Joint testing of overall and simple effects for the two-by-two factorial trial design

Background/aims: The two-by-two factorial design randomizes participants to receive treatment A alone, treatment B alone, both treatments A and B( AB), or neither treatment ( C). When the combined effect of A and B is less than the sum of the A and B effects, called a subadditive interaction, there can be low power to detect the A effect using an overall test, that is, factorial analysis, which compares the A and AB groups to the C and B groups. Such an interaction may have occurred in the Action to Control Cardiovascular Risk in Diabetes blood pressure trial (ACCORD BP) which simultaneously randomized participants to receive intensive or standard blood pressure, control and intensive or standard glycemic control. For the primary outcome of major cardiovascular event, the overall test for efficacy of intensive blood pressure control was nonsignificant. In such an instance, simple effect tests of A versus C and B versus C may be useful since they are not affected by a subadditive interaction, but they can have lower power since they use half the participants of the overall trial. We investigate multiple testing procedures which exploit the overall tests’ sample size advantage and the simple tests’ robustness to a potential interaction. Methods: In the time-to-event setting, we use the stratified and ordinary logrank statistics’ asymptotic means to calculate the power of the overall and simple tests under various scenarios. We consider the A and B research questions to be unrelated and allocate 0.05 significance level to each. For each question, we investigate three multiple testing procedures which allocate the type 1 error in different proportions for the overall and simple effects as well as the AB effect. The Equal Allocation 3 procedure allocates equal type 1 error to each of the three effects, the Proportional Allocation 2 procedure allocates 2/3 of the type 1 error to the overall A (respectively, B) effect and the remaining type 1 error to the AB effect, and the Equal Allocation 2 procedure allocates equal amounts to the simple A (respectively, B) and AB effects. These procedures are applied to ACCORD BP. Results: Across various scenarios, Equal Allocation 3 had robust power for detecting a true effect. For ACCORD BP, all three procedures would have detected a benefit of intensive glycemia control. Conclusions: When there is no interaction, Equal Allocation 3 has less power than a factorial analysis. However, Equal Allocation 3 often has greater power when there is an interaction. The R package factorial2x2 can be used to explore the power gain or loss for different scenarios.

The Romano–Wolf multiple-hypothesis correction in Stata

When considering multiple-hypothesis tests simultaneously, standard statistical techniques will lead to overrejection of null hypotheses unless the multiplicity of the testing framework is explicitly considered. In this article, we discuss the Romano–Wolf multiple-hypothesis correction and document its implementation in Stata. The Romano–Wolf correction (asymptotically) controls the familywise error rate, that is, the probability of rejecting at least one true null hypothesis among a family of hypotheses under test. This correction is considerably more powerful than earlier multiple-testing procedures, such as the Bonferroni and Holm corrections, given that it takes into account the dependence structure of the test statistics by resampling from the original data. We describe a command, rwolf, that implements this correction and provide several examples based on a wide range of models. We document and discuss the performance gains from using rwolf over other multiple-testing procedures that control the familywise error rate.

Optimized multiple testing procedures for nested sub-populations based on a continuous biomarker

An important step in the development of targeted therapies is the identification and confirmation of sub-populations where the treatment has a positive treatment effect compared to a control. These sub-populations are often based on continuous biomarkers, measured at baseline. For example, patients can be classified into biomarker low and biomarker high subgroups, which are defined via a threshold on the continuous biomarker. However, if insufficient information on the biomarker is available, the a priori choice of the threshold can be challenging and it has been proposed to consider several thresholds and to apply appropriate multiple testing procedures to test for a treatment effect in the corresponding subgroups controlling the family-wise type 1 error rate. In this manuscript we propose a framework to select optimal thresholds and corresponding optimized multiple testing procedures that maximize the expected power to identify at least one subgroup with a positive treatment effect. Optimization is performed over a prior on a family of models, modelling the relation of the biomarker with the expected outcome under treatment and under control. We find that for the considered scenarios 3 to 4 thresholds give the optimal power. If there is a prior belief on a small subgroup where the treatment has a positive effect, additional optimization of the spacing of thresholds may result in a large benefit. The procedure is illustrated with a clinical trial example in depression.

Design, analysis and reporting of multi-arm trials and strategies to address multiple testing

Background It is unclear how multiple treatment comparisons are managed in the analysis of multi-arm trials, particularly related to reducing type I (false positive) and type II errors (false negative). Methods We conducted a cohort study of clinical-trial protocols that were approved by research ethics committees in the UK, Switzerland, Germany and Canada in 2012. We examined the use of multiple-testing procedures to control the overall type I error rate. We created a decision tool to determine the need for multiple-testing procedures. We compared the result of the decision tool to the analysis plan in the protocol. We also compared the pre-specified analysis plans in trial protocols to their publications. Results Sixty-four protocols for multi-arm trials were identified, of which 50 involved multiple testing. Nine of 50 trials (18%) used a single-step multiple-testing procedures such as a Bonferroni correction and 17 (38%) used an ordered sequence of primary comparisons to control the overall type I error. Based on our decision tool, 45 of 50 protocols (90%) required use of a multiple-testing procedure but only 28 of the 45 (62%) accounted for multiplicity in their analysis or provided a rationale if no multiple-testing procedure was used. We identified 32 protocol–publication pairs, of which 8 planned a global-comparison test and 20 planned a multiple-testing procedure in their trial protocol. However, four of these eight trials (50%) did not use the global-comparison test. Likewise, 3 of the 20 trials (15%) did not perform the multiple-testing procedure in the publication. The sample size of our study was small and we did not have access to statistical-analysis plans for the included trials in our study. Conclusions Strategies to reduce type I and type II errors are inconsistently employed in multi-arm trials. Important analytical differences exist between planned analyses in clinical-trial protocols and subsequent publications, which may suggest selective reporting of analyses.

Chicdiff: a computational pipeline for detecting differential chromosomal interactions in Capture Hi-C data

Summary Capture Hi-C is a powerful approach for detecting chromosomal interactions involving, at least on one end, DNA regions of interest, such as gene promoters. We present Chicdiff, an R package for robust detection of differential interactions in Capture Hi-C data. Chicdiff enhances a state-of-the-art differential testing approach for count data with bespoke normalization and multiple testing procedures that account for specific statistical properties of Capture Hi-C. We validate Chicdiff on published Promoter Capture Hi-C data in human Monocytes and CD4+ T cells, identifying multitudes of cell type-specific interactions, and confirming the overall positive association between promoter interactions and gene expression. Availability and implementation Chicdiff is implemented as an R package that is publicly available at https://github.com/RegulatoryGenomicsGroup/chicdiff. Supplementary information Supplementary data are available at Bioinformatics online.

Large-Scale Simultaneous Inference with Hypothesis Testing: Multiple Testing Procedures in Practice

A statistical hypothesis test is one of the most eminent methods in statistics. Its pivotal role comes from the wide range of practical problems it can be applied to and the sparsity of data requirements. Being an unsupervised method makes it very flexible in adapting to real-world situations. The availability of high-dimensional data makes it necessary to apply such statistical hypothesis tests simultaneously to the test statistics of the underlying covariates. However, if applied without correction this leads to an inevitable increase in Type 1 errors. To counteract this effect, multiple testing procedures have been introduced to control various types of errors, most notably the Type 1 error. In this paper, we review modern multiple testing procedures for controlling either the family-wise error (FWER) or the false-discovery rate (FDR). We emphasize their principal approach allowing categorization of them as (1) single-step vs. stepwise approaches, (2) adaptive vs. non-adaptive approaches, and (3) marginal vs. joint multiple testing procedures. We place a particular focus on procedures that can deal with data with a (strong) correlation structure because real-world data are rarely uncorrelated. Furthermore, we also provide background information making the often technically intricate methods accessible for interdisciplinary data scientists.