scholarly journals The Robustness of the Modified H-Statistic in the Test of Comparing Independent Groups

2020 ◽  
pp. 1-5
Author(s):  
Suhaida Abdullah ◽  
Teh Kian Wooi ◽  
Sharipah Soaad Syed Yahaya ◽  
Zahayu Md Yusof
Keyword(s):  
Error Rate ◽  
Type I Error ◽  
Type I ◽  
Central Tendency ◽  
Test Statistic ◽  
Robust Test ◽  
Central Tendency Measure ◽  
Type I Error Rate ◽  
One Step ◽  
The Mean

The H-statistic is a robust test statistic in comparing the equality of two and more than two independent groups. This statistic is one of a good alternative to the F-statistic in the analysis of variance (ANOVA). The F-statistic is good only when the distribution of data is normal with homogeneous variances. If there is a violation of at least one of these assumptions, it affects the Type I error rate of the test. The main weakness of the F-statistic is its calculation based on the mean. The mean is well-known as a very sensitive central tendency measure with 0 breakdown point, whereas the H-statistic provides a test with fewer assumptions yet powerful. This statistic is readily adaptable to any measure of central tendency, and it appears to give reasonably good results. Hence, this paper provides a detailed study on the robustness of the H-statistic and its performance using different robust central tendency measures such that the modified one-step M (MOM) estimator and Winsorized MOM estimator. Based on the simulation study, this paper also investigates the performance of the H-statistic under various data conditions. The findings reveal that this statistic performs as well as the F-statistic under normal and homogeneous variance, yet it provides better control of Type I error rate under non-normal data or heterogeneous variances or both. Keywords: H-statistic; robust test; mean; modified one-step M-estimator

scholarly journals Winsorized Modified One Step M-Estimator As a Measure of the Central Tendency in the Alexander-Govern Test

2016 ◽  
Vol 7 (3) ◽  
pp. 233
Author(s):  
Tobi Kingsley Ochuko ◽  
Suhaida Abdullah ◽  
Zakiyah Zain ◽  
Sharipah Syed Soaad Yahaya
Keyword(s):  
Type I Error ◽  
Good Control ◽  
Error Rates ◽  
Extreme Condition ◽  
Type I ◽  
Central Tendency ◽  
Central Tendency Measure ◽  
Type I Error Rates ◽  
M Estimator ◽  
One Step

This research dealt with making comparison of the independent group tests with the use of parametric technique. This test used mean as its central tendency measure. It was a better alternative to the ANOVA, the Welch test and the James test, because it gave a good control of Type I error rates and high power with ease in its calculation, for variance heterogeneity under a normal data. But the test was found not to be robust to non-normal data. Trimmed mean was used on the test as its central tendency measure under non-normality for two group condition, but as the number of groups increased above two, the test failed to give a good control of Type I error rates. As a result of this, the MOM estimator was applied on the test as its central tendency measure and is not influenced by the number of groups. However, under extreme condition of skewness and kurtosis, the MOM estimator could no longer control the Type I error rates. In this study, the Winsorized MOM estimator was used in the AG test, as a measure of its central tendency under non-normality. 5,000 data sets were simulated and analysed for each of the test in the research design with the use of Statistical Analysis Software (SAS) package. The results of the analysis shows that the Winsorized modified one step M-estimator in the Alexander-Govern (AGWMOM) test, gave the best control of Type I error rates under non-normality compared to the AG test, the AGMOM test, and the ANOVA, with the highest number of conditions for both lenient and stringent criteria of robustness. 

scholarly journals How to keep the Type I Error Rate in ANOVA if Variances are Heteroscedastic

2016 ◽  
Vol 36 (3) ◽  
Author(s):  
Karl Moder
Keyword(s):  
Error Rate ◽  
Type I Error ◽  
Type I ◽  
Test Statistic ◽  
Underlying Distribution ◽  
Hotelling's T2 ◽  
Type I Error Rate ◽  
Hotelling’S T2 ◽  
F Distribution ◽  
Alternative Test

One essential prerequisite to ANOVA is homogeneity of variances in underlying populations. Violating this assumption may lead to an increased type I error rate. The reason for this undesirable effect is due to the calculation of the corresponding F-value. A slightly different test statistic keeps the level ®. The underlying distribution of this alternative method is Hotelling’s T2. As Hotelling’s T2 can be approximated by a Fisher’s F-distribution, this alternative test is very similar to an ordinary analysis of variance.

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.

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.

Group sequential designs with robust semiparametric recurrent event models

2018 ◽  
Vol 28 (8) ◽  
pp. 2385-2403 ◽  
Author(s):  
Tobias Mütze ◽  
Ekkehard Glimm ◽  
Heinz Schmidli ◽  
Tim Friede
Keyword(s):  
Error Rate ◽  
Joint Distribution ◽  
Recurrent Events ◽  
Type I Error ◽  
Type I ◽  
Sequential Designs ◽  
Group Sequential ◽  
Type I Error Rate ◽  
Sequential Procedures ◽  
Group Sequential Designs

Robust semiparametric models for recurrent events have received increasing attention in the analysis of clinical trials in a variety of diseases including chronic heart failure. In comparison to parametric recurrent event models, robust semiparametric models are more flexible in that neither the baseline event rate nor the process inducing between-patient heterogeneity needs to be specified in terms of a specific parametric statistical model. However, implementing group sequential designs in the robust semiparametric model is complicated by the fact that the sequence of Wald statistics does not follow asymptotically the canonical joint distribution. In this manuscript, we propose two types of group sequential procedures for a robust semiparametric analysis of recurrent events. The first group sequential procedure is based on the asymptotic covariance of the sequence of Wald statistics and it guarantees asymptotic control of the type I error rate. The second procedure is based on the canonical joint distribution and does not guarantee asymptotic type I error rate control but is easy to implement and corresponds to the well-known standard approach for group sequential designs. Moreover, we describe how to determine the maximum information when planning a clinical trial with a group sequential design and a robust semiparametric analysis of recurrent events. We contrast the operating characteristics of the proposed group sequential procedures in a simulation study motivated by the ongoing phase 3 PARAGON-HF trial (ClinicalTrials.gov identifier: NCT01920711) in more than 4600 patients with chronic heart failure and a preserved ejection fraction. We found that both group sequential procedures have similar operating characteristics and that for some practically relevant scenarios, the group sequential procedure based on the canonical joint distribution has advantages with respect to the control of the type I error rate. The proposed method for calculating the maximum information results in appropriately powered trials for both procedures.

scholarly journals Data-driven region-of-interest selection without inflating Type I error rate

2016 ◽  
Vol 54 (1) ◽  
pp. 100-113 ◽  
Author(s):  
Joseph L. Brooks ◽  
Alexia Zoumpoulaki ◽  
Howard Bowman
Keyword(s):  
Error Rate ◽  
Type I Error ◽  
Region Of Interest ◽  
Data Driven ◽  
Type I ◽  
Type I Error Rate
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