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Article: On improved EM algorithm and confidence interval construction for incomplete r(x)c tables

TitleOn improved EM algorithm and confidence interval construction for incomplete r(x)c tables
Authors
KeywordsBootstrap
Confidence Interval
Convergence Rate
Data Augmentation
Em Algorithm
Incomplete Data
Paired Binary Data
Small Sample Size
Issue Date2007
PublisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/csda
Citation
Computational Statistics and Data Analysis, 2007, v. 51 n. 6, p. 2919-2933 How to Cite?
AbstractConstructing confidence interval (CI) for functions of cell probabilities (e.g. rate difference, rate ratio and odds ratio) is a standard procedure for categorical data analysis in clinical trials and medical studies. In the presence of incomplete data, existing methods could be problematic. For example, the inverse of the observed information matrix may not exist and the asymptotic CIs based on delta methods are hence not available. Even though the inverse of the observed information matrix exists, the large-sample delta methods are generally not reliable in small-sample studies. In addition, existing expectation-maximization (EM) algorithm via the conventional data augmentation (DA) may suffer from slow convergence due to the introduction of too many latent variables. In this article, for r × c tables with incomplete data, we propose a novel DA scheme that requires fewer latent variables and this will consequently lead to a more efficient EM algorithm. We present two bootstrap-type CIs for parameters of interest via the new EM algorithm with and without the normality assumption. For r × c tables with only one incomplete/supplementary margin, the improved EM algorithm converges in only one step and the associated maximum likelihood estimates can hence be obtained in closed form. Theoretical and simulation results showed that the proposed EM algorithm outperforms the existing EM algorithm. Three real data from a neurological study, a rheumatoid arthritis study and a wheeze study are used to illustrate the methodologies. © 2006 Elsevier B.V. All rights reserved.
Persistent Identifierhttp://hdl.handle.net/10722/172428
ISSN
2015 Impact Factor: 1.179
2015 SCImago Journal Rankings: 1.283
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorTang, MLen_US
dc.contributor.authorNg, KWen_US
dc.contributor.authorTian, GLen_US
dc.contributor.authorTan, Men_US
dc.date.accessioned2012-10-30T06:22:28Z-
dc.date.available2012-10-30T06:22:28Z-
dc.date.issued2007en_US
dc.identifier.citationComputational Statistics and Data Analysis, 2007, v. 51 n. 6, p. 2919-2933en_US
dc.identifier.issn0167-9473en_US
dc.identifier.urihttp://hdl.handle.net/10722/172428-
dc.description.abstractConstructing confidence interval (CI) for functions of cell probabilities (e.g. rate difference, rate ratio and odds ratio) is a standard procedure for categorical data analysis in clinical trials and medical studies. In the presence of incomplete data, existing methods could be problematic. For example, the inverse of the observed information matrix may not exist and the asymptotic CIs based on delta methods are hence not available. Even though the inverse of the observed information matrix exists, the large-sample delta methods are generally not reliable in small-sample studies. In addition, existing expectation-maximization (EM) algorithm via the conventional data augmentation (DA) may suffer from slow convergence due to the introduction of too many latent variables. In this article, for r × c tables with incomplete data, we propose a novel DA scheme that requires fewer latent variables and this will consequently lead to a more efficient EM algorithm. We present two bootstrap-type CIs for parameters of interest via the new EM algorithm with and without the normality assumption. For r × c tables with only one incomplete/supplementary margin, the improved EM algorithm converges in only one step and the associated maximum likelihood estimates can hence be obtained in closed form. Theoretical and simulation results showed that the proposed EM algorithm outperforms the existing EM algorithm. Three real data from a neurological study, a rheumatoid arthritis study and a wheeze study are used to illustrate the methodologies. © 2006 Elsevier B.V. All rights reserved.en_US
dc.languageengen_US
dc.publisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/csdaen_US
dc.relation.ispartofComputational Statistics and Data Analysisen_US
dc.rightsComputational Statistics and Data Analysis. Copyright © Elsevier BV.-
dc.subjectBootstrapen_US
dc.subjectConfidence Intervalen_US
dc.subjectConvergence Rateen_US
dc.subjectData Augmentationen_US
dc.subjectEm Algorithmen_US
dc.subjectIncomplete Dataen_US
dc.subjectPaired Binary Dataen_US
dc.subjectSmall Sample Sizeen_US
dc.titleOn improved EM algorithm and confidence interval construction for incomplete r(x)c tablesen_US
dc.typeArticleen_US
dc.identifier.emailWang Ng, K: kaing@hkucc.hku.hken_US
dc.identifier.emailTian, GL: gltian@hku.hken_US
dc.identifier.authorityWang Ng, K=rp00765en_US
dc.identifier.authorityTian, GL=rp00789en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1016/j.csda.2006.11.035en_US
dc.identifier.scopuseid_2-s2.0-33846633805en_US
dc.identifier.hkuros138170-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-33846633805&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume51en_US
dc.identifier.issue6en_US
dc.identifier.spage2919en_US
dc.identifier.epage2933en_US
dc.identifier.isiWOS:000244630500013-
dc.publisher.placeThe Netherlandsen_US
dc.identifier.scopusauthoridTang, ML=7401974011en_US
dc.identifier.scopusauthoridWang Ng, K=7403178774en_US
dc.identifier.scopusauthoridTian, GL=25621549400en_US
dc.identifier.scopusauthoridTan, M=7401464906en_US

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