Power Of Statistical Tests Research Articles

MEScan: a powerful statistical framework for genome-scale mutual exclusivity analysis of cancer mutations.

Cancer somatic driver mutations associated with genes within a pathway often show a mutually exclusive pattern across a cohort of patients. This mutually exclusive mutational signal has been frequently used to distinguish driver from passenger mutations and to investigate relationships among driver mutations. Current methods for de novo discovery of mutually exclusive mutational patterns are limited because the heterogeneity in background mutation rate can confound mutational patterns, and the presence of highly mutated genes can lead to spurious patterns. In addition, most methods only focus on a limited number of pre-selected genes and are unable to perform genome-wide analysis due to computational inefficiency. We introduce a statistical framework, MEScan, for accurate and efficient mutual exclusivity analysis at the genomic scale. Our framework contains a fast and powerful statistical test for mutual exclusivity with adjustment of the background mutation rate and impact of highly mutated genes, and a multi-step procedure for genome-wide screening with the control of false discovery rate. We demonstrate that MEScan more accurately identifies mutually exclusive gene sets than existing methods and is at least two orders of magnitude faster than most methods. By applying MEScan to data from four different cancer types and pan-cancer, we have identified several biologically meaningful mutually exclusive gene sets. MEScan is available as an R package at https://github.com/MarkeyBBSRF/MEScan. Supplementary data are available at Bioinformatics online.

Tail-Robust Quantile Normalization.

High-throughput biological data-such as mass spectrometry (MS)-based proteomics data-suffer from systematic non-biological variance due to systematic errors. This hinders the estimation of "real" biological signals and, in turn, decreases the power of statistical tests and biases the identification of differentially expressed proteins. To remove such unintended variation, while retaining the biological signal of interest, analysis workflows for quantitative MS data typically comprise normalization prior to their statistical analysis. Several normalization methods, such as quantile normalization (QN), have originally been developed for microarray data. In contrast to microarray data proteomics data may contain features, in the form of protein intensities that are consistently high across experimental conditions and, hence, are encountered in the tails of the protein intensity distribution. If QN is applied in the presence of such proteins statistical inferences of the features' intensity profiles are impeded due to the biased estimation of their variance. A freely available, novel approach is introduced which serves as an improvement of the classical QN by preserving the biological signals of features in the tails of the intensity distribution and by accounting for sample-dependent missing values (MVs): The "tail-robust quantile normalization" (TRQN).

TEST OF SIGNIFICANCE FOR HIGH-DIMENSIONAL LONGITUDINAL DATA.

This paper concerns statistical inference for longitudinal data with ultrahigh dimensional covariates. We first study the problem of constructing confidence intervals and hypothesis tests for a low dimensional parameter of interest. The major challenge is how to construct a powerful test statistic in the presence of high-dimensional nuisance parameters and sophisticated within-subject correlation of longitudinal data. To deal with the challenge, we propose a new quadratic decorrelated inference function approach, which simultaneously removes the impact of nuisance parameters and incorporates the correlation to enhance the efficiency of the estimation procedure. When the parameter of interest is of fixed dimension, we prove that the proposed estimator is asymptotically normal and attains the semiparametric information bound, based on which we can construct an optimal Wald test statistic. We further extend this result and establish the limiting distribution of the estimator under the setting with the dimension of the parameter of interest growing with the sample size at a polynomial rate. Finally, we study how to control the false discovery rate (FDR) when a vector of high-dimensional regression parameters is of interest. We prove that applying the Storey (2002)'s procedure to the proposed test statistics for each regression parameter controls FDR asymptotically in longitudinal data. We conduct simulation studies to assess the finite sample performance of the proposed procedures. Our simulation results imply that the newly proposed procedure can control both Type I error for testing a low dimensional parameter of interest and the FDR in the multiple testing problem. We also apply the proposed procedure to a real data example.

Iteratively reweighted total least squares for PEIV model

The weighted total least-squares (WTLS) estimate for the partial EIV (PEIV) model is very susceptible to outliers. In view of outliers in observations and coefficient matrix, a robust estimate of WTLS which makes using of iteratively reweighted technique (IRTLS) for the PEIV model is developed by combining a new two-step iterated algorithm of the WTLS estimate with the sensitivity-analysis based on the robust M-estimation. The uniformly most powerful test statistics are constructed to determine the down-weighting factor and the variance of unit weight is estimated by least median squares (LMS) method possessing high break-down point. Depended on the PEIV model, two different down-weighting schemes are presented. In the first scheme down-weighting is only implemented for the coefficient matrix and not for observations when the elements of the coefficient matrix are estimated, and the second scheme is contrary. The most attractive aspect is that the suggested computational formulae are the same with the traditional robust least-squares (LS) methods. The two-dimensional affine transformation and liner fitting example are analyzed, and some comparisons are performed with different available weight functions. The proposed approach (Scheme 1) proves to be a powerful tool in detecting outliers for the PEIV model.

Software-Based Approach towards Automated Authorship Acknowledgement—Chi-Square Test on One Consonant Group

A one-consonant group approach to the authorship attribution has been proposed. The approach is based on determining, by the chi-square test, the consonant group in which the difference between the texts by different authors is statistically significant. The developed model determines author-differentiating capability of each consonant group in a relation of the number of comparisons, in which the difference between the texts by two authors is statistically significant to the total number of comparisons. The determined general author-differentiating capability of the group of stop consonants, which is a statistical parameter of the authorial style, is the highest in the comparisons of texts from the publicist and belles-lettres styles. The one-consonant group approach simplifies the whole process of authorship attribution and ensures a higher level of automation. The conducted experiments on the Java programming language have proved that the chi-square test is a powerful nonparametric statistical test that can be used for author identification on the level of English consonants with a test validity of 95%.

Testing the equality of the spectral densities of several uncorrelated almost cyclostationary processes

In this work, a new approach to compare the spectral densities of several uncorrelated almost cyclostationary processes is proposed. The asymptotic distribution of the discrete Fourier transform is used to establish a powerful test statistic. The behavior of the introduced technique is examined in both simulation study and real data case. The results verify the suitability and applicability of the given approach.

Influence of group sample size on statistical power of tests for quantitative data with an imbalanced design

To explore the relationship between sample size in the groups and statistical power of ANOVA and Kruskal-Wallis H test with an imbalanced design. The sample sizes of the two tests were estimated by SAS program with given parameter settings, and Monte Carlo simulation was used to examine the changes in power when the total sample size varied or remained fixed. In ANOVA, when the total sample size was fixed, increasing the sample size in the group with a larger mean square error improved the statistical power, but an excessively large difference in the sample sizes between groups led to reduced power. When the total sample size was not fixed, a larger mean square error in the group with increased sample size was associated with a greater increase of the statistical power. In Kruskal-wallis H test, when the total sample size was fixed, increasing the sample size in groups with large mean square errors increased the statistical power irrespective of the sample size difference between the groups; when total sample size was not fixed, a larger mean square error in the group with increased sample size resulted in an increased statistical power, and the increment was similar to that for a fixed total sample size. The relationship between statistical power and sample size in groups is affected by the mean square error, and increasing the sample size in a group with a large mean square error increases the statistical power. In Kruskal-Wallis H test, increasing the sample size in a group with a large mean square error is more cost- effective than increasing the total sample size to improve the statistical power.

Large‐scale identification of expression quantitative trait loci in Arabidopsis reveals novel candidate regulators of immune responses and other processes

The extensive phenotypic diversity within natural populations of Arabidopsis is associated with differences in gene expression. Transcript levels can be considered as inheritable quantitative traits, and used to map expression quantitative trait loci (eQTL) in genome-wide association studies (GWASs). In order to identify putative genetic determinants for variations in gene expression, we used publicly available genomic and transcript variation data from 665 Arabidopsis accessions and applied the single nucleotide polymorphism-set (Sequence) Kernel Association Test (SKAT) method for the identification of eQTL. Moreover, we used the penalized orthogonal-components regression (POCRE) method to increase the power of statistical tests. Then, gene annotations were used as test units to identify genes that are associated with natural variations in transcript accumulation, which correspond to candidate regulators, some of which may have a broad impact on gene expression. Besides increasing the chances to identify real associations, the analysis using POCRE and SKAT significantly reduced the computational cost required to analyze large datasets. As a proof of concept, we used this approach to identify eQTL that represent novel candidate regulators of immune responses. The versatility of this approach allows its application to any process that is subjected to natural variation among Arabidopsis accessions.

Sequential hypothesis tests for multinomial processing tree models

Stimulated by William H. Batchelder’s seminal contributions in the 1980s and 1990s, multinomial processing tree (MPT) modeling has become a powerful and frequently used method in various research fields, most prominently in cognitive psychology and social cognition research. MPT models allow for estimation of, and statistical tests on, parameters that represent psychological processes underlying responses to cognitive tasks. Therefore, their use has also been proposed repeatedly for purposes of psychological assessment, for example, in clinical settings to identify specific cognitive deficits in individuals. However, a considerable drawback of individual MPT analyses emerges from the limited number of data points per individual, resulting in estimation bias, large standard errors, and low power of statistical tests. Classical test procedures such as Neyman–Pearson tests often require very large sample sizes to ensure sufficiently low Type 1 and Type 2 error probabilities. Herein, we propose sequential probability ratio tests (SPRTs) as an efficient alternative. Unlike Neyman–Pearson tests, sequential tests continuously monitor the data and terminate when a predefined criterion is met. As a consequence, SPRTs typically require only about half of the Neyman–Pearson sample size without compromising error probability control. We illustrate the SPRT approach to statistical inference for simple hypotheses in single-parameter MPT models. Moreover, a large-sample approximation, based on ML theory, is presented for typical MPT models with more than one unknown parameter. We evaluate the properties of the proposed test procedures by means of simulations. Finally, we discuss benefits and limitations of sequential MPT analysis.

Pitfalls in statistical analysis – A Reviewers' perspective

Statistics are a quintessential part of scientific manuscripts. Few journals are free of statistics-related errors. Errors can occur in data reporting and presentation, choosing the appropriate or the most powerful statistical test, misinterpretation or overinterpretations of statistics, and ignoring tests of normality. Statistical software used, one-tailed versus two-tailed tests, and exclusion or inclusion of outliers can all influence outcomes and should be explicitly mentioned. This review presents the corresponding nonparametric tests for common parametric tests, popular misinterpretations of the P value, and usual nuances in data reporting. The importance of distinguishing clinical significance from statistical significance using confidence intervals, number needed to treat, and minimal clinically important difference is highlighted. The problem of multiple comparisons may lead to false interpretations, especially in p-hacking when nonsignificant comparisons are concealed. The review also touches upon a few advanced topics such as heteroscedasticity and multicollinearity in multivariate analyses. Journals have various strategies to minimize inaccuracies, but it is invaluable for authors and reviewers to have good concepts of statistics. Furthermore, it is imperative for the reader to understand these concepts to properly interpret studies and judge the validity of the conclusions independently.

ARFIMA Model for Short Term Forecasting of New Death Cases COVID-19

COVID-19 is an infectious disease that can spread from one person to another and has a high potential for death. The infection of COVID-19 is spreading massive and fast that causes the extreme fluctuating data spread and long memory effects. One of the ways in which the death of COVID-19 can be reduce is to produce a prediction model that could be used as a reference in taking countermeasures. There are various prediction models, from regression to Autoregressive Fractional Integrated Moving Average (ARIMA), but it still shows shortcomings when disturbances occur from extreme fluctuations and the existence of long memory effects in the form of analysis of a series of data becomes biased, and the power of statistical tests generated for identification become weak. Therefore, the prediction model with the Autoregressive Fractional Integrated Moving Average (ARFIMA) approach was used in this study to accommodate these weaknesses because of their flexible nature and high accuracy. The results of this study prove that ARFIMA (1,0,431.0) with an RMSE of 2,853 is the best model to predict data on the addition of new cases of patients dying from COVID-19.

Review of Outlier Detection and Identifying Using Robust Regression Model

Outliers are observations that have extreme value relations. Herewith leverage is a measure of how an independent variable deviates from its mean. An observation with an extreme value on a predictor variable is a point with high leverage. The presence of outliers can lead to inflated error rates and substantial distortions of parameter and statistic estimates when using either parametric or nonparametric tests. Casual observation of the literature suggests that researchers rarely report checking for outliers of any sort and taking remedial measures for outliers. Outliers can have positive deleterious effects on statistical analyses. For instance, they serve to increase error variance and reduce the power of statistical tests; they can decrease normality, altering the odds of making both Type I and Type II errors for non- randomly distributed; and they can seriously bias or influence estimates that may be of substantive interest. These outliers are cased from incorrect recording data, intentional or motivated mis-reporting, sampling error and Outliers as legitimate cases sampled from the correct population. According to some literatures; Point outliers, Contextual Outliers and Collective Outliers are the three types of outliers. Robust regression estimators can be a powerful tool for detection and identifying outliers in complicated data sets. Robust regression, deals with the problem of outliers in a regression and produce different coefficient estimates than OLS does.

A modified Spearman’s rho parameter-free test statistic for early detection of newly emerging phenomena

This paper presents a new and powerful parameter-free test statistic for early detection of newly emerging phenomena, especially for small sample sizes. The exact distribution of the proposed test statistic is obtained. First four cumulants of it and its critical values at some selected levels of significances are calculated and summarized. A comparative simulation study is performed with some well-known rank-based tests to see its power performance.

Defining a termite sampling protocol for ecological studies: An effective method to increase statistical power

Protocols for sampling soil fauna are usually designed to increase the number of species found when one or a few plots are heavily sampled. However, no previous study has evaluated how the number of plots sampled affect the power of statistical tests associating community composition and the environment. We test the effect of the number of transects (plots) and the sampling effort in each transect on the representation of trophic groups and on the association of termite species composition with environmental variables. Data were collected in 30 250m-long transects located in central Amazonia. Each transect was subdivided into 10 non-contiguous sections of 5 m × 2 m each (separation of 22 m between sections). We rarefied the data to determine arrangement of transects and sections that 1) best characterizes the distribution of species in trophic groups and 2) maximizes the chances to detect true associations between termite species composition and environmental predictor variables. When more than six transects (plots) were sampled with at least five non-contiguous sections each, the distribution of trophic groups was similar to the known distribution for the area. However, the detection of the association between termite species composition and environmental variables was more easily detected by increasing the number of transects sampled (plots) than the sampling effort per transect. Our results suggest that spreading sampling effort into at least 15 transects (plots) improves the ability to detect trophic groups and the performance of regression tests associating the composition of species with the environment.

Neural network integration of classical statistical tests for processing small samples of biometrics data

The Aim of this paper is to increase the power of statistical tests through their joint application to reduce the requirement for the size of the test sample. Methods. It is proposed to combine classical statistical tests, i.e. chi square, Cram r-von Mises and Shapiro-Wilk by means of using equivalent artificial neurons. Each neuron compares the input statistics with a precomputed threshold and has two output states. That allows obtaining three bits of binary output code of a network of three artificial neurons. Results. It is shown that each of such criteria on small samples of biometric data produces high values of errors of the first and second kind in the process of normality hypothesis testing. Neural network integration of three tests under consideration enables a significant reduction of the probabilities of errors of the first and second kind. The paper sets forth the results of neural network integration of pairs, as well as triples of statistical tests under consideration. Conclusions. Expected probabilities of errors of the first and second kind are predicted for neural network integrations of 10 and 30 classical statistical tests for small samples that contain 21 tests. An important element of the prediction process is the symmetrization of the problem, when the probabilities of errors of the first and second kind are made identical and averaged out. Coefficient modules of pair correlation of output states are averaged out as well by means of artificial neuron adders. Only in this case the connection between the number of integrated tests and the expected probabilities of errors of the first and second kind becomes linear in logarithmic coordinates.

Introduction of a User-oriented Application for Biometrical Sample Size Calculation in Clinical and Epidemiological Trials

Clinical journals strongly recommend the use of confidence intervals to present study results, since these comprise both the statistical significance and the clinical relevance of a study's outcome. However, the mandatory sample size calculations performed during a study's planning stage are mostly reported via significance test-based approaches, as there are currently only a few methods available for planning approaches via confidence intervals. As a result, many articles show a mismatch between the planning (based on significance tests) and result presentation (based on confidence intervals). To overcome this gap, a user interface will be illustrated that offers the opportunity of sample size calculation both by means of significance tests and confidence intervals, with intuitive access for clinical researchers. Estimating sample sizes via confidence intervals requires the predetermination of the interval's maximum width, whereas the calculation of sample sizes via significance test has the minimum requirement of the test's statistical power. The resulting sample size formulas are compatible for all practically relevant cases and mainly differ in the specification of the parameters "width" and "power". For the choice of a suitable statistical power, there are established reference values (usually 80 or 90%), while the calculation of sample size by means of confidence intervals is still difficult for clinical researchers, due to the unavailability of guidelines for the choice of the interval width. The application of both approaches is demonstrated by planning a clinical trial on the rotational stability of toric intraocular lenses with or without an implemented capsular tension ring. A user interface was developed to implement both of the publicly accessible approaches for sample size calculation. The interface allows comparison of the approaches based on significance test and confidence interval and their interchangeability for a two-armed clinical trial design. The operator firstly chooses one of the approaches; then the necessary planning information is inputted and the calculated sample size per trial as well as the corresponding planning information for the other approach are provided. The presented sample size tool enables an intuitively accessible way to calculate sample sizes both via significance tests and via confidence intervals for two-armed study designs.

Identifying and Computing the Exact Core-determining Class

The indeterministic relations between unobservable events and observed outcomes in partially identified models can be characterized by a bipartite graph. Given a probability measure on observed outcomes, the set of feasible probability measures on unobservable events can be defined by a set of linear inequality constraints, according to Artstein's Theorem. This set of inequalities is called the “core-determining class”. However, the number of inequalities defined by Artstein's Theorem is exponentially increasing with the number of unobservable events, and many inequalities may in fact be redundant. In this paper, we show that the exact core-determining class, i.e., the smallest possible core-determining class, can be characterized by a set of combinatorial rules of the bipartite graph. We prove that if the bipartite graph and the measure on observed outcomes are non-degenerate, the exact core-determining class is unique and it only depends on the structure of the bipartite graph. We then propose an algorithm that explores the structure of the bipartite graph to construct the exact core-determining class. We design and implement the model and algorithm in a set of examples to show that our methodology could efficiently discard the redundant inequalities that are not useful to identify the parameter of interest. We also demonstrate that, by using the inequalities corresponding to the exact core-determining class to perform set inference, the power of test statistics against local alternatives can be improved.

Long–term spatio–temporal warming tendency in the Vietnamese Mekong Delta based on observed and high–resolution gridded datasets

The Vietnamese Mekong Delta is among the most vulnerable deltas to climate–related hazards across the globe. In this study, the annual mean and extreme temperatures from 11 meteorological stations over the Vietnamese Mekong Delta were subjected to normality, homogeneity and trend analysis by employing a number of powerful statistical tests (i.e. Shapiro–Wilk, Buishand Range test, classical/modified Mann–Kendall test and Sen’s slope estimator). As for spatio–temporal assessment, the well–known (0.5° × 0.5°) high–resolution gridded dataset (i.e. CRU TS4.02) was also utilized to examine trend possibilities for three different time periods (i.e. 1901–2017, 1951–2017 and 1981–2017) by integrating spatial interpolation algorithms (i.e. IDW and Ordinary Kriging) with statistical trend tests. Comparing the calculated test–statistics to their critical values (a = 0.05), it is evident that most of the temperature records can be considered to be normal and non–homogeneous with respect to normality and homogeneity test respectively. As for temporal trend detection, the outcomes show high domination of significantly increasing trends. Additionally, the results of trend estimation indicate that the magnitude of increase in minimum temperature was mostly greater than mean and maximum ones and the recent period (1981–2017) also revealed greater increasing rates compared to the entire analyzed period and second half of the 20th century. In general, these findings yield various evident indications of warming tendency in the Vietnamese Mekong Delta over the last three decades.

Testing Cointegrating Relationships Using Irregular and Non‐Contemporaneous Series with an Application to Paleoclimate Data

Time series that are observed neither regularly nor contemporaneously pose problems for most multivariate analyses. Common and intuitive solutions to these problems include interpolation and other types of imputation to a higher, regular frequency. However, interpolation is known to cause serious problems with the size and power of statistical tests. Due to the difficulty in dating paleoclimate data such as CO2concentrations and surface temperatures, time series of such measurements are observed neither regularly nor contemporaneously. This article presents large‐ and small‐sample analyses of the size and power of cointegration tests of time series with these features and supports the robustness of cointegration of these two series found in the extant literature. Compared to linear or higher‐order polynomial interpolation, step interpolation results in the least size distortion and is therefore recommended.

Indices of Rank Histogram Flatness and Their Sampling Properties

Abstract Quantitative evaluation of the flatness of the verification rank histogram can be approached through formal hypothesis testing. Traditionally, the familiar χ2 test has been used for this purpose. Recently, two alternatives—the reliability index (RI) and an entropy statistic (Ω)—have been suggested in the literature. This paper presents approximations to the sampling distributions of these latter two rank histogram flatness metrics, and compares the statistical power of tests based on the three statistics, in a controlled setting. The χ2 test is generally most powerful (i.e., most sensitive to violations of the null hypothesis of rank uniformity), although for overdispersed ensembles and small sample sizes, the test based on the entropy statistic Ω is more powerful. The RI-based test is preferred only for unbiased forecasts with small ensembles and very small sample sizes.