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Let us say that a coincidence involving two events, where one seems to predict the other, happens a number of times. How many times until it can be considered not only a coincidence, but a statistically significant pattern? We propose a framework to answer this question. Using the framework, we find that the number of times required is 7. We illustrate the practical application of our framework in the context of a very important phenomenon: When the percentage difference between 10-year and 3-month U.S. Treasury yields falls below zero, a U.S. recession appears to occur within the next 18 months. [ABSTRACT FROM AUTHOR]

ABSTRACT In preclinical drug discovery, at the step of lead optimization of a compound, in vivo experimentation can differentiate several compounds in terms of efficacy and potency in a biological system of whole living organisms. For the lead optimization study, it may be desirable to implement a dose–response design so that compound comparisons can be made from nonlinear curves fitted to the data. A dose–response design requires more thought relative to a simpler study design, needing parameters for the number of doses, the dose values, and the sample size per dose. This tutorial illustrates how to calculate statistical power, choose doses, and determine sample size per dose for a comparison of two or more dose–response curves for a future in vivo study. [ABSTRACT FROM AUTHOR]

Genome-wide association studies (GWAS) are often underpowered due to small effect sizes of common single nucleotide polymorphisms (SNPs) on phenotypes and extreme multiple testing thresholds. The most common approach for increasing statistical power is to increase sample size. We propose an alternative strategy of redefining case-control outcomes into ordinal case-subthreshold-asymptomatic variables. While maintaining the clinical case threshold, we subdivide controls into two groups: individuals who are symptomatic but do not meet the clinical criteria for diagnosis (subthreshold) and individuals who are effectively asymptomatic. We conducted a simulation study to examine the impact of effect size, minor allele frequency, population prevalence, and the prevalence of the subthreshold group on statistical power to detect genetic associations in three scenarios: a standard case-control, an ordinal, and a case-asymptomatic control analysis. Our results suggest the ordinal model consistently provides the greatest statistical power while the case-control model the least. Power in the case-asymptomatic control model reflects the case-control or ordinal model depending on the population prevalence and size of the subthreshold category. We then analyzed a major depression phenotype from the UK Biobank to corroborate our simulation results. Overall, the ordinal model improves statistical power in GWAS consistent with increasing the sample size by approximately 10%. [ABSTRACT FROM AUTHOR]

The use of both sexes or genders should be considered in experimental design, analysis, and reporting. Since there is no requirement to double the sample size or to have sufficient power to study sex differences, challenges for the statistical analysis can arise. In this article, we focus on the topics of statistical power and ways to increase this power. We also discuss the choice of an appropriate design and statistical method and include a separate section on equivalence tests needed to show the absence of a relevant difference. [ABSTRACT FROM AUTHOR]

Dependent upon the statistical significance p-value and statistical power, the sample size estimation is widely used in various experimental sciences. Nevertheless, the p-value based paradigm, which has resulted in numerous fake conclusions that originate partly from insufficient sample sizes, has been widely criticized in recent years for serious problems. Therefore, I developed a platform-independent computational tool, SampSizeCal, for sample sizes in the paradigm of new statistics. In this tool, both default p-values and the maximum p-values were greatly enhanced, which will lead to the reasonable increase of sample sizes. The computational tool harbors more than 120 sample size methods for experimental designs. SampSizeCal includes both online and offline versions, and can be used for various computing devices (PCs, iPads, smartphones, etc.), operating systems (Windows, Mac, Android, Harmony, etc.) and web browsers (Chrome, Firefox, Sougo, 360, etc). It is currently the most comprehensive platform-independent computational tool for sample sizes, and can be used in experimental sciences such as medicine (clinical medicine, experimental zoology, public health, pharmacy, etc.), biology, ecology, agronomy, psychology and engineering technology.

For decades, the exercise psychology research literature echoed the conclusion that exercise makes most people feel better, with no clear evidence that this "feel-better effect" is moderated by intensity. An overhaul of the methodological approach subsequently showed that high-intensity exercise is experienced as unpleasant, and the "feel-better effect," although possible, is conditional and therefore not as robust or prevalent as initially thought. Recently, several studies investigating high-intensity interval training (HIIT) have concluded that HIIT is pleasant and enjoyable, despite the high intensity. Considering that HIIT is emerging as an option in physical activity recommendations and exercise prescription guidelines, in part due to these claims, a methodological checklist is presented to aid researchers, peer reviewers, editors, and other readers in critically appraising studies examining the effects of HIIT on affect and enjoyment. This first part addresses the characteristics and number of participants, as well as the selection of measures of affect and enjoyment. [ABSTRACT FROM AUTHOR]

Multisite cluster randomized trials (MCRTs), in which, the intermediate-level clusters (e.g., classrooms) are randomly assigned to the treatment or control condition within each site (e.g., school), are among the most commonly used experimental designs across a broad range of disciplines. MCRTs often align with the theory that programs are delivered at a cluster-level (e.g., teacher professional development) and provide opportunities to explore treatment effect heterogeneity across sites. In designing experimental studies, a critical step is the statistical power analysis and sample size determination. However, the statistical tools for power analysis of moderator effects in three-level MCRTs are not available. In this study, we derived formulas for calculating the statistical power and the minimum detectable effect size difference (MDESD) with confidence intervals for investigating the effects of various moderators in three-level MCRTs. We considered the levels of the moderators (level-1, −2, and −3), the scales of the moderators (binary and continuous), and random and nonrandomly varying slopes of the (moderated) treatment effects. We validated our formulas through Monte Carlo simulations. Finally, we conclude with directions for future work. [ABSTRACT FROM AUTHOR]

Pearson’s correlation is widely used to test for an association between two variables and also forms the basis of several multivariate statistical procedures including many latent variable models. Spearman’s ρ\rho is a popular alternative. These procedures are compared with ranking the data and then applying the inverse normal transformation, or for short the normrank transformation. Using the normrank transformation was more powerful than Pearson’s and Spearman’s procedures when the distributions have less than normal kurtosis (platykurtic), when the distributions have greater than normal kurtosis (leptokurtic), and when the distribution is skewed. This is examined for testing if there is an association between two variables, identifying the number of factors in an exploratory factor analysis, identifying appropriate loadings in these analyses, and identifying relations among latent variables in structural equation models. R functions and their use are shown.

Abstract Background Statistical epistasis, or “gene–gene interaction” in genetic association studies, means the nonadditive effects between the polymorphic sites on two different genes affecting the same phenotype. In the genetic association analysis of complex traits, nevertheless, the researchers haven’t found enough clues of statistical epistasis so far. Methods We developed a statistical model where the statistical epistasis was presented as an extra linkage disequilibrium between the polymorphic sites of different risk genes. The power of statistical test for identifying the gene–gene interaction was calculated and then compared in different hypothesis scenarios. Results Our results show the statistical power increases with the increasing of interaction coefficient, relative risk, and linkage disequilibrium with genetic markers. However, the power of interaction discovery is much lower than that of regular single-site association test. When rigorous criteria were employed in statistical tests, the identification of gene–gene interaction became a very difficult task. Since the criterion of significance was given to be p-value ≤ 5.0 × 10–8, the same as that of many genome-wide association studies, there is little chance to identify the gene–gene interaction in all kind of circumstances. Conclusions The lack of epistasis tends to be an inevitable result caused by the statistical principles of methods in the genetic association studies and therefore is the inherent characteristic of the research itself.

We consider the problem of evaluating designs for a small-sample two-arm randomized experiment using the power of the one-sided randomization test as a criterion. Our evaluation assumes a linear response in one observed covariate, an unobserved component and an additive treatment effect where the model's randomness is due to different treatment allocations. It is well-known that the power depends on the allocations' imbalance in the observed covariate. We show that power is additionally affected by two other design choices: the number of allocations and the degree of the allocations' dependence. We prove that the more allocations, the higher the power and the lower the variability in power. Our theoretical findings and simulation studies show that the designs with the highest power provide thousands of highly independent allocations each providing nominal imbalance in the observed covariates. These high-powered designs exhibit less randomness than complete randomization and more randomness than recently proposed designs that employ numerical optimization. This advantage of high power is easily accessible to practicing experimenters via the popular rerandomization design and a greedy pair switching design, where both outperform complete randomization and numerical optimization. The tradeoff we find also provides a means to specify rerandomization's imbalance threshold parameter. [ABSTRACT FROM AUTHOR]

Determining effectiveness of restoration treatments is an important requirement of adaptive management, but it can be non‐trivial where only portions of large and heterogeneous landscapes of concern can be treated and sampled. Bias and non‐randomness in the spatial deployment of treatment and thus sampling is nearly unavoidable in the data available for large‐scale management trials, and the biophysical landscape characteristics underlying the bias are key but rare considerations in analyses of treatment effects.Treatment effects from large‐scale management trials are typically estimated with multivariable regression (MVR) models. However, this method is unsuited to reliable estimations of treatment effects when treated and untreated areas differ in their underlying biophysical variability. An alternative to conventional regression is to use propensity score (PS) matching, which can limit the differences in confounding variables among treatment groups and assure the data collected or selected for analysis are more consistent with a randomized and unconfounded experiment. Thus, PS is expected to identify treatment effects more accurately.We used data from a large‐scale monitoring effort of a megafire to evaluate the efficacy of PS matching in making inferences on treatment effects when treatments are applied non‐randomly over a large heterogeneous area. We compared the resulting inference to both traditional MVR methods and to "naïve" methods that do not consider treatment allocation bias.Treatment effects varied between the different statistical methods for controlling selection bias and confounding biophysical factors. The PS‐matched model revealed a weaker treatment effect of drill seeding and a greater effect of herbicide spraying on the cover of perennial bunchgrasses when compared to MVR or naïve modelled estimates. The inferences from the PS‐matched model are considered more reliable because the treated and untreated plots are more similar in their underlying biophysical characteristics.Synthesis and applications. Failure to consider the non‐random and selective deployment of restoration treatments by managers leads to faulty inference on their effectiveness. However, tools such as propensity‐score matching can be used to remove the bias from analyses of the outcomes of management trials or to devise sampling plans that efficiently protect against the bias. [ABSTRACT FROM AUTHOR]

Planning longitudinal studies can be challenging as various design decisions need to be made. Often, researchers are in search for the optimal design that maximizes statistical power to test certain parameters of the employed model. We provide a user-friendly Shiny app OptDynMo available at that helps to find the optimal number of persons (N) and the optimal number of time points (T) for which the power of the likelihood ratio test (LRT) for a model parameter is maximal given a fixed budget for conducting the study. The total cost of the study is computed from two components: the cost to include one person in the study and the cost for measuring one person at one time point. Currently supported models are the cross-lagged panel model (CLPM), factor CLPM, random intercepts cross-lagged panel model (RI-CLPM), stable trait autoregressive trait and state model (STARTS), latent curve model with structured residuals (LCM-SR), autoregressive latent trajectory model (ALT), and the latent change score model (LCS). [ABSTRACT FROM AUTHOR]

Purpose: Statistical power for response shift detection with structural equation modeling (SEM) is currently underreported. The present paper addresses this issue by providing worked-out examples and syntaxes of power calculations relevant for the statistical tests associated with the SEM approach for response shift detection. Methods: Power calculations and related sample-size requirements are illustrated for two modelling goals: (1) to detect misspecification in the measurement model, and (2) to detect response shift. Power analyses for hypotheses regarding (exact) overall model fit and the presence of response shift are demonstrated in a step-by-step manner. The freely available and user-friendly R-package lavaan and shiny-app 'power4SEM' are used for the calculations. Results: Using the SF-36 as an example, we illustrate the specification of null-hypothesis (H0) and alternative hypothesis (H1) models to calculate chi-square based power for the test on overall model fit, the omnibus test on response shift, and the specific test on response shift. For example, we show that a sample size of 506 is needed to reject an incorrectly specified measurement model, when the actual model has two-medium sized cross loadings. We also illustrate power calculation based on the RMSEA index for approximate fit, where H0 and H1 are defined in terms of RMSEA-values. Conclusion: By providing accessible resources to perform power analyses and emphasizing the different power analyses associated with different modeling goals, we hope to facilitate the uptake of power analyses for response shift detection with SEM and thereby enhance the stringency of response shift research. [ABSTRACT FROM AUTHOR]

Background: Statistical epistasis, or "gene–gene interaction" in genetic association studies, means the nonadditive effects between the polymorphic sites on two different genes affecting the same phenotype. In the genetic association analysis of complex traits, nevertheless, the researchers haven't found enough clues of statistical epistasis so far. Methods: We developed a statistical model where the statistical epistasis was presented as an extra linkage disequilibrium between the polymorphic sites of different risk genes. The power of statistical test for identifying the gene–gene interaction was calculated and then compared in different hypothesis scenarios. Results: Our results show the statistical power increases with the increasing of interaction coefficient, relative risk, and linkage disequilibrium with genetic markers. However, the power of interaction discovery is much lower than that of regular single-site association test. When rigorous criteria were employed in statistical tests, the identification of gene–gene interaction became a very difficult task. Since the criterion of significance was given to be p-value ≤ 5.0 × 10–8, the same as that of many genome-wide association studies, there is little chance to identify the gene–gene interaction in all kind of circumstances. Conclusions: The lack of epistasis tends to be an inevitable result caused by the statistical principles of methods in the genetic association studies and therefore is the inherent characteristic of the research itself. [ABSTRACT FROM AUTHOR]

AbstractMultisite trials that randomize individuals (e.g., students) within sites (e.g., schools) or clusters (e.g., teachers/classrooms) within sites (e.g., schools) are commonly used for program evaluation because they provide opportunities to learn about treatment effects as well as their heterogeneity across sites and subgroups (defined by moderating variables). Despite the rich opportunities they present, a critical step in ensuring those opportunities is identifying the sample size that provides sufficient power to detect the desired effects if they exist. Although a strong literature base for conducting power analyses for the moderator effects in multisite trials already exists, software for power analysis of moderator effects is not readily available in an accessible platform. The purpose of this tutorial paper is to provide practical guidance on implementing power analyses of moderator effects in multisite individual and cluster randomized trials. We conceptually motivate, describe, and demonstrate the calculation of statistical power and minimum detectable effect size difference (MDESD) using highly accessible software. We conclude by outlining guidelines on power analysis of moderator effects in multisite individual randomized trials (MIRTs) and multisite cluster randomized trials (MCRTs). [ABSTRACT FROM AUTHOR]

Structural equation modeling (SEM) is a widespread and commonly used approach to test substantive hypotheses in the social and behavioral sciences. When performing hypothesis tests, it is vital to rely on a sufficiently large sample size to achieve an adequate degree of statistical power to detect the hypothesized effect. However, applications of SEM rarely consider statistical power in informing sample size considerations or determine the statistical power for the focal hypothesis tests performed. One reason is the difficulty in translating substantive hypotheses into specific effect size values required to perform power analyses, as well as the lack of user-friendly software to automate this process. The present paper presents the second version of the R package semPower which includes comprehensive functionality for various types of power analyses in SEM. Specifically, semPower 2 allows one to perform both analytical and simulated a priori, post hoc, and compromise power analysis for structural equation models with or without latent variables, and also supports multigroup settings and provides user-friendly convenience functions for many common model types (e.g., standard confirmatory factor analysis [CFA] models, regression models, autoregressive moving average [ARMA] models, cross-lagged panel models) to simplify power analyses when a model-based definition of the effect in terms of model parameters is desired. [ABSTRACT FROM AUTHOR]

While the SARS-CoV-2 (COVID-19) pandemic has led to an impressive and unprecedented initiation of clinical research, it has also led to considerable disruption of clinical trials in other disease areas, with around 80% of non-COVID-19 trials stopped or interrupted during the pandemic. In many cases the disrupted trials will not have the planned statistical power necessary to yield interpretable results. This article describes methods to compensate for the information loss arising from trial disruptions by incorporating additional information available from auxiliary data sources. The methods described include the use of auxiliary data on baseline and early outcome data available from the trial itself and frequentist and Bayesian approaches for the incorporation of information from external data sources. The methods are illustrated by application to the analysis of artificial data based on the Primary care pediatrics Learning Activity Nutrition (PLAN) study, a clinical trial assessing a diet and exercise intervention for overweight children, that was affected by the COVID-19 pandemic. We show how all of the methods proposed lead to an increase in precision relative to use of complete case data only. [ABSTRACT FROM AUTHOR]

The calculation of statistical power has been taken up as a simple yet informative tool to assist in designing an experiment, particularly in justifying sample size. A difficulty with using power for this purpose is that the classical power formula does not incorporate sources of uncertainty (e.g., sampling variability) that can impact the computed power value, leading to a false sense of precision and confidence in design choices. We use simulations to demonstrate the consequences of adding two common sources of uncertainty to the calculation of power. Sampling variability in the estimated effect size (Cohen's d) can introduce a large amount of uncertainty (e.g., sometimes producing rather flat distributions) in power and sample-size determination. The addition of random fluctuations in the population effect size can cause values of its estimates to take on a sign opposite the population value, making calculated power values meaningless. These results suggest that calculated power values or use of such values to justify sample size add little to planning a study. As a result, researchers should put little confidence in power-based choices when planning future studies. [ABSTRACT FROM AUTHOR]

How much data are needed to obtain useful parameter estimations from a computational model? The standard approach to address this question is to carry out a goodness-of-recovery study. Here, the correlation between individual-participant true and estimated parameter values determines when a sample size is large enough. However, depending on one's research question, this approach may be suboptimal, potentially leading to sample sizes that are either too small (underpowered) or too large (overcostly or unfeasible). In this paper, we formulate a generalized concept of statistical power and use this to propose a novel approach toward determining how much data is needed to obtain useful parameter estimates from a computational model. We describe a Python-based toolbox (COMPASS) that allows one to determine how many participants are needed to fit one specific computational model, namely the Rescorla-Wagner model of learning and decision-making. Simulations revealed that a high number of trials per person (more than the number of persons) are a prerequisite for high-powered studies in this particular setting. [ABSTRACT FROM AUTHOR]

Due to limitations in the resources available for carrying out reaction time (RT) experiments, researchers often have to choose between testing relatively few participants with relatively many trials each or testing relatively many participants with relatively few trials each. To compare the experimental power that would be obtained under each of these options, I simulated virtual experiments using subsets of participants and trials from eight large real RT datasets examining 19 experimental effects. The simulations compared designs using the first N T trials from N P randomly selected participants, holding constant the total number of trials across all participants, N P × N T . The [ N P , N T ] combination maximizing the power to detect each effect depended on how the mean and variability of that effect changed with practice. For most effects, power was greater in designs having many participants with few trials each rather than the reverse, suggesting that researchers should usually try to recruit large numbers of participants for short experimental sessions. In some cases, power for a fixed total number of trials across all participants was maximized by having as few as two trials per participant in each condition. Where researchers can make plausible predictions about how their effects will change over the course of a session, they can use those predictions to increase their experimental power. [ABSTRACT FROM AUTHOR]

Intensive temporal and spatial sampling of benthic infauna have rarely been analysed to improve impact assessment or conservation planning. An impact assessment started in the late 1980s in Jervis Bay (Australia) provided a spatially, temporally and taxonomically comprehensive benthic invertebrate dataset. While the proposed development did not eventuate, the area was later declared a multi‐zone marine park.We specifically used the polychaete data which included nine sampling times (February 1989 to June 1991) in seagrass and unvegetated sediments across multiple sites to identify ecological patterns that could inform current and future conservation management and impact assessment.The polychaete assemblage was diverse with 171 species, many of them rare (40% < 10 individuals). Variation was greatest at small spatial scales (metres) for abundances and diversity, and there was substantial spatio‐temporal variation due to inconsistent site differences. Most species occurred in both unvegetated and seagrass sediments, though several were more abundant or restricted to one habitat (39% and 3% only found in unvegetated or seagrass, respectively), or showed bathymetric differences in abundances (e.g., Eunice cultrifera and Lumbrineris cf. latrelli).The current marine park zoning representatively covered polychaete biodiversity, as all sites were generally similar in terms of abundances and species richness. It also representatively covered seagrass and unvegetated sediments and the bathymetric range of the embayment. These findings reinforce the utility of using habitats as surrogates to representatively zone for biological diversity.The high levels of spatial and spatio‐temporal variation in abundances and diversity only allowed detection of environmental impacts with >70% effect sizes even if numerous sites and times were sampled (i.e., > seven sites and > eight times). This suggests that most univariate measures for polychaetes would only be useful to detect enormous effects, and effective impact assessment might require more sophisticated multivariate approaches. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Field Ornithology is the property of Resilience Alliance and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Summary: Since the first genome-wide association studies (GWASs), thousands of variant-trait associations have been discovered. However, comprehensively mapping the genetic determinant of complex traits through univariate testing can require prohibitive sample sizes. Multi-trait GWAS can circumvent this issue and improve statistical power by leveraging the joint genetic architecture of human phenotypes. Although many methodological hurdles of multi-trait testing have been solved, the strategy to select traits has been overlooked. In this study, we conducted multi-trait GWAS on approximately 20,000 combinations of 72 traits using an omnibus test as implemented in the Joint Analysis of Summary Statistics. We assessed which genetic features of the sets of traits analyzed were associated with an increased detection of variants compared with univariate screening. Several features of the set of traits, including the heritability, the number of traits, and the genetic correlation, drive the multi-trait test gain. Using these features jointly in predictive models captures a large fraction of the power gain of the multi-trait test (Pearson’s r between the observed and predicted gain equals 0.43, p

IntroductionCognitive composite scales constructed by combining existing neuropsychometric tests are seeing wide application as endpoints for clinical trials and cohort studies of Alzheimer's disease (AD) predementia conditions. Preclinical Alzheimer's Cognitive Composite (PACC) scales are composite scores calculated as the sum of the component test scores weighted by the reciprocal of their standard deviations at the baseline visit. Reciprocal standard deviation is an arbitrary weighting in this context, and may be an inefficient utilization of the data contained in the component measures. Mathematically derived optimal composite weighting is a promising alternative.MethodsSample size projections using standard power calculation formulas were used to describe the relative performance of component measures and their composites when used as endpoints for clinical trials. Power calculations were informed by (n=1,333) amnestic mild cognitive impaired participants in the National Alzheimer's Coordinating Center (NACC) Uniform Data Set.ResultsA composite constructed using PACC reciprocal standard deviation weighting was both less sensitive to change than one of its component measures and less sensitive to change than its optimally weighted counterpart. In standard sample size calculations informed by NACC data, a clinical trial using the PACC weighting would require 38% more subjects than a composite calculated using optimal weighting.DiscussionThese findings illustrate how reciprocal standard deviation weighting can result in inefficient cognitive composites, and underscore the importance of component weights to the performance of composite scales. In the future, optimal weighting parameters informed by accumulating clinical trial data may improve the efficiency of clinical trials in AD.

Abstract When multiple influential covariates need to be balanced during a clinical trial, stratified blocked randomization and covariate-adaptive randomization procedures are frequently used in trials to prevent bias and enhance the validity of data analysis results. The latter approach is increasingly used in practice for a study with multiple covariates and limited sample sizes. Among a group of these approaches, the covariate-adaptive procedures proposed by Pocock and Simon are straightforward to be utilized in practice. We aim to investigate the optimal design parameters for the patient treatment assignment probability of their developed three methods. In addition, we seek to answer the question related to the randomization performance when additional covariates are added to the existing randomization procedure. We conducted extensive simulation studies to address these practically important questions.

The article addresses the issue of underpowered trials in evaluating new care models, particularly in randomized controlled trials (RCTs). It highlights challenges like implementation issues and incomplete engagement, leading to ambiguous results. It suggests strategies for improving trial power, including cautious estimation of effect sizes, anticipating uptake challenges, using preparatory studies and others.

Determination of the required sample size is an important step in the planning of any research study. A large number of commercial and online resources are readily available for calculation of sample size required for various research designs. However, this abundance of information, the complexity, and the variation in calculation formulations and terminology used make it more confusing to researchers, particularly those with limited statistical knowledge. Therefore, there is a need for more simplified, easy to implement formulas for calculation of sample size. Here, we present a short review of the rules for calculation of sample size for common experimental designs used in research and provide more simplified forms for some of these formulas. Also, data are presented on sample size required for various scenarios with the intent to provide guidelines for researchers. A simpleto-use Excel sheet was developed to perform sample size calculations and is available online as a supplementary file. This Excel sheet was used to generate the data presented in this publication. [ABSTRACT FROM AUTHOR]

When multiple influential covariates need to be balanced during a clinical trial, stratified blocked randomization and covariate-adaptive randomization procedures are frequently used in trials to prevent bias and enhance the validity of data analysis results. The latter approach is increasingly used in practice for a study with multiple covariates and limited sample sizes. Among a group of these approaches, the covariate-adaptive procedures proposed by Pocock and Simon are straightforward to be utilized in practice. We aim to investigate the optimal design parameters for the patient treatment assignment probability of their developed three methods. In addition, we seek to answer the question related to the randomization performance when additional covariates are added to the existing randomization procedure. We conducted extensive simulation studies to address these practically important questions. [ABSTRACT FROM AUTHOR]

AbstractWhen designing cluster-randomized trials (CRTs), one important consideration is determining the proper sample sizes across levels and treatment conditions to cost-efficiently achieve adequate statistical power. This consideration is usually addressed in an optimal design framework by leveraging the cost structures of sampling and optimizing the sampling ratios across treatment conditions and levels of the hierarchy. Traditionally, optimization is done through the first-order derivative approach by setting the first-order derivatives equal to zero to solve for the optimal design parameters. However, the first-order derivative method is incapable of properly handling the optimization task when statistical power formulas are complex, such as those for CRTs detecting mediation effects under the joint significance test. The current study proposes using an ant colony optimization (ACO) algorithm to identify optimal allocations. We evaluate the algorithm’s performance for CRTs detecting main and mediation effects. The results show that the ACO algorithm can identify optimal sample allocations for CRTs investigating main effects with the same design efficiency as those identified through the first-order derivative method. Furthermore, it can efficiently identify optimal sample allocations for CRTs investigating mediation effects under the joint significance test. We have implemented the proposed methods in the R package odr. [ABSTRACT FROM AUTHOR]

Comprehensive evaluation of treatment effects is aided by considerations for moderated effects. In educational research, the combination of natural hierarchical structures and prevalence of group-administered or shared facilitator treatments often produces three-level partially nested data structures. Literature details planning strategies for a variety of experimental designs when moderation effects are of interest but has yet to establish power formulas for detecting moderation effects in three-level partially nested designs. To address this gap, we derive and assess the accuracy of power formulas for detecting the different types of moderation effects possible in these designs. Using Monte Carlo simulation studies, we probe power rates and adequate sample sizes for detecting the different moderation effects while varying common influential factors including variance in the outcome explained by covariates, magnitude of the moderation effect, and sample sizes. The power formulas developed improve the planning of experimental studies with partial nesting and encourage the inclusion of moderator variables to capture for whom and under what conditions a treatment is effective. Educational researchers also have some initial guidance regarding adequate sample sizes and the factors that influence detecting moderation effects in three-level partially nested designs. [ABSTRACT FROM AUTHOR]

The delayed treatment effect is a common feature of immunotherapy, characterized by a gradual onset of action ranging from no effect to full effect. In this study, we propose a generalized delayed treatment effect function to depict the delayed effective process precisely and flexibly. To reduce potential power loss caused by the delayed treatment effect in a group sequential trial, we employ the maximin efficiency robust test, which enhances power robustness across a range of possible delays. We present novel approaches based on the Markov chain method for determining group sequential boundaries, calculating the power function, and estimating the maximum sample size through iterative regressions between the square root of the maximum sample size and the normal quantile of power. Extensive simulation studies validate the effectiveness of our approaches, particularly in balanced trials, demonstrating the validity of group sequential boundaries and the accuracy of maximum sample size estimations. Additionally, we utilize a real trial as an example to compare our considered trial with group sequential trials using the log‐rank and generalized piecewise weighted log‐rank tests. The results show significantly reduced maximum sample sizes, highlighting the economic advantage of our approach. [ABSTRACT FROM AUTHOR]

Many measurement designs produce domain factors with small variances and factor loadings. The current study investigates the cause, prevalence, and problematic consequences of such domain factors. We collected a meta-analytic sample of empirical applications, conducted a simulation study on statistical power and estimation precision, and provide a reanalysis of an empirical example. The meta-analysis shows that about a quarter of all standardized domain factor loadings is in the range of −.2 < λ <.2 and about a third of all domains is measured by five or fewer indicators, resulting in small factor variances. The simulation study examines the associated difficulties concerning statistical power, trait recovery, irregular estimates, and estimation precision for a range of such realistic cases. The empirical example illustrates the challenge to develop measures that produce clearly interpretable domain factors. Study planning and interpretation need to take the (expected) sum of squared factor loadings per domain factor into account. This is relevant even if influences of domain factors are desired to be small, and equally applies to different model variants. We propose several strategies for how researchers may better unlock the bifactor model's full potential and clarify its interpretation. [ABSTRACT FROM AUTHOR]

When comparing the performance of two or more competing tests, simulation studies commonly focus on statistical power. However, if the size of the tests being compared are either different from one another or from the nominal size, comparing tests based on power alone may be misleading. By analogy with diagnostic accuracy studies, we introduce relative positive and negative likelihood ratios to factor in both power and size in the comparison of multiple tests. We derive sample size formulas for a comparative simulation study. As an example, we compared the performance of six statistical tests for small‐study effects in meta‐analyses of randomized controlled trials: Begg's rank correlation, Egger's regression, Schwarzer's method for sparse data, the trim‐and‐fill method, the arcsine‐Thompson test, and Lin and Chu's combined test. We illustrate that comparing power alone, or power adjusted or penalized for size, can be misleading, and how the proposed likelihood ratio approach enables accurate comparison of the trade‐off between power and size between competing tests. [ABSTRACT FROM AUTHOR]

INTRODUCTION: Alzheimer's disease (AD) is a complex disease influenced by genetics and environment. More than 75 susceptibility loci have been linked to late‐onset AD, but most of these loci were discovered in genome‐wide association studies (GWAS) exclusive to non‐Hispanic White individuals. There are wide disparities in AD risk across racially stratified groups, and while these disparities are not due to genetic differences, underrepresentation in genetic research can further exacerbate and contribute to their persistence. We investigated the racial/ethnic representation of participants in United States (US)‐based AD genetics and the statistical implications of current representation. METHODS: We compared racial/ethnic data of participants from array and sequencing studies in US AD genetics databases, including National Institute on Aging Genetics of Alzheimer's Disease Data Storage Site (NIAGADS) and NIAGADS Data Sharing Service (dssNIAGADS), to AD and related dementia (ADRD) prevalence and mortality. We then simulated the statistical power of these datasets to identify risk variants from non‐White populations. RESULTS: There is insufficient statistical power (probability <80%) to detect single nucleotide polymorphisms (SNPs) with low to moderate effect sizes (odds ratio [OR]<1.5) using array data from Black and Hispanic participants; studies of Asian participants are not powered to detect variants OR <= 2. Using available and projected sequencing data from Black and Hispanic participants, risk variants with OR = 1.2 are detectable at high allele frequencies. Sample sizes remain insufficiently powered to detect these variants in Asian populations. DISCUSSION: AD genetics datasets are largely representative of US ADRD burden. However, there is a wide discrepancy between proportional representation and statistically meaningful representation. Most variation identified in GWAS of non‐Hispanic White individuals have low to moderate effects. Comparable risk variants in non‐White populations are not detectable given current sample sizes, which could lead to disparities in future studies and drug development. We urge AD genetics researchers and institutions to continue investing in recruiting diverse participants and use community‐based participatory research practices. [ABSTRACT FROM AUTHOR]

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Testing the association between objects is central in ecology, evolution, and quantitative sciences in general. Two types of variables can describe the relationships between objects: point variables (measured on individual objects), and distance variables (measured between pairs of objects). The Mantel test and derived methods have been extensively used for distance variables. Yet, these methods have been criticized due to low statistical power and inflated type I error when spatial autocorrelation is present. Here, we assessed the statistical power between different types of tested variables and the type I error rate over a wider range of autocorrelation intensities than previously assessed, both on univariate and multivariate data. We also illustrated the performance of distance matrix statistics through computational simulations of genetic diversity. We show that the Mantel test and derived methods are not affected by inflated type I error when spatial autocorrelation affects only one variable when investigating correlations, or when either the response or the explanatory variable(s) is affected by spatial autocorrelation while investigating causal relationships. As previously noted, with autocorrelation affecting more variables, inflated type I error could be reduced by modifying the significance threshold. Additionally, the Mantel test has no problem of statistical power when the hypothesis is formulated in terms of distance variables. We highlight that transformation of variable types should be avoided because of the potential information loss and modification of the tested hypothesis. We propose a set of guidelines to help choose the appropriate method according to the type of variables and defined hypothesis. [ABSTRACT FROM AUTHOR]

Power analysis informs a priori planning of behavioral and medical research, including for randomized clinical trials that are nomothetic (i.e., studies designed to infer results to the general population based on interindividual variabilities). Far fewer investigations and resources are available for power analysis of clinical trials that follow an idiographic approach, which emphasizes intraindividual variabilities between baseline (control) phase versus one or more treatment phases. We tested the impact on statistical power to detect treatment outcomes of four idiographic trial design factors that are under researchers' control, assuming a multiple baseline design: sample size, number of observations per participant, proportion of observations in the baseline phase, and competing statistical models (i.e., hierarchical modeling versus piecewise regression). We also tested the impact of four factors that are largely outside of researchers' control: population size, proportion of intraindividual variability due to residual error, treatment effect size, and form of outcomes during the treatment phase (phase jump versus gradual change). Monte Carlo simulations using all combinations of the factors were sampled with replacement from finite populations of 200, 1750, and 3500 participants. Analyses characterized the unique relative impact of each factor individually and all two-factor combinations, holding all others constant. Each factor impacted power, with the greatest impact being from larger treatment effect sizes, followed respectively by more observations per participant, larger samples, less residual variance, and the unexpected improvement in power associated with assigning closer to 50% of observations to the baseline phase. This study's techniques and R package better enable a priori rigorous design of idiographic clinical trials for rare diseases, precision medicine, and other small-sample studies. [ABSTRACT FROM AUTHOR]

Trend is one of the data aspects that is an object of assessment in the context of single-case experimental designs. This assessment can be performed both visually and quantitatively. Given that trend, just like other relevant data features such as level, immediacy, or overlap does not have a single operative definition, a comparison among the existing alternatives is necessary. Previous studies have included illustrations of differences between trend-line fitting techniques using real data. In the current study, I carry out a simulation to study the degree to which different trend-line fitting techniques lead to different degrees of bias, mean square error, and statistical power for a variety of quantifications that entail trend lines. The simulation involves generating both continuous and count data, for several phase lengths, degrees of autocorrelation, and effect sizes (change in level and change in slope). The results suggest that, in general, ordinary least squares estimation performs well in terms of relative bias and mean square error. Especially, a quantification of slope change is associated with better statistical results than quantifying an average difference between conditions on the basis of a projected baseline trend. In contrast, the performance of the split-middle (bisplit) technique is less than optimal. [ABSTRACT FROM AUTHOR]

It is not uncommon for randomised trials in education to have the performance of sample members in national examinations as their primary outcome. In many cases, examination results are available as summary measures only. Taking the example of GCSE examination results in England, this paper shows that using summary measures of an underlying score or mark, such as exam grade, complicates the design of trials and can lead to underpowered studies. Simple simulations are used to explore the consequences of powering trials to detect a difference assuming grade or summary measures are the only outcome metric available, where the effects of an intervention are primarily captured in the unknown mark or score distribution. The analysis draws on data that relate the entire distribution of marks in English language and mathematics examinations to grades. Recommendations are made in order to address this problem. [ABSTRACT FROM AUTHOR]

The main purpose of this study is to examine the Type I error and statistical power ratios of Differential Item Functioning (DIF) techniques based on different theories under different conditions. For this purpose, a simulation study was conducted by using Mantel-Haenszel (MH), Logistic Regression (LR), Lord's ?2, and Raju's Areas Measures techniques. In the simulation-based research model, the two-parameter item response model, group's ability distribution, and DIF type were the fixed conditions while sample size (1800, 3000), rates of sample size (0.50, 1), test length (20, 80) and DIF-containing item rate (0, 0.05, 0.10) were manipulated conditions. The total number of conditions is 24 (2x2x2x3), and statistical analysis was performed in the R software. The current study found that the Type I error rates in all conditions were higher than the nominal error level. It was also demonstrated that MH had the highest error rate while Raju's Areas Measures had the lowest error rate. Also, MH produced the highest statistical power rates. The analysis of the findings of Type 1 error and statistical power rates illustrated that techniques based on both of the theories performed better in the 1800 sample size. Furthermore, the increase in the sample size affected techniques based on CTT rather than IRT. Also, the findings demonstrated that the techniques' Type 1 error rates were lower while their statistical power rates were higher under conditions where the test length was 80, and the sample sizes were not equal. [ABSTRACT FROM AUTHOR]

Abstract Background Since 1997, research on Gulf War illness (GWI) has predominantly used 3 case definitions—the original Research definition, the CDC definition, and modifications of the Kansas definition—but they have not been compared against an objective standard. Methods All 3 case definitions were measured in the U.S. Military Health Survey by a computer-assisted telephone interview in a random sample (n = 6,497) of the 1991 deployed U.S. military force. The interview asked whether participants had heard nerve agent alarms during the conflict. A random subsample (n = 1,698) provided DNA for genotyping the PON1 Q192R polymorphism. Results The CDC and the Modified Kansas definition without exclusions were satisfied by 41.7% and 39.0% of the deployed force, respectively, and were highly overlapping. The Research definition, a subset of the others, was satisfied by 13.6%. The majority of veterans meeting CDC and Modified Kansas endorsed fewer and milder symptoms; whereas, those meeting Research endorsed more symptoms of greater severity. The group meeting Research was more highly enriched with the PON1 192R risk allele than those meeting CDC and Modified Kansas, and Research had twice the power to detect the previously described gene-environment interaction between hearing alarms and RR homozygosity (adjusted relative excess risk due to interaction [aRERI] = 7.69; 95% CI 2.71–19.13) than CDC (aRERI = 2.92; 95% CI 0.96–6.38) or Modified Kansas without exclusions (aRERI = 3.84; 95% CI 1.30–8.52) or with exclusions (aRERI = 3.42; 95% CI 1.20–7.56). The lower power of CDC and Modified Kansas relative to Research was due to greater false-positive disease misclassification from lower diagnostic specificity. Conclusions The original Research case definition had greater statistical power to detect a genetic predisposition to GWI. Its greater specificity favors its use in hypothesis-driven research; whereas, the greater sensitivity of the others favor their use in clinical screening for application of future diagnostic biomarkers and clinical care.

Background: Since 1997, research on Gulf War illness (GWI) has predominantly used 3 case definitions—the original Research definition, the CDC definition, and modifications of the Kansas definition—but they have not been compared against an objective standard. Methods: All 3 case definitions were measured in the U.S. Military Health Survey by a computer-assisted telephone interview in a random sample (n = 6,497) of the 1991 deployed U.S. military force. The interview asked whether participants had heard nerve agent alarms during the conflict. A random subsample (n = 1,698) provided DNA for genotyping the PON1 Q192R polymorphism. Results: The CDC and the Modified Kansas definition without exclusions were satisfied by 41.7% and 39.0% of the deployed force, respectively, and were highly overlapping. The Research definition, a subset of the others, was satisfied by 13.6%. The majority of veterans meeting CDC and Modified Kansas endorsed fewer and milder symptoms; whereas, those meeting Research endorsed more symptoms of greater severity. The group meeting Research was more highly enriched with the PON1 192R risk allele than those meeting CDC and Modified Kansas, and Research had twice the power to detect the previously described gene-environment interaction between hearing alarms and RR homozygosity (adjusted relative excess risk due to interaction [aRERI] = 7.69; 95% CI 2.71–19.13) than CDC (aRERI = 2.92; 95% CI 0.96–6.38) or Modified Kansas without exclusions (aRERI = 3.84; 95% CI 1.30–8.52) or with exclusions (aRERI = 3.42; 95% CI 1.20–7.56). The lower power of CDC and Modified Kansas relative to Research was due to greater false-positive disease misclassification from lower diagnostic specificity. Conclusions: The original Research case definition had greater statistical power to detect a genetic predisposition to GWI. Its greater specificity favors its use in hypothesis-driven research; whereas, the greater sensitivity of the others favor their use in clinical screening for application of future diagnostic biomarkers and clinical care. [ABSTRACT FROM AUTHOR]

The N1, Tb, and P2 components of the event‐related potential (ERP) are thought to reflect the sequential processing of auditory stimuli in the human brain. Despite their extensive use in biological, cognitive, and clinical neuroscience, there are no guidelines for how to appropriately power ERP studies using these components. In the present study, we investigated how the number of trials, number of participants, effect magnitude, and study design influenced statistical power. Using Monte Carlo simulations of ERP data from a passive listening task, we determined the probability of finding a statistically significant effect in 58,900 experiments repeated 1,000 times each. We found that as the number of trials, number of participants, and effect magnitude increased, so did statistical power. We also found that increasing the number of trials had a bigger effect on statistical power for within‐subject designs than for between‐subject designs, and that within‐subject designs required a smaller number of trials and participants to provide the same level of statistical power for a given effect magnitude than between‐subject designs. These results show that it is important to carefully consider these factors when designing ERP studies, rather than relying on tradition or anecdotal evidence. To improve the robustness and reproducibility of ERP research, we have built an online statistical power calculator (https://bradleynjack.shinyapps.io/ErpPowerCalculator), which we hope will allow researchers to estimate the statistical power of previous studies, as well as help them design appropriately‐powered studies in the future. Using Monte Carlo simulations of ERP data from a passive listening task, we found that the number of trials, number of participants, effect magnitude, and study design interacted to influence statistical power for the N1, Tb, and P2 components. We hope that these results will improve the robustness and reproducibility of ERP research. [ABSTRACT FROM AUTHOR]

It is well-known that designing a cluster randomized trial (CRT) requires an advance estimate of the intra-cluster correlation coefficient (ICC). In the case of longitudinal CRTs, where outcomes are assessed repeatedly in each cluster over time, estimates for more complex correlation structures are required. Three common types of correlation structures for longitudinal CRTs are exchangeable, nested/block exchangeable and exponential decay correlations—the latter two allow the strength of the correlation to weaken over time. Determining sample sizes under these latter two structures requires advance specification of the within-period ICC and cluster autocorrelation coefficient as well as the intra-individual autocorrelation coefficient in the case of a cohort design. How to estimate these coefficients is a common challenge for investigators. When appropriate estimates from previously published longitudinal CRTs are not available, one possibility is to re-analyse data from an available trial dataset or to access observational data to estimate these parameters in advance of a trial. In this tutorial, we demonstrate how to estimate correlation parameters under these correlation structures for continuous and binary outcomes. We first introduce the correlation structures and their underlying model assumptions under a mixed-effects regression framework. With practical advice for implementation, we then demonstrate how the correlation parameters can be estimated using examples and we provide programming code in R, SAS, and Stata. An Rshiny app is available that allows investigators to upload an existing dataset and obtain the estimated correlation parameters. We conclude by identifying some gaps in the literature. [ABSTRACT FROM AUTHOR]

Cluster randomized trials (CRTs) are commonly used to evaluate educational interventions, particularly their effectiveness. Recently there has been greater emphasis on using these trials to explore cost-effectiveness. However, methods for establishing the power of cluster randomized cost-effectiveness trials (CRCETs) are limited. This study develops power computation formulas and statistical software to help researchers plan two- and three-level CRCETs. We illustrate the application of our formulas and software for the designs of CRCETs and discuss the influence of sample size, nesting effects, covariates, and the covariance between cost and effectiveness measures on the statistical power of cost-effectiveness estimates. [ABSTRACT FROM AUTHOR]