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Author: search.filters.author.Shieh, Gwowen

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Now showing 1 - 10 of 53
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    Appraising Minimum Effect of Standardized Contrasts in ANCOVA Designs: Statistical Power, Sample Size, and Covariate Imbalance Considerations
    (1970-01-01)
    Shieh, Gwowen
    ;
    管理科學系
    ;
    Department of Management Science
    The concepts and implementation of standardized mean differences and minimum effect tests have been emphasized in ANOVA. The corresponding processes and implications are, however, not yet well explicated in the context of ANCOVA. To enhance the usefulness of ANCOVA, this article describes the minimum effect tests of standardized contrast as a valuable alternative to the hypothesis testing of no effect difference and the conventional evaluation of unstandardized effects in ANCOVA. Power and sample size procedures are developed to accommodate covariate randomness and imbalance for randomized and nonrandomized designs. The data from a clinical study of comparing two treatments for gingivitis are used to illustrate the application of the suggested approaches. The emphases of numerical appraisal are on the merit of minimum effect detection in comparative analysis and the influence of covariate feature in power and sample size computation. The proposed power and sample size calculations improve upon approximate formulas by fully accounting for the stochastic property and intrinsic disparity of the covariate variables. Computer algorithms are available for calculating thep-value, power level, and sample size of one- and two-sided minimum effect tests.
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    Power Analysis and Sample Size Planning in ANCOVA Designs
    (2020-03-01)
    Shieh, Gwowen
    ;
    交大名義發表
    ;
    管理科學系
    ;
    National Chiao Tung University
    ;
    Department of Management Science
    The analysis of covariance (ANCOVA) has notably proven to be an effective tool in a broad range of scientific applications. Despite the well-documented literature about its principal uses and statistical properties, the corresponding power analysis for the general linear hypothesis tests of treatment differences remains a less discussed issue. The frequently recommended procedure is a direct application of the ANOVA formula in combination with a reduced degrees of freedom and a correlation-adjusted variance. This article aims to explicate the conceptual problems and practical limitations of the common method. An exact approach is proposed for power and sample size calculations in ANCOVA with random assignment and multinormal covariates. Both theoretical examination and numerical simulation are presented to justify the advantages of the suggested technique over the current formula. The improved solution is illustrated with an example regarding the comparative effectiveness of interventions. In order to facilitate the application of the described power and sample size calculations, accompanying computer programs are also presented.
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    Comparison of alternative approaches for difference, noninferiority, and equivalence testing of normal percentiles
    (2020-03-13)
    Shieh, Gwowen
    ;
    管理科學系
    ;
    Department of Management Science
    Background Percentiles are widely used in scientific research for determining the comparative magnitude and reference limit of quantitative measurements. The investigations for point and interval estimation of normal percentiles are well documented in the literature. However, the corresponding statistical tests of hypothesis have received relatively little attention. Methods To facilitate data analysis and design planning of percentile study, this paper aims to present hypothesis testing procedures and associated power functions for assessing the difference, noninferiority, and equivalence of normal percentiles. Results Numerical illustrations about drug dissolution are provided to demonstrate the usefulness of the suggested exact approaches and the deficiency of approximate methods. Conclusions The exact approaches are superior to the approximate methods on the basis of control of Type I errors. Computer algorithms are constructed to implement the recommended test procedures and sample size calculations for percentile analysis.
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    Assessing Agreement Between Two Methods of Quantitative Measurements: Exact Test Procedure and Sample Size Calculation
    (1970-01-01)
    Shieh, Gwowen
    ;
    管理科學系
    ;
    Department of Management Science
    Assessment of agreement between measurement methods is an important problem in medical practice and research. Several two one-sided tests (TOST) procedures have been proposed to evaluate whether two methods have sufficient agreement. These TOST techniques of limits of agreement or normal percentiles are natural generalizations of the favorable TOST procedure of mean differences. But their fundamental behavior of Type I error control has not been examined. This article describes an improved and exact approach for declaring agreement between two measurement methods when the range of central proportion of paired differences is within the designated threshold interval around zero. Theoretical examinations and numerical investigations are provided to justify the advantages of the proposed approach and to illustrate the shortcomings of the existing TOST procedures for assessing agreement between two methods. To facilitate the suggested agreement appraisal in design planning, the corresponding power and sample size formulas are also derived. Both SAS and R algorithms are presented for conducting agreement test, power calculation, and sample size determination in method comparison studies.
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    On the Extended Welch Test for Assessing Equivalence of Standardized Means
    (1970-01-01)
    Jan, Show-Li
    ;
    Shieh, Gwowen
    ;
    管理科學系
    ;
    Department of Management Science
    This article proposes a useful extension of the ANOVA F-test for examining mean differences for evaluating the comparability of standardized mean effects. The equivalence procedure presumably suffers from the same disadvantage as the traditional ANOVA F-statistic regarding the violations of homogeneous variance assumption. In view of the absence of vital clarification for theory development and supportive technique, this article provides a critical exposition of the extended Welch test for the equivalence of standardized means. To enhance the usefulness of equivalence testing, the theoretical properties and practical implications of the Welch-type procedure are demonstrated. Moreover, the corresponding power and sample size algorithms are described for advance planning of equivalence studies. Despite the approximate nature, the accuracy of Type I error rate, statistical power, and sample size calculations of the suggested equivalence test is justified under a wide range of model configurations. The proposed procedures are demonstrated with the data of a clinical trial regarding the comparative study of four antihypertensive treatments. A complete set of computer codes is presented to calculate the corresponding critical values, p-values, power levels, and sample sizes for data analysis and design planning of equivalence studies.
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    On Sample-Size Calculations for Precise Contrast Analysis in ANCOVA
    (2019-04-03)
    Shieh, Gwowen
    ;
    交大名義發表
    ;
    管理科學系
    ;
    National Chiao Tung University
    ;
    Department of Management Science
    The analysis of covariance (ANCOVA) is a useful statistical procedure that incorporates covariate features into the adjustment of treatment effects. The consequences of omitted prognostic covariates on the statistical inferences of ANCOVA are well documented in the literature. However, the corresponding influence on sample-size calculations for precise interval estimation has not been fully evaluated. This article aims to explicate the deficiency of approximate methods for ignoring the stochastic nature of covariate variables and to present exact approaches for precise interval estimation of treatment contrasts under the assumption that the covariate variables have a joint multinormal distribution. The desired precision of a confidence interval is assessed with respect to the control of expected half-width and to the assurance probability of interval half-width within a designated value. Numerical appraisals show that the suggested approaches outperform the approximate formulas for the two precision considerations.
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    Optimal contrast analysis with heterogeneous variances and budget concerns
    (2019-03-26)
    Jan, Show-Li
    ;
    Shieh, Gwowen
    ;
    管理科學系
    ;
    Department of Management Science
    The omnibus test is commonly applied to evaluate the overall disparity between group means in ANOVA. Alternatively, linear contrasts are more informative in detecting specific pattern of mean differences that cannot be obtained via the omnibus test. This article concerns power and sample size calculations for contrast analysis with heterogeneous variances and budget concerns. Optimal allocation procedures for the Welch-Satterthwaite tests of standardized and unstandardized contrasts are presented to minimize the total sample size with the designated ratios, to meet a desirable power level for the least cost, and to attain the maximum power performance under a fixed cost. Currently available methods rely exclusively on simple allocation formula and direct rounding rule. The proposed allocation strategies combine the computing techniques of nonlinear optimization search and iterative screening process. Numerical assessments of a randomized control trial for the overcoming depression on the Internet are conducted to demonstrate and confirm that the approximate procedures do not guarantee optimal solution. The suggested approaches extend and outperform the existing findings in methodological soundness and overall performance. The corresponding computer algorithms are developed to implement the recommended power and sample size calculations for optimal contrast analysis.
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    On tests of treatment-covariate interactions: An illustration of appropriate power and sample size calculations
    (2017-05-17)
    Shieh, Gwowen
    ;
    管理科學系
    ;
    Department of Management Science
    The appraisals of treatment-covariate interaction have theoretical and substantial implications in all scientific fields. Methodologically, the detection of interaction between categorical treatment levels and continuous covariate variables is analogous to the homogeneity of regression slopes test in the context of ANCOVA. A fundamental assumption of ANCOVA is that the regression slopes associating the response variable with the covariate variable are presumed constant across treatment groups. The validity of homogeneous regression slopes accordingly is the most essential concern in traditional ANCOVA and inevitably determines the practical usefulness of research findings. In view of the limited results in current literature, this article aims to present power and sample size procedures for tests of heterogeneity between two regression slopes with particular emphasis on the stochastic feature of covariate variables. Theoretical implications and numerical investigations are presented to explicate the utility and advantage for accommodating covariate properties. The exact approach has the distinct feature of accommodating the full distributional properties of normal covariates whereas the simplified approximate methods only utilize the partial information of covariate variances. According to the overall accuracy and robustness, the exact approach is recommended over the approximate methods as a reliable tool in practical applications. The suggested power and sample size calculations can be implemented with the supplemental SAS and R programs.
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    A systematic approach to designing statistically powerful heteroscedastic 2 x 2 factorial studies while minimizing financial costs
    (2016-08-31)
    Jan, Show-Li
    ;
    Shieh, Gwowen
    ;
    管理科學系
    ;
    Department of Management Science
    Background: The 2 x 2 factorial design is widely used for assessing the existence of interaction and the extent of generalizability of two factors where each factor had only two levels. Accordingly, research problems associated with the main effects and interaction effects can be analyzed with the selected linear contrasts. Methods: To correct for the potential heterogeneity of variance structure, the Welch-Satterthwaite test is commonly used as an alternative to the t test for detecting the substantive significance of a linear combination of mean effects. This study concerns the optimal allocation of group sizes for the Welch-Satterthwaite test in order to minimize the total cost while maintaining adequate power. The existing method suggests that the optimal ratio of sample sizes is proportional to the ratio of the population standard deviations divided by the square root of the ratio of the unit sampling costs. Instead, a systematic approach using optimization technique and screening search is presented to find the optimal solution. Results: Numerical assessments revealed that the current allocation scheme generally does not give the optimal solution. Alternatively, the suggested approaches to power and sample size calculations give accurate and superior results under various treatment and cost configurations. Conclusions: The proposed approach improves upon the current method in both its methodological soundness and overall performance. Supplementary algorithms are also developed to aid the usefulness and implementation of the recommended technique in planning 2 x 2 factorial designs.
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    Effect size, statistical power, and sample size for assessing interactions between categorical and continuous variables
    (2019-02-01)
    Shieh, Gwowen
    ;
    管理科學系
    ;
    Department of Management Science
    The reporting and interpretation of effect size estimates are widely advocated in many academic journals of psychology and related disciplines. However, such concern has not been adequately addressed for analyses involving interactions between categorical and continuous variables. For the purpose of improving current practice, this article presents fundamental features and theoretical developments for the variance of standardized slopes as a desirable standardized effect size measure for the degree of disparity between several slope coefficients. To estimate the effect size, a consistent and nearly unbiased estimator is described and a simple refinement is emphasized for extreme situations whenever appropriate. The essential problems of power and sample size calculations for testing the equality of slope coefficients are also considered. According to the analytic justification and empirical assessment, the exact approach has a clear advantage over the approximate methods. Both SAS and R computer codes are provided to facilitate practical accessibility of the proposed techniques in interaction studies.