wise error, we adapt the cross-sectional multivariate normative comparisons (MNC) method to the longitudinal setting. The cross-sectional MNC was proposed to control family-wise error by measuring the distance between multiple domain scores of a participant and the norms of healthy controls and specifically accounting for intercorrelations among all domain scores. However, in a longitudinal setting where domain scores are recorded multiple times, applying the cross-sectional MNC at each visit will still have inflated family-wise error rate due to multiple testing over repeated visits. Thus, we propose longitudinal MNC procedures that are constructed based on multivariate mixed effects models. A χ2 test procedure is adapted from the cross-sectional MNC to classify impairment on longitudinal multivariate normal data. Meanwhile, a permutation procedure is proposed to handle skewed data. Through simulations we show that our methods can effectively control family-wise error at a predetermined level. A dataset from a neuropsychological substudy of the MACS is used to illustrate the applications of our proposed classification procedures.

Controlling type I error rates in multi-arm clinical trials: A case for the false discovery rate.

Multi-arm trials are an efficient way of simultaneously testing several experimental treatments against a shared control group. As well as reducing the sample size required compared to running each trial separately, they have important administrative and logistical advantages. There has been debate over whether multi-arm trials should correct for the fact that multiple null hypotheses are tested within the same experiment. Previous opinions have ranged from no correction is required, to a stringent correction (controlling the probability of making at least one type I error) being needed, with regulators arguing the latter for confirmatory settings. In this article, we propose that controlling the false-discovery rate (FDR) is a suitable compromise, with an appealing interpretation in multi-arm clinical trials. We investigate the properties of the different correction methods in terms of the positive and negative predictive value (respectively how confident we are that a recommended treatment is effective and that a non-recommended treatment is ineffective). The number of arms and proportion of treatments that are truly effective is varied. Controlling the FDR provides good properties. It retains the high positive predictive value of FWER correction in situations where a low proportion of treatments is effective. It also has a good negative predictive value in situations where a high proportion of treatments is effective. In a multi-arm trial testing distinct treatment arms, we recommend that sponsors and trialists consider use of the FDR.

Non-adjustment for multiple testing in multi-arm trials of distinct treatments: Rationale and justification.

There is currently a lack of consensus and uncertainty about whether one should adjust for multiple testing in multi-arm trials of distinct treatments. A detailed rationale is presented to justify non-adjustment in this situation. We argue that non-adjustment should be the default starting position in simple multi-arm trials of distinct treatments.

Analysis of family-wise error rates in statistical parametric mapping using random field theory.

This technical report revisits the analysis of family-wise error rates in statistical parametric mapping-using random field theory-reported in (Eklund et al. []: arXiv 1511.01863). Contrary to the understandable spin that these sorts of analyses attract, a review of their results suggests that they endorse the use of parametric assumptions-and random field theory-in the analysis of functional neuroimaging data. We briefly rehearse the advantages parametric analyses offer over nonparametric alternatives and then unpack the implications of (Eklund et al. []: arXiv 1511.01863) for parametric procedures. Hum Brain Mapp, 40:2052-2054, 2019. © 2017 The Authors Human Brain Mapping Published by Wiley Periodicals, Inc.

Efficient methods for signal detection from correlated adverse events in clinical trials.

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.

Marginal screening of 2 × 2 tables in large-scale case-control studies.

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.

Marginal screening for high-dimensional predictors of survival outcomes.

This study develops a marginal screening test to detect the presence of significant predictors for a right-censored time-to-event outcome under a high-dimensional accelerated failure time (AFT) model. Establishing a rigorous screening test in this setting is challenging, because of the right censoring and the post-selection inference. In the latter case, an implicit variable selection step needs to be included to avoid inflating the Type-I error. A prior study solved this problem by constructing an adaptive resampling test under an ordinary linear regression. To accommodate right censoring, we develop a new approach based on a maximally selected Koul-Susarla-Van Ryzin estimator from a marginal AFT working model. A regularized bootstrap method is used to calibrate the test. Our test is more powerful and less conservative than both a Bonferroni correction of the marginal tests and other competing methods. The proposed method is evaluated in simulation studies and applied to two real data sets.