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Chernoff Index for Cox Test of Separate Parametric Families.

ABSTRACT: The asymptotic efficiency of a generalized likelihood ratio test proposed by Cox is studied under the large deviations framework for error probabilities developed by Chernoff. In particular, two separate parametric families of hypotheses are considered (Cox, 1961, 1962). The significance level is set such that the maximal type I and type II error probabilities for the generalized likelihood ratio test decay exponentially fast with the same rate. We derive the analytic form of such a rate that is also known as the Chernoff index (Chernoff, 1952), a relative efficiency measure when there is no preference between the null and the alternative hypotheses. We further extend the analysis to approximate error probabilities when the two families are not completely separated. Discussions are provided concerning the implications of the present result on model selection.

SUBMITTER: Li X

PROVIDER: S-EPMC5865707 | biostudies-literature | 2018 Feb

REPOSITORIES: biostudies-literature

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Chernoff Index for Cox Test of Separate Parametric Families.

Li Xiaoou X Liu Jingchen J Ying Zhiliang Z

Annals of statistics 20180222 1

The asymptotic efficiency of a generalized likelihood ratio test proposed by Cox is studied under the large deviations framework for error probabilities developed by Chernoff. In particular, two separate parametric families of hypotheses are considered (Cox, 1961, 1962). The significance level is set such that the maximal type I and type II error probabilities for the generalized likelihood ratio test decay exponentially fast with the same rate. We derive the analytic form of such a rate that is ...[more]

PMID: 29581648

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Project description:BackgroundDysbiosis of the human gut microbiome is defined as a maladaptive or clinically relevant deviation of the community profile from the healthy or normal state. Dysbiosis has been implicated in an extensive set of metabolic, auto-immune, and infectious diseases, and yet there is substantial inter-individual variation in microbiome composition even within body sites of healthy humans. An individual's microbiome varies over time in a high-dimensional space to form their personal microbiome cloud. This cloud may or may not be similar to that of other people, both in terms of the average microbiome profile (conformity) and the diameter of the cloud (stability). However, there is currently no robust non-parametric test that determines whether a patient's microbiome cloud is an outlier with respect to a reference group of healthy individuals with widely varying microbiome profiles.MethodsHere, we propose a test for outliers' detection in the human gut microbiome that accounts for the wide range of microbiome phenotypes observed in a typical set of healthy individuals and for intra-individual temporal variation. Our robust nonparametric outlier detection test, the CLOUD test, performs two assessments of a patient's microbiome health: conformity, the extent to which the patient's microbiome cloud is ecologically similar to a subset of healthy subjects; and stability, which compares the cloud diameter of a patient to those of healthy subjects. The CLOUD test is based on locally linear embedded ecological distances, allowing it to account for widely varying microbiome compositions among reference individuals. It also leverages temporal variability within patients and reference individuals to increase the robustness of the test.ResultsWe describe the CLOUD test, and we apply it to one novel and two previously published cohorts of patients receiving fecal microbiota transplantation for recurrent Clostridium difficile colitis, as well as to two known healthy cohorts, demonstrating high concordance of the CLOUD conformity and stability indices with clinical outcomes.ConclusionsAlthough the CLOUD test is not, on its own, a test for clinical dysbiosis, it nonetheless provides a framework for outlier testing that could be incorporated into evaluation of suspected dysbiosis, which may play a role in diagnosis and prognosis of numerous pediatric and adult diseases.

Dataset Information

Chernoff Index for Cox Test of Separate Parametric Families.

Publications

Chernoff Index for Cox Test of Separate Parametric Families.

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