Quantifying the Fraction of Missing Information for Hypothesis Testing in Statistical and Genetic Studies

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Quantifying the Fraction of Missing Information for Hypothesis Testing in Statistical and Genetic Studies

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dc.contributor.author Nicolae, Dan L.
dc.contributor.author Meng, Xiao-Li
dc.contributor.author Kong, Augustine
dc.date.accessioned 2009-04-01T14:26:46Z
dc.date.issued 2008
dc.identifier.citation Nicolae, Dan L., Xiao-Li Meng, and Augustine Kong. 2008. Quantifying the fraction of missing information for hypothesis testing in statistical and genetic studies. statistical science 23(3): 287-312. en
dc.identifier.issn 0883-4237 en
dc.identifier.uri http://nrs.harvard.edu/urn-3:HUL.InstRepos:2766348
dc.description.abstract Many practical studies rely on hypothesis testing procedures applied to data sets with missing information. An important part of the analysis is to determine the impact of the missing data on the performance of the test, and this can be done by properly quantifying the relative (to complete data) amount of available information. The problem is directly motivated by applications to studies, such as linkage analyses and haplotype-based association projects, designed to identify genetic contributions to complex diseases. In the genetic studies the relative information measures are needed for the experimental design, technology comparison, interpretation of the data, and for understanding the behavior of some of the inference tools. The central difficulties in constructing such information measures arise from the multiple, and sometimes conflicting, aims in practice. For large samples, we show that a satisfactory, likelihood-based general solution exists by using appropriate forms of the relative Kullback–Leibler information, and that the proposed measures are computationally inexpensive given the maximized likelihoods with the observed data. Two measures are introduced, under the null and alternative hypothesis respectively. We exemplify the measures on data coming from mapping studies on the inflammatory bowel disease and diabetes. For small-sample problems, which appear rather frequently in practice and sometimes in disguised forms (e.g., measuring individual contributions to a large study), the robust Bayesian approach holds great promise, though the choice of a general-purpose “default prior” is a very challenging problem. We also report several intriguing connections encountered in our investigation, such as the connection with the fundamental identity for the EM algorithm, the connection with the second CR (Chapman–Robbins) lower information bound, the connection with entropy, and connections between likelihood ratios and Bayes factors. We hope that these seemingly unrelated connections, as well as our specific proposals, will stimulate a general discussion and research in this theoretically fascinating and practically needed area. en
dc.description.sponsorship Statistics en
dc.language.iso en_US en
dc.publisher Institute of Mathematical Statistics en
dc.relation.isversionof http://dx.doi.org/10.1214/07-STS244 en
dash.license LAA
dc.subject entropy en
dc.subject Fisher information en
dc.subject EM algorithm en
dc.subject relative information en
dc.subject noninformative prior en
dc.subject haplotype-based association studies en
dc.subject genetic linkage studies en
dc.subject Kullback–Leibler information en
dc.subject partial likelihood en
dc.subject Cox regression en
dc.title Quantifying the Fraction of Missing Information for Hypothesis Testing in Statistical and Genetic Studies en
dc.type Journal Article
dc.description.version Version of Record
dc.relation.journal Statistical Science en
dash.depositing.author Meng, Xiao-Li

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  • FAS Scholarly Articles [7594]
    Peer reviewed scholarly articles from the Faculty of Arts and Sciences of Harvard University

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