Power Of Statistical Tests Research Articles

The role of cluster size and intra-cluster correlations when adjusting for covariates in the analysis of cluster randomised trials

Reports of clinical trials often include adjusted analyses, which incorporate covariate data into the analysis model. Adjusting for covariates can increase the precision of treatment effect estimates and increase the power of statistical tests, without the need to increase sample size. In individually randomised trials, the main reason to adjust for a particular covariate is that it is expected to be strongly associated with the primary outcome. The larger the association between covariate and outcome, the greater the increase in power achieved from an adjusted analysis. A valid analysis of a cluster randomised trial (CRT) must take into account the clustered structure of the data, for example by using a mixed effects model. The selection of covariates for an adjusted analysis of a CRT is more complicated because covariates exist at both the cluster level and individual level. Further, adjustment for an individual level covariate can affect the residual variance of the outcome at both the cluster and individual levels. Using results from simulations, and some analytic investigation, I show how the size of clusters and the intra-cluster correlations of the covariate and outcome affect power and precision in adjusted analyses of CRTs using linear mixed effects models. I also consider logistic mixed effects models and show how adjusting for individual level or cluster level covariates affect what treatment effect is being estimated.

Reducing sample size in experiments with animals: historical controls and related strategies.

Reducing the number of animal subjects used in biomedical experiments is desirable for ethical and practical reasons. Previous reviews of the benefits of reducing sample sizes have focused on improving experimental designs and methods of statistical analysis, but reducing the size of control groups has been considered rarely. We discuss how the number of current control animals can be reduced, without loss of statistical power, by incorporating information from historical controls, i.e. subjects used as controls in similar previous experiments. Using example data from published reports, we describe how to incorporate information from historical controls under a range of assumptions that might be made in biomedical experiments. Assuming more similarities between historical and current controls yields higher savings and allows the use of smaller current control groups. We conducted simulations, based on typical designs and sample sizes, to quantify how different assumptions about historical controls affect the power of statistical tests. We show that, under our simulation conditions, the number of current control subjects can be reduced by more than half by including historical controls in the analyses. In other experimental scenarios, control groups may be unnecessary. Paying attention to both the function and to the statistical requirements of control groups would result in reducing the total number of animals used in experiments, saving time, effort and money, and bringing research with animals within ethically acceptable bounds.

Iso-population partition: An innovative epidemiological approach to mapping and analyzing spatially aggregated data

In epidemiology, data are often aggregated using administrative boundaries or regular spatial lattices. Iso-population partitioning methods allow the aggregation of small units for which population data are available into larger units that are contiguous, as compact as possible, and have a similar population size. The objective of this paper was to study the influence of three spatial data aggregation approaches on data visualization and data analysis: iso-populated units (IPUs), administrative units, and iso-geometric units. This study was conducted using results and simulations from the brucellosis clinical surveillance system for dairy cattle in France. Our findings indicate that using spatial partitioning methods for generating IPUs enhances the ability to interpret the spatial distribution of epidemiological indicators under study. In addition, it provides information on population density and improves the consistency of the power of statistical tests across units. By defining the target population size per spatial unit, IPUs can be used to control the statistical power of a study. Finally, by adding criteria based on environmental factors to generate spatial units, they can be used to control the variation of exposure to these factors within the units.

An adaptive step-down procedure for fault variable identification

In a process with a large number of process variables (high-dimensional process), identifying which variables cause an out-of-control signal is a challenging issue for quality engineers. In this paper, we propose an adaptive step-down procedure using conditional T2 statistic for fault variable identification. While existing procedures focus on selecting variables that have strong evidence of a change, the proposed step-down procedure selects a variable having the weakest evidence of a change at each step based on the variables that are selected in previous steps. The information of selected unchanged variables is effectively utilised in obtaining a powerful conditional T2 test statistic for identifying the changed elements of the mean vector. The proposed procedure is designed to utilise the correlation information between fault and non-fault variables for the efficient fault variables identification. Further, the simulation results show that the proposed procedure has the better diagnostic performance compared with existing methods in terms of fault variable identification and computational complexity, especially when the number of the variables is high and the number of fault variables is small.

A powerful test for Balaam's design.

The crossover trial design (AB/BA design) is often used to compare the effects of two treatments in medical science because it performs within-subject comparisons, which increase the precision of a treatment effect (i.e., a between-treatment difference). However, the AB/BA design cannot be applied in the presence of carryover effects and/or treatments-by-period interaction. In such cases, Balaam's design is a more suitable choice. Unlike the AB/BA design, Balaam's design inflates the variance of an estimate of the treatment effect, thereby reducing the statistical power of tests. This is a serious drawback of the design. Although the variance of parameter estimators in Balaam's design has been extensively studied, the estimators of the treatment effect to improve the inference have received little attention. If the estimate of the treatment effect is obtained by solving the mixed model equations, the AA and BB sequences are excluded from the estimation process. In this study, we develop a new estimator of the treatment effect and a new test statistic using the estimator. The aim is to improve the statistical inference in Balaam's design. Simulation studies indicate that the type I error of the proposed test is well controlled, and that the test is more powerful and has more suitable characteristics than other existing tests when interactions are substantial. The proposed test is also applied to analyze a real dataset.

FASHION CONSUMERS' ACCEPTANCE OF RETAIL TECHNOLOGY: A META-ANALYSIS OF TAM IN FASHION RETAIL CONTEXT

The information technology has affected many aspects of retail world as in other areas of human life. This makes understanding consumers’ acceptance and usage of such technological innovations a critical task for both retail businesses and scholars alike. The technology acceptance model (TAM; Davis 1989) is one of the most widely adopted theoretical frameworks for explaining and predicting consumers’ acceptance of technology. Implementing the meta-analysis method, this study aimed at testing the validity of TAM for understanding consumers’ attitudes and behaviors toward the various technologies adopted in fashion retail stores and online commerce sites. Specifically, the effect sizes of two TAM antecedents of perceived usefulness (PU) and ease of use (PEOU) were estimated and compared. Moderating factors that affect the effect sizes of PU and PEOU on attitudes and behaviors were also explored. A meta-analytical SEM methodology was expected to deliver more thorough and valid test of the model than single sample studies, because accumulation of multiple samples through meta-analysis would bolster the test's statistical power (Hom et al., 1992).A sample of studies on consumers’ acceptance of retail technology in fashion retail context that adopted the TAM model were collected through a systematic search through the databases such as EBSCO, Google Scholars, and Dissertation Abstracts. Efforts were made to include unpublished studies to avoid publication bias. A total of 31 published and unpublished research reports that allowed the calculation of effect sizes of the key paths in the model were included in the final analysis.The effect sizes were calculated out of the identified samples, and the homogeneities of the effect sizes were tested using comprehensive meta-analysis software. The types of technology, product type (apparel vs. general merchandise), subject characteristics (gender; country; student vs. general), and study setting (actual experience vs. simulated situation) were considered as moderators to explain for the variances in correlations among variables. Finally, a meta-SEM model was tested on the aggregated data using AMOS.

An Iterative Leave-One-Out Approach to Outlier Detection in RNA-Seq Data.

The discrete data structure and large sequencing depth of RNA sequencing (RNA-seq) experiments can often generate outlier read counts in one or more RNA samples within a homogeneous group. Thus, how to identify and manage outlier observations in RNA-seq data is an emerging topic of interest. One of the main objectives in these research efforts is to develop statistical methodology that effectively balances the impact of outlier observations and achieves maximal power for statistical testing. To reach that goal, strengthening the accuracy of outlier detection is an important precursor. Current outlier detection algorithms for RNA-seq data are executed within a testing framework and may be sensitive to sparse data and heavy-tailed distributions. Therefore, we propose a univariate algorithm that utilizes a probabilistic approach to measure the deviation between an observation and the distribution generating the remaining data and implement it within in an iterative leave-one-out design strategy. Analyses of real and simulated RNA-seq data show that the proposed methodology has higher outlier detection rates for both non-normalized and normalized negative binomial distributed data.

Nonlinearity testing and modeling for threshold moving average models

In this paper, we suggest a simple test and an easily applicable modeling procedure for threshold moving average (TMA) models. Firstly, based on the fitted residuals by maximum likelihood estimate (MLE) for MA models, we construct a simple statistic, which is obtained by linear arrange regression and follows F-distribution approximately, to test for threshold nonlinearity and specify the threshold variables. And then, we use some scatterplots to identify the number and locations of the potential thresholds. Finally, with the statistic and Akaike information criterion, we propose the procedure to build TMA models. Both the power of test statistic and the convenience of modeling procedure can work very well demonstrated by simulation experiments and the application to a real example.

A Brief Ode to the Empirical Likelihood Concept

robust likelihood-type techniques. Towards this end, the modern biostatistical literature has shifted focus towards robust and efficient nonparametric likelihood methods [2]. The empirical likelihood (EL) methodology employs the likelihood concept in a distribution-free manner, approximating optimal parametric likelihood-based procedures. Since EL techniques and parametric likelihood methods are closely related concepts, one may apply corresponding EL functions to replace their parametric likelihood counterparts in known and well developed parametric procedures, e.g. constructing novel nonparametric Bayesian inference [3] and the confidence interval estimation [4]. This provides the impetus for an impressive expansion in the number of EL developments based on combinations of likelihoods of different types, e.g., when incomplete data should be analyzed, nonparametric likelihood ratio techniques can be combined with parametric likelihoods [5]. The classical EL methodology, which is a distribution functionbased approach, has been shown to have attractive properties for testing hypotheses regarding parameters (e.g. moments) of distributions [6]. In practice, statisticians commonly face a variety of distribution-free comparisons and/or evaluations over all distribution functions of complete and incomplete data subject to different types of measurement errors. In these frameworks, the density-based EL methodology is shown to be very efficient [710]. According to the Neyman-Pearson lemma, the most powerful test statistics have structures that are related to density-based likelihood ratios. The density-based EL method can be easily and satisfactorily applied to construct highly efficient test procedures, approximating non-parametrically most powerful NeymanPearson test-rules, given aims of clinical studies. Similarly to the parametric likelihood concept, the EL methodology provides relatively simple strategies to construct powerful statistical tests that can be applied in various complex biostatistical studies. The extreme generality of EL methods and their wide ranges of usefulness partly result from the simple derivation of the EL statistics as components of composite parametric and nonparametric likelihood based systems, efficiently attending to any observed data and relevant information. The EL based methods are employed in much of modern biostatistical practice.

A statistical approach for detecting common features

BackgroundWith increasing numbers of datasets in neuroimaging studies, it has become an important task to pool information, in order to increase the statistical power of tests and for cross validation. However, no robust global approach unambiguously identifies the common biological abnormalities in, for example, resting-state functional magnetic resonance imaging in a number of mental disorders, where there are multiple datasets/attributes. Here we propose a novel and efficient statistical approach to this problem that finds common features in multiple datasets. New methodBy collecting the statistics of each dataset into a vector, our method uses a ‘multi-dimensional local false discovery’ rate to pool information and make full use of the joint distribution of datasets. ResultsWe have tested our approach extensively on both simulated and clinical datasets. By conducting simulation studies, we find that our approach has a higher statistical power than existing approaches, especially on correlated datasets. Employing our approach on clinical data yields findings that are consistent with the existing literature. Comparison with existing methodsConventional methods cannot determine the false discovery rate underlying multiple datasets/attributes. Our approach can effectively handle these datasets. It has a solid Bayesian interpretation, and a higher power than other approaches in numerical simulations. This can be explained by the incorporation of correlations, between different attributes, into the new method. ConclusionsIn this work, we present a natural, novel and powerful statistical approach to tackle situations involving multiple datasets or attributes. This new method has significant advantages over existing approaches and wide applications.

Calcular e apresentar tamanhos do efeito em trabalhos científicos (1): As limitações do p < 0,05 na análise de diferenças de médias de dois grupos

A Revista Portuguesa de Investigação Comportamental e Social exige que os autores sigam as recomendações do Publication Manual of the American Psychological Association (APA, 2010) na apresentação da informação estatística. Uma das recomendações da APA é de que os tamanhos do efeito sejam apresentados associados aos níveis de significância estatística.Uma vez que os valores de p decorrentes dos resultados dos testes estatísticos não informam sobre a magnitude ou importância de uma diferença, devem então reportar-se os tamanhos do efeito (TDE). De facto, os TDE dão significado aos testes estatísticos, enfatizam o poder dos testes estatísticos, reduzem o risco de a mera variação amostral ser interpretada como relação real, podem aumentar o relato de resultados “não-significativos” e permitem acumular conhecimento de vários estudos usando a meta-análise.Assim, os objetivos deste artigo são os de apresentar os limites do nível de significância; descrever os fundamentos da apresentação dos TDE dos testes estatísticos para análise de diferenças entre dois grupos; apresentar as fórmulas para calcular os TDE, fornecendo exemplos de estudos nossos; apresentar procedimentos de cálculo dos intervalos de confiança; fornecer as fórmulas de conversão para revisão da literatura; indicar como interpretar os TDE; e ainda mostrar que, apesar de frequentemente ser interpretável, o significado (efeito pequeno, médio ou grande para uma métrica arbitrária) pode ser impreciso, havendo necessidade de ser interpretado no contexto da área de investigação e de variáveis do mundo real.

Protection of a Nuclear Reactor Monitoring System against Gross Measurement Errors

Data Validation and Reconciliation (DVR) is a basic tool for protection of industrial monitoring systems against gross measurement errors. However, the power of this approach is frequently not fully exploited. This paper concentrates on protection of key results against gross and systematic errors. On‐line monitoring can allow a continuous protection of measurement targets against gross errors in measurement chains. The measurement target can be, for example, a nuclear reactor heat output while errors can be hidden in measured flows and state variables of steam and water. The methodology presented here allows a gross error to be identified while maintaining an accurate value of the target variable. In analogy with statistics (power of statistical tests) we can define the probability of success as a power of the Monitoring System Self‐Protection (MSSP). A new simple method for assessing the MSSP power is presented. The MSSP is important for monitoring system maintenance and the optimal placement of additional instruments. It shows which primary variables are self‐checked by the redundancy of the system and which should be checked (calibrated) independently. The problem is illustrated by an example taken from one nuclear power station.

Understanding Effect Sizes

In most medical research the P value is commonly used to describe test results. Because the power of statistical test is influenced by sample size, the null hypothesis can be rejected (P< 0.05) in most cases if the sample size is tremendously big even if the real difference (or relationship) is extremly small. To overcome the weakness of using the P value, effect size can be used in the statistical analysis. Effect size can be defined as the “degree to which the phenomenon (difference or relationship) is present in the population”. The effect size is used in sample size calculation, data interpretation and conducting meta-analysis. This manuscript describes limitations in using the P value and further introduces the concept of effect size.

The power of statistical tests using field trial count data of nontarget organisms in environmental risk assessment of genetically modified plants

Publications on power analyses for field trial count data comparing transgenic and conventional crops have reported widely varying requirements for the replication needed to obtain statistical tests with adequate power. These studies are critically reviewed and complemented with a new simulation study. The reasons for the different reports are elucidated and can be classified as additional (but hidden) replication, selection of favourable endpoints with low variation, and reporting at an unusual scale. A new simulation study was performed to investigate the relationship between statistical power and replication under a variety of data-generating and analysis methods. Approximately 60 replications should be sufficient to detect a 50% (two-fold) decrease in taxon numbers, provided that the coefficient of variation in the counts does not exceed 100%. Replication can be accomplished not only by using multiple blocks in a single trial, but also by repeating the experiment in multiple years and/or at different sites. With other (e.g. agronomic) treatment factors in the field trial, without interaction with variety, the effective replication can be increased by investigating the main variety effect summed over the other treatment factors. Repeated measures may also increase the power if the expected difference is equal over time and the time points are sufficiently spaced.

Macrolepidoptera biodiversity in Wooster, Ohio from 2001 through 2009.

A Skinner mercury vapor light trap was operated from 2001 through 2009 in a residential backyard to document biodiversity within the moth families Thyatiridae, Drepanidae, Geometridae, Mimallonidae, Apatelodidae, Lasiocampidae, Saturniidae, Sphingidae, Erebidae (including Lymantriinae and Arctiinae), Euteliidae, Nolidae, and Noctuidae. When making comparisons to older literature, we recalculated our results to conform to the older classification of the Noctuoidea. Moths were released after identification. There were 501 species documented in 77581 captures from 1290 sampling dates. There was a perceived risk that released moths would fly back into the trap the following evening. This should result in an abnormal number of rare moths that are caught multiple times. The number of species caught twice versus the number caught once was no different than a similar ratio for surveys that used more traditional sampling methods. Therefore this concern does not seem to be valid for these data. These data are provided in a supplementary file available for download.There were three previous surveys conducted in nearby natural areas. They documented fewer species than were documented here. To understand this better, we examined several specialized groups of moths that tend to use host plants not typically found in an urban residential yard. More species in Schinia Hübner, Catocala Schrank, Acronicta Ochsenheimer, and Herminiinae Leech were found in this survey than the other local surveys. Only in the Papaipema Smith did we recover fewer species, though it was still above 70% of what was expected. This diversity could be a result of sampling effort, but it shows that this urban location has a very diverse moth fauna. We suggest that this diversity is partly due to the planting of native plant species in the area about the light trap. Therefore we would concur with others that urban landscapes can be planned to increase biodiversity relevant to more natural ecosystems.In this study we looked at the ratio of the number of species of Geometridae divided by the number of species of Noctuidae as one approach to evaluating the level of disturbance in the moth assemblage. Although the yearly average was nearly constant, the seasonal ratio ranged from 0.09 to 0.91 depending on the sampling date. We also calculated alpha diversity and found that seasonal change in alpha diversity greatly exceeded yearly differences. This strong seasonal component means that a comparison between two studies requires a correction for seasonality and similar sampling intervals. In this study, a shift of two weeks would be sufficient to result in a significant difference in alpha diversity. This is the equivalent of increasing temperature by 1.53 °C. Seasonal shifts limit the usefulness of this methodology for environmental assessment because the within season change exceeds the between season change. This problem is compounded when sampling designs interact with this seasonality.In describing our data, we made use of a growing degree day (GDD) model. This approach corrects for simple temperature dependent shifts in moth biology. Consequently, some of the variability in the data was removed, which should improve the power of statistical tests involving survey data. If sampling protocols were based on growing degree days rather than calendar dates, the bias caused by temperature induced shifts in seasonal cycles could be reduced.

Multilevel Modeling in the Context of Growth Modeling

Multilevel modeling is a flexible approach for the analysis of nested data structures, such as those encountered in longitudinal studies with repeated measures of an outcome of interest taken across time and nested within subjects. The baseline score on the outcome and rate of change vary across subjects, and subject level predictor variables may be used to explain part of the between-subject variability. This contribution shows how to formulate linear and logistic models for continuous and binary outcomes. A study of the effect of growth hormone in adolescents with short stature is used as an illustrative example to demonstrate the use of these models and to aid in the interpretation of model parameter estimates. Attention is also paid to sufficient sample sizes, and two methods to explore the relation between sample size and power of statistical tests are discussed.

Testing predictor significance with ultra high dimensional multivariate responses

We consider here the problem of testing the effect of a subset of predictors for a regression model with predictor dimension fixed but ultra high dimensional responses. Because the response dimension is ultra high, the classical method of likelihood ratio test is no longer applicable. To solve the problem, we propose a novel solution, which decomposes the original problem into many testing problems with univariate responses. Subsequently, the usual residual sum of squares (RSS) type test statistics can be obtained. Those statistics are then integrated together across different responses to form an overall and powerful test statistic. Under the null hypothesis, the resulting test statistic is asymptotically standard normal after some appropriate standardization. Numerical studies are presented to demonstrate the finite sample performance of the test statistic and a real example about paid search advertising is analyzed for illustration purpose.

Detecting associated single-nucleotide polymorphisms on the X chromosome in case control genome-wide association studies

In the past decade, hundreds of genome-wide association studies have been conducted to detect the significant single-nucleotide polymorphisms that are associated with certain diseases. However, most of the data from the X chromosome were not analyzed and only a few significant associated single-nucleotide polymorphisms from the X chromosome have been identified from genome-wide association studies. This is mainly due to the lack of powerful statistical tests. In this paper, we propose a novel statistical approach that combines the information of single-nucleotide polymorphisms on the X chromosome from both males and females in an efficient way. The proposed approach avoids the need of making strong assumptions about the underlying genetic models. Our proposed statistical test is a robust method that only makes the assumption that the risk allele is the same for both females and males if the single-nucleotide polymorphism is associated with the disease for both genders. Through simulation study and a real data application, we show that the proposed procedure is robust and have excellent performance compared to existing methods. We expect that many more associated single-nucleotide polymorphisms on the X chromosome will be identified if the proposed approach is applied to current available genome-wide association studies data.

Robust analysis with related samples under the presence of population substructure and its application to body mass index

Recent investigations such as a more powerful quasi-likelihoods score test (MQLS) statistic have enabled the efficient association analysis with related samples. Although those approaches are robust against the mis-specified phenotypic distribution and covariance structure, it has been shown that MQLS statistic becomes violated under the presence of the population substructure if the level of population substructure depends on the genomic location. In this report, we propose a new statistical method which combines EIGENSTRAT approach and MQLS-statistic. The proposed method was evaluated with simulation data under various scenarios and we found that proposed method performs better than the traditional methods such as transmission disequilibrium test. The proposed method was applied to genetic association analysis for body mass index with Framingham heart study, and we found that rs1121980 and rs9940128 in the linkage block in FTO gene are associated with the body mass index.

L.U.St: a tool for approximated maximum likelihood supertree reconstruction.

BackgroundSupertrees combine disparate, partially overlapping trees to generate a synthesis that provides a high level perspective that cannot be attained from the inspection of individual phylogenies. Supertrees can be seen as meta-analytical tools that can be used to make inferences based on results of previous scientific studies. Their meta-analytical application has increased in popularity since it was realised that the power of statistical tests for the study of evolutionary trends critically depends on the use of taxon-dense phylogenies. Further to that, supertrees have found applications in phylogenomics where they are used to combine gene trees and recover species phylogenies based on genome-scale data sets.ResultsHere, we present the L.U.St package, a python tool for approximate maximum likelihood supertree inference and illustrate its application using a genomic data set for the placental mammals. L.U.St allows the calculation of the approximate likelihood of a supertree, given a set of input trees, performs heuristic searches to look for the supertree of highest likelihood, and performs statistical tests of two or more supertrees. To this end, L.U.St implements a winning sites test allowing ranking of a collection of a-priori selected hypotheses, given as a collection of input supertree topologies. It also outputs a file of input-tree-wise likelihood scores that can be used as input to CONSEL for calculation of standard tests of two trees (e.g. Kishino-Hasegawa, Shimidoara-Hasegawa and Approximately Unbiased tests).ConclusionThis is the first fully parametric implementation of a supertree method, it has clearly understood properties, and provides several advantages over currently available supertree approaches. It is easy to implement and works on any platform that has python installed.Availability: bitBucket page - https://afro-juju@bitbucket.org/afro-juju/l.u.st.git.Contact: Davide.Pisani@bristol.ac.uk.