6,636 research outputs found

    Confidence-interval construction for rate ratio in matched-pair studies with incomplete data

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    Matched-pair design is often used in clinical trials to increase the efficiency of establishing equivalence between two treatments with binary outcomes. In this article, we consider such a design based on rate ratio in the presence of incomplete data. The rate ratio is one of the most frequently used indices in comparing efficiency of two treatments in clinical trials. In this article, we propose 10 confidence-interval estimators for the rate ratio in incomplete matched-pair designs. A hybrid method that recovers variance estimates required for the rate ratio from the confidence limits for single proportions is proposed. It is noteworthy that confidence intervals based on this hybrid method have closed-form solution. The performance of the proposed confidence intervals is evaluated with respect to their exact coverage probability, expected confidence interval width, and distal and mesial noncoverage probability. The results show that the hybrid Agresti–Coull confidence interval based on Fieller’s theorem performs satisfactorily for small to moderate sample sizes. Two real examples from clinical trials are used to illustrate the proposed confidence intervals.postprin

    Crack propagation in brittle solid containing 3D surface fracture under uniaxial compression

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    2003-2004 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

    The nested dirichlet distribution and incomplete categorical data analysis

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    The nested Dirichlet distribution (NDD) is an important distribution defined on the closed n-dimensional simplex. It includes the classical Dirichlet distribution and is useful in incomplete categorical data (ICD) analysis. In this article, we develop the distributional properties of NDD. New large-sample likelihood and small-sample Bayesian approaches for analyzing ICD are proposed and compared with existing likelihood/Bayesian strategies. We show that the new approaches have at least three advantages over existing approaches based on the traditional Dirichlet distribution in both frequentist and conjugate Bayesian inference for ICD. The new methods possess closed-form expressions for both the maximum likelihood and Bayes estimates when the likelihood function is in NDD form; produce computationally efficient EM and data augmentation algorithms when the likelihood is not in NDD form; and provide exact sampling procedures for some special cases. The methodologies are illustrated with simulated and real data.published_or_final_versio

    Further properties and new applications of the nested Dirichlet distribution

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    Recently, Ng et al. (2009) studied a new family of distributions, namely the nested Dirichlet distributions. This family includes the traditional Dirichlet distribution as a special member and can be adopted to analyze incomplete categorical data. However, other important aspects of the family, such as marginal and conditional distributions and related properties are not yet available in the literature. Moreover, diverse applications of the family to the real world need to be further explored. In this paper, we first obtain the marginal and conditional distributions and other related properties of the nested Dirichlet distribution. We then present new applications of the family in fitting competing-risks model, analyzing incomplete categorical data and evaluating cancer diagnosis tests. Three real data involving failure times of radio transmitter receivers, attitude toward the death penalty and ultrasound ratings for breast cancer metastasis are provided. © 2009 Elsevier B.V. All rights reserved.postprin

    A robust computational algorithm for inverse photomask synthesis in optical projection lithography

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    Inverse lithography technology formulates the photomask synthesis as an inverse mathematical problem. To solve this, we propose a variational functional and develop a robust computational algorithm, where the proposed functional takes into account the process variations and incorporates several regularization terms that can control the mask complexity. We establish the existence of the minimizer of the functional, and in order to optimize it effectively, we adopt an alternating minimization procedure with Chambolle's fast duality projection algorithm. Experimental results show that our proposed algorithm is effective in synthesizing high quality photomasks as compared with existing methods.published_or_final_versio

    Dirichlet composition distribution for compositional data with zero components: An application to fluorescence in situ hybridization (FISH) detection of chromosome

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    Copyright © 2021 The Authors. Zeros in compositional data are very common and can be classified into rounded and essential zeros. The rounded zero refers to a small proportion or below detection limit value, while the essential zero refers to the complete absence of the component in the composition. In this article, we propose a new framework for analyzing compositional data with zero entries by introducing a stochastic representation. In particular, a new distribution, namely the Dirichlet composition distribution, is developed to accommodate the possible essential-zero feature in compositional data. We derive its distributional properties (e.g., its moments). The calculation of maximum likelihood estimates via the Expectation-Maximization (EM) algorithm will be proposed. The regression model based on the new Dirichlet composition distribution will be considered. Simulation studies are conducted to evaluate the performance of the proposed methodologies. Finally, our method is employed to analyze a dataset of fluorescence in situ hybridization (FISH) for chromosome detection.National Natural Science Foundation of China. Grant Numbers: 12171167, 11801184; Research Grant Council of the Hong Kong Special Administrative Region. Grant Numbers: UGC/FDS14/P06/17, UGC/FDS14/P02/18

    Sample Size Determination for Interval Estimation of the Prevalence of a Sensitive Attribute Under Randomized Response Models

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    National Natural Science Foundation of China (Grant No. 11871124); Research Grant Council of the Hong Kong Special Administrative Region (projects UGC/FDS14/P06/17 and UGC/FDS14/P02/18)
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