Browsing by Author "Shieh, G"

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A comparative study of power and sample size calculations for multivariate general linear models
(2003)
Shieh, G
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管理科學系
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Department of Management Science
Repeated measures and longitudinal studies arise often in social and behavioral science research. During the planning stage of such studies, the calculations of sample size are of particular interest to the investigators and should be an integral part of the research projects. In this article, we consider the power and sample size calculations for normal outcomes within the framework of multivariate general linear models that represent the most fundamental method for the analysis of repeated measures and longitudinal data. Direct extensions of the existing generalized estimating equation and likelihood-based approaches are presented. The major feature of the proposed modification is the accommodation of. both fixed and random models. A child development example is provided to illustrate the usefulness of the methods. The adequacies of the sample size formulas are evaluated through Monte Carlo simulation study.
A comparison of two approaches for power and sample size calculations in logistic regression models
(2000)
Shieh, G
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管理科學系
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Department of Management Science
Whittemore (1981) proposed an approach for calculating the sample size needed to test hypotheses with specified significance and power against a given alternative for logistic regression with small response probability. Based on the distribution of covariate, which could be either discrete or continuous, this approach first provides a simple closed-form approximation to the asymptotic covariance matrix of the maximum likelihood estimates, and then uses it to calculate the sample size needed to test a hypothesis about the parameter. Self et al. (1992) described a general approach for power and sample size calculations within the framework of generalized linear models, which include logistic regression as a special case. Their approach is based on an approximation to the distribution of the likelihood ratio statistic. Unlike the Whittemore approach, their approach is not limited to situations of small response probability. However, it is restricted to models with a finite number of covariate configurations. This study compares these two approaches to see how accurate they would be for the calculations of power and sample size in logistic regression models with various response probabilities and covariate distributions. The results indicate that the Whittemore approach has a slight advantage in achieving the nominal power only for one case with small response probability. It is outperformed for all other cases with larger response probabilities. In general, the approach proposed in Self et al. (1992) is recommended for all values of the response probability. However, its extension for logistic regression models with an infinite number of covariate configurations involves an arbitrary decision for categorization and leads to a discrete approximation. As shown in this paper, the examined discrete approximations appear to be sufficiently accurate for practical purpose.
Bayesian prediction analysis for growth curve model using noninformative priors
(2002-06-01)
Shieh, G
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Lee, JC
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統計學研究所
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管理科學系
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Institute of Statistics
We apply a Bayesian approach to the problem of prediction in an unbalanced growth curve model using noninformative priors. Due to the complexity of the model, no analytic forms of the predictive densities are available. We propose both approximations and a prediction-oriented Metropolis-Hastings sampling algorithm for two types of prediction, namely the prediction of future observations for a new subject and the prediction of future values for a partially observed subject. They are illustrated and compared through real data and simulation studies. Two of the approximations compare favorably with the approximation in Fearn (1975, Biometrika, 62, 89-100) and are very comparable to the more accurate Rao-Blackwellization from Metropolis-Hastings sampling algorithm.
Nonparametric multiple test procedures for dose finding
(2004)
Jan, SL
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Shieh, G
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管理科學系
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Department of Management Science
We consider identifying the minimum effective dose (MED) in a one-way layout, where the MED is defined to be the lowest dose level that is more effective than the zero-dose control. Proposed herein are two rank-based nonparametric step-down closed testing procedures that do not make order assumptions on the dose-response relationship. The corresponding p-value for the estimated MED is computed. A numerical example is given to illustrate the proposed tests. Finally, the results of a Monte Carlo study of the relative error rate and power performances are reported.
On power and sample size calculations for likelihood ratio tests in generalized linear models
(2000-12-01)
Shieh, G
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管理科學系
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Department of Management Science
A direct extension of the approach described in Self, Mauritsen, and Ohara (1992, Biometrics 48, 31-39) for power and sample size calculations in generalized linear models is presented. The major feature of the proposed approach is that the modification accommodates both a finite and an infinite number of covariate configurations. Furthermore, for the approximation of the noncentrality of the noncentral chi-square distribution for the likelihood ratio statistic, a simplification is provided that not only reduces substantial computation but also maintains the accuracy. Simulation studies are conducted to assess the accuracy for various model configurations and covariate distributions.
On power and sample size calculations for Wald tests in generalized linear models
(2005-01-15)
Shieh, G
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管理科學系
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Department of Management Science
A Wald test-based approach for power and sample size calculations has been presented recently for logistic and Poisson regression models using the asymptotic normal distribution of the maximum likelihood estimator, which is applicable to tests of a single parameter. Unlike the previous procedures involving the use of score and likelihood ratio statistics, there is no simple and direct extension of this approach for tests of more than a single parameter. In this article, we present a method for computing sample size and statistical power employing the discrepancy between the noncentral and central chi-square approximations to the distribution of the Wald statistic with unrestricted and restricted parameter estimates, respectively. The distinguishing features of the proposed approach are the accommodation of tests about multiple parameters, the flexibility of covariate configurations and the generality of overall response levels within the framework of generalized linear models. The general procedure is illustrated with some special situations that have motivated this research. Monte Carlo simulation studies are conducted to assess and compare its accuracy with existing approaches under several model specifications and covariate distributions. (C) 2003 Elsevier B.V. All rights reserved.
On power and sample size determinations for the Wilcoxon-Mann-Whitney test
(2006-01-01)
Shieh, G
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Jan, SL
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Randles, RH
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管理科學系
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Department of Management Science
This article considers power and sample size calculations for the Wilcoxon-Mann-Whitney test. An exact variance large-sample method is introduced and explicit formulas are derived for the uniform, normal, double exponential and exponential shift models. A Monte Carlo Simulation Study is conducted to evaluate the exact variance procedure and compare its performance with some other large sample methods. The results show the remarkable accuracy of the suggested formula and the fundamental limitations of the other approximations. Practical considerations in determination of sample size for the two-sample location problem are also discussed.
Power and sample size calculations for multivariate linear models with random explanatory variables
(2005-06-01)
Shieh, G
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管理科學系
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Department of Management Science
This article considers the problem of power and sample size calculations for normal outcomes within the framework of multivariate linear models. The emphasis is placed on the practical situation that not only the values of response variables for each subject are just available after the observations are made, but also the levels of explanatory variables cannot be predetermined before data collection. Using analytic justification, it is shown that the proposed methods extend the existing approaches to accommodate the extra variability and arbitrary configurations of the explanatory variables. The major modification involves the noncentrality parameters associated with the F approximations to the transformations of Wilks likelihood ratio, Pillai trace and Hotelling-Lawley trace statistics. A treatment of multivariate analysis of covariance models is employed to demonstrate the distinct features of the proposed extension. Monte Carlo simulation studies are conducted to assess the accuracy using a child's intellectual development model. The results update and expand upon current work in the literature.
Sample size calculations for logistic and Poisson regression models
(2001-12-01)
Shieh, G
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管理科學系
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Department of Management Science
A method is proposed for improving sample size calculations for logistic and Poisson regression models by incorporating the limiting value of the maximum likelihood estimates of nuisance parameters under the composite null hypothesis. The method modifies existing approaches of Whittemore (1981) and Signorini (1991) and provides explicit formulae for determining the sample size needed to test hypotheses about a single parameter at a specified significance level and power. Simulation studies assess its accuracy for various model configurations and covariate distributions. The results show that the proposed method is more accurate than the previous approaches over the range of conditions considered here.
Suppression situations in multiple linear regression
(2006-06-01)
Shieh, G
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管理科學系
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Department of Management Science
This article proposes alternative expressions for the two most prevailing definitions of suppression without resorting to the standardized regression modeling. The formulation provides a simple basis for the examination of their relationship. For the two-predictor regression, the author demonstrates that the previous results in the literature are incomplete and oversimplified. The proposed approach also allows a natural extension for multiple regression with more than two predictor variables. It is shown that the conditions under which both types of suppression can occur are not fully congruent with the significance of the partial F test. This implies that all the standard variable selection techniques-backward elimination, forward selection, and stepwise regression procedures-can fail to detect suppression situations. This also explains the controversial findings in the redundancy or importance of correlated variables in applied settings. Furthermore, informative visual representations of various aspects of these phenomena are provided.
The effectiveness of randomized complete block design
(2004-02-01)
Shieh, G
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Jan, SL
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管理科學系
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Department of Management Science
This paper examines the relative efficiency of randomized complete block design as compared with that of completely randomized design. The most widely used measure of relative efficiency considers only the error variances of the two designs, therefore it does not provide the complete information concerning the sensitivity of the experiment in the final results. We study three alternative criteria related to the sensitivity issue and design planning consideration. The proposed relative measures employ the p-value, Scheffe confidence interval estimation and power of both designs. The distinct feature of this study is the focus on the estimated relative efficiency measures and their relation with the coefficient of partial determination between responses and block effects, given that treatment effects are present in the models. Furthermore, informative visual representations and numerical assessments of various aspects of their properties are also presented.