scholarly journals A BINOMIAL MODEL APPROXIMATION FOR MULTIPLE TESTING

2019 ◽  
Vol 16 (2) ◽  
pp. 73-82
Author(s):  
I. A. ADELEKE ◽  
A. O. ADEYEMI ◽  
E. E.E. AKARAWAK
Keyword(s):  
Error Rate ◽  
Multiple Testing ◽  
Type I Error ◽  
Type I ◽  
Binomial Model ◽  
Model Approximation ◽  
False Discovery ◽  
Simultaneous Testing ◽  
Significance Levels ◽  
Level Of Significance

Multiple testing is associated with simultaneous testing of many hypotheses, and frequently calls for adjusting level of significance in some way that the probability of observing at least one significant result due to chance remains below the desired significance levels. This study developed a Binomial Model Approximations (BMA) method as an alternative to addressing the multiplicity problem associated with testing more than one hypothesis at a time. The proposed method has demonstrated capacity for controlling Type I Error Rate as sample size increases when compared with the existing Bonferroni and False Discovery Rate (FDR).      

scholarly journals Multiple Testing. Part I. Single-Step Procedures for Control of General Type I Error Rates

2004 ◽  
Vol 3 (1) ◽  
pp. 1-69 ◽  
Author(s):  
Sandrine Dudoit ◽  
Mark J. van der Laan ◽  
Katherine S. Pollard
Keyword(s):  
Error Rate ◽  
Multiple Testing ◽  
Type I Error ◽  
Null Distribution ◽  
Error Rates ◽  
Single Step ◽  
Type I ◽  
Test Statistics ◽  
Testing Procedures ◽  
Multiple Testing Procedures

The present article proposes general single-step multiple testing procedures for controlling Type I error rates defined as arbitrary parameters of the distribution of the number of Type I errors, such as the generalized family-wise error rate. A key feature of our approach is the test statistics null distribution (rather than data generating null distribution) used to derive cut-offs (i.e., rejection regions) for these test statistics and the resulting adjusted p-values. For general null hypotheses, corresponding to submodels for the data generating distribution, we identify an asymptotic domination condition for a null distribution under which single-step common-quantile and common-cut-off procedures asymptotically control the Type I error rate, for arbitrary data generating distributions, without the need for conditions such as subset pivotality. Inspired by this general characterization of a null distribution, we then propose as an explicit null distribution the asymptotic distribution of the vector of null value shifted and scaled test statistics. In the special case of family-wise error rate (FWER) control, our method yields the single-step minP and maxT procedures, based on minima of unadjusted p-values and maxima of test statistics, respectively, with the important distinction in the choice of null distribution. Single-step procedures based on consistent estimators of the null distribution are shown to also provide asymptotic control of the Type I error rate. A general bootstrap algorithm is supplied to conveniently obtain consistent estimators of the null distribution. The special cases of t- and F-statistics are discussed in detail. The companion articles focus on step-down multiple testing procedures for control of the FWER (van der Laan et al., 2004b) and on augmentations of FWER-controlling methods to control error rates such as tail probabilities for the number of false positives and for the proportion of false positives among the rejected hypotheses (van der Laan et al., 2004a). The proposed bootstrap multiple testing procedures are evaluated by a simulation study and applied to genomic data in the fourth article of the series (Pollard et al., 2004).

scholarly journals Evaluations of the Optimal Discovery Procedure for Multiple Testing

2016 ◽  
Vol 12 (1) ◽  
pp. 21-29 ◽  
Author(s):  
Daniel B. Rubin
Keyword(s):  
Error Rate ◽  
Optimality Theory ◽  
Multiple Testing ◽  
Type I Error ◽  
Type I ◽  
Test Statistics ◽  
Testing Procedures ◽  
Type I Error Rate ◽  
Rate Measure ◽  
Optimal Discovery Procedure

Abstract The Optimal Discovery Procedure (ODP) is a method for simultaneous hypothesis testing that attempts to gain power relative to more standard techniques by exploiting multivariate structure [1]. Specializing to the example of testing whether components of a Gaussian mean vector are zero, we compare the power of the ODP to a Bonferroni-style method and to the Benjamini-Hochberg method when the testing procedures aim to respectively control certain Type I error rate measures, such as the expected number of false positives or the false discovery rate. We show through theoretical results, numerical comparisons, and two microarray examples that when the rejection regions for the ODP test statistics are chosen such that the procedure is guaranteed to uniformly control a Type I error rate measure, the technique is generally less powerful than competing methods. We contrast and explain these results in light of previously proven optimality theory for the ODP. We also compare the ordering given by the ODP test statistics to the standard rankings based on sorting univariate p-values from smallest to largest. In the cases we considered the standard ordering was superior, and ODP rankings were adversely impacted by correlation.

scholarly journals Power and type I error rate of false discovery rate approaches in genome-wide association studies

BMC Genetics ◽  
2005 ◽  
Vol 6 (Suppl 1) ◽  
pp. S134 ◽  
Author(s):  
Qiong Yang ◽  
Jing Cui ◽  
Irmarie Chazaro ◽  
L Adrienne Cupples ◽  
Serkalem Demissie
Keyword(s):  
False Discovery Rate ◽  
Error Rate ◽  
Type I Error ◽  
Association Studies ◽  
Genome Wide Association ◽  
Type I ◽  
Genome Wide Association Studies ◽  
Type I Error Rate ◽  
False Discovery ◽  
Genome Wide

scholarly journals Solutions for Determining the Significance Region Using the Johnson-Neyman Type Procedure in Generalized Linear (Mixed) Models

2011 ◽  
Vol 36 (6) ◽  
pp. 699-719 ◽  
Author(s):  
Ann A. Lazar ◽  
Gary O. Zerbe
Keyword(s):  
Error Rate ◽  
Multiple Testing ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
Type I Error ◽  
Hierarchical Linear Model ◽  
Wald Test ◽  
Analysis Of Covariance ◽  
Type I ◽  
Type I Error Rate

Researchers often compare the relationship between an outcome and covariate for two or more groups by evaluating whether the fitted regression curves differ significantly. When they do, researchers need to determine the “significance region,” or the values of the covariate where the curves significantly differ. In analysis of covariance (ANCOVA), the Johnson-Neyman procedure can be used to determine the significance region; for the hierarchical linear model (HLM), the Miyazaki and Maier (M-M) procedure has been suggested. However, neither procedure can assume nonnormally distributed data. Furthermore, the M-M procedure produces biased (downward) results because it uses the Wald test, does not control the inflated Type I error rate due to multiple testing, and requires implementing multiple software packages to determine the significance region. In this article, we address these limitations by proposing solutions for determining the significance region suitable for generalized linear (mixed) model (GLM or GLMM). These proposed solutions incorporate test statistics that resolve the biased results, control the Type I error rate using Scheffé’s method, and uses a single statistical software package to determine the significance region.

scholarly journals Multiple Testing. Part II. Step-Down Procedures for Control of the Family-Wise Error Rate

2004 ◽  
Vol 3 (1) ◽  
pp. 1-33 ◽  
Author(s):  
Mark J. van der Laan ◽  
Sandrine Dudoit ◽  
Katherine S. Pollard
Keyword(s):  
Error Rate ◽  
Multiple Testing ◽  
Type I Error ◽  
Null Distribution ◽  
Type I ◽  
Test Statistics ◽  
P Values ◽  
Family Wise Error Rate ◽  
The Family ◽  
Step Down

The present article proposes two step-down multiple testing procedures for asymptotic control of the family-wise error rate (FWER): the first procedure is based on maxima of test statistics (step-down maxT), while the second relies on minima of unadjusted p-values (step-down minP). A key feature of our approach is the characterization and construction of a test statistics null distribution (rather than data generating null distribution) for deriving cut-offs for these test statistics (i.e., rejection regions) and the resulting adjusted p-values. For general null hypotheses, corresponding to submodels for the data generating distribution, we identify an asymptotic domination condition for a null distribution under which the step-down maxT and minP procedures asymptotically control the Type I error rate, for arbitrary data generating distributions, without the need for conditions such as subset pivotality. Inspired by this general characterization, we then propose as an explicit null distribution the asymptotic distribution of the vector of null value shifted and scaled test statistics. Step-down procedures based on consistent estimators of the null distribution are shown to also provide asymptotic control of the Type I error rate. A general bootstrap algorithm is supplied to conveniently obtain consistent estimators of the null distribution.

Correction: “Influence of Selection Bias on the Test Decision – A Simulation Study”

2014 ◽  
Vol 53 (05) ◽  
pp. 343-343
Keyword(s):  
Selection Bias ◽  
Simulation Study ◽  
Error Rate ◽  
Type I Error ◽  
Block Size ◽  
Error Rates ◽  
Type I ◽  
Type I Error Rate ◽  
Representation Error ◽  
Numeric Representation

We have to report marginal changes in the empirical type I error rates for the cut-offs 2/3 and 4/7 of Table 4, Table 5 and Table 6 of the paper “Influence of Selection Bias on the Test Decision – A Simulation Study” by M. Tamm, E. Cramer, L. N. Kennes, N. Heussen (Methods Inf Med 2012; 51: 138 –143). In a small number of cases the kind of representation of numeric values in SAS has resulted in wrong categorization due to a numeric representation error of differences. We corrected the simulation by using the round function of SAS in the calculation process with the same seeds as before. For Table 4 the value for the cut-off 2/3 changes from 0.180323 to 0.153494. For Table 5 the value for the cut-off 4/7 changes from 0.144729 to 0.139626 and the value for the cut-off 2/3 changes from 0.114885 to 0.101773. For Table 6 the value for the cut-off 4/7 changes from 0.125528 to 0.122144 and the value for the cut-off 2/3 changes from 0.099488 to 0.090828. The sentence on p. 141 “E.g. for block size 4 and q = 2/3 the type I error rate is 18% (Table 4).” has to be replaced by “E.g. for block size 4 and q = 2/3 the type I error rate is 15.3% (Table 4).”. There were only minor changes smaller than 0.03. These changes do not affect the interpretation of the results or our recommendations.

Controlling type I error rate for fast track drug development programmes

2003 ◽  
Vol 22 (5) ◽  
pp. 665-675 ◽  
Author(s):  
Weichung J. Shih ◽  
Peter Ouyang ◽  
Hui Quan ◽  
Yong Lin ◽  
Bart Michiels ◽  
...  
Keyword(s):  
Drug Development ◽  
Error Rate ◽  
Fast Track ◽  
Type I Error ◽  
Type I ◽  
Type I Error Rate

Alternative models and randomization techniques for Bayesian response-adaptive randomization with binary outcomes

2021 ◽  
pp. 174077452110101
Author(s):  
Jennifer Proper ◽  
John Connett ◽  
Thomas Murray
Keyword(s):  
Logistic Regression ◽  
Sample Size ◽  
Error Rate ◽  
Adaptive Design ◽  
Type I Error ◽  
Probability Model ◽  
Binary Outcomes ◽  
Type I ◽  
Operating Characteristics ◽  
Type I Error Rate

Background: Bayesian response-adaptive designs, which data adaptively alter the allocation ratio in favor of the better performing treatment, are often criticized for engendering a non-trivial probability of a subject imbalance in favor of the inferior treatment, inflating type I error rate, and increasing sample size requirements. The implementation of these designs using the Thompson sampling methods has generally assumed a simple beta-binomial probability model in the literature; however, the effect of these choices on the resulting design operating characteristics relative to other reasonable alternatives has not been fully examined. Motivated by the Advanced R2 Eperfusion STrategies for Refractory Cardiac Arrest trial, we posit that a logistic probability model coupled with an urn or permuted block randomization method will alleviate some of the practical limitations engendered by the conventional implementation of a two-arm Bayesian response-adaptive design with binary outcomes. In this article, we discuss up to what extent this solution works and when it does not. Methods: A computer simulation study was performed to evaluate the relative merits of a Bayesian response-adaptive design for the Advanced R2 Eperfusion STrategies for Refractory Cardiac Arrest trial using the Thompson sampling methods based on a logistic regression probability model coupled with either an urn or permuted block randomization method that limits deviations from the evolving target allocation ratio. The different implementations of the response-adaptive design were evaluated for type I error rate control across various null response rates and power, among other performance metrics. Results: The logistic regression probability model engenders smaller average sample sizes with similar power, better control over type I error rate, and more favorable treatment arm sample size distributions than the conventional beta-binomial probability model, and designs using the alternative randomization methods have a negligible chance of a sample size imbalance in the wrong direction. Conclusion: Pairing the logistic regression probability model with either of the alternative randomization methods results in a much improved response-adaptive design in regard to important operating characteristics, including type I error rate control and the risk of a sample size imbalance in favor of the inferior treatment.

On the Adaptive Control of the False Discovery Rate in Multiple Testing With Independent Statistics

2000 ◽  
Vol 25 (1) ◽  
pp. 60-83 ◽  
Author(s):  
Yoav Benjamini ◽  
Yosef Hochberg
Keyword(s):  
False Discovery Rate ◽  
Multiple Testing ◽  
Meta Analysis ◽  
Test Statistics ◽  
Adaptive Procedure ◽  
New Approach ◽  
False Discovery ◽  
Behavioral Studies ◽  
Simultaneous Testing ◽  
Independent Test

A new approach to problems of multiple significance testing was presented in Benjamini and Hochberg (1995), which calls for controlling the expected ratio of the number of erroneous rejections to the number of rejections–the False Discovery Rate (FDR). The procedure given there was shown to control the FDR for independent test statistics. When some of the hypotheses are in fact false, that procedure is too conservative. We present here an adaptive procedure, where the number of true null hypotheses is estimated first as in Hochberg and Benjamini (1990), and this estimate is used in the procedure of Benjamini and Hochberg (1995). The result is still a simple stepwise procedure, to which we also give a graphical companion. The new procedure is used in several examples drawn from educational and behavioral studies, addressing problems in multi-center studies, subset analysis and meta-analysis. The examples vary in the number of hypotheses tested, and the implication of the new procedure on the conclusions. In a large simulation study of independent test statistics the adaptive procedure is shown to control the FDR and have substantially better power than the previously suggested FDR controlling method, which by itself is more powerful than the traditional family wise error-rate controlling methods. In cases where most of the tested hypotheses are far from being true there is hardly any penalty due to the simultaneous testing of many hypotheses.

Anova Tests for Homogeneity of Variance: Nonnormality and Unequal Samples

1977 ◽  
Vol 2 (3) ◽  
pp. 187-206 ◽  
Author(s):  
Charles G. Martin ◽  
Paul A. Games
Keyword(s):  
Error Rate ◽  
Type I Error ◽  
Type I ◽  
Empirical Comparison ◽  
Jackknife Test ◽  
Type I Error Rate ◽  
Power And Control ◽  
Homogeneity Of Variance ◽  
Test Use ◽  
And Control

This paper presents an exposition and an empirical comparison of two potentially useful tests for homogeneity of variance. Control of Type I error rate, P(EI), and power are investigated for three forms of the Box test and for two forms of the jackknife test with equal and unequal n's under conditions of normality and nonnormality. The Box test is shown to be robust to violations of the assumption of normality. The jackknife test is shown not to be robust. When n's are unequal, the problem of heterogeneous within-cell variances of the transformed values and unequal n's affects the jackknife and Box tests. Previously reported suggestions for selecting subsample sizes for the Box test are shown to be inappropriate, producing an inflated P(EI). Two procedures which alleviate this problem are presented for the Box test. Use of the jack-knife test with a reduced alpha is shown to provide power and control of P(EI) at approximately the same level as the Box test. Recommendations for the use of these techniques and computational examples of each are provided.

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