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An omnibus non-parametric test of equality in distribution for unknown functions.

ABSTRACT: We present a novel family of nonparametric omnibus tests of the hypothesis that two unknown but estimable functions are equal in distribution when applied to the observed data structure. We developed these tests, which represent a generalization of the maximum mean discrepancy tests described in Gretton et al. [2006], using recent developments from the higher-order pathwise differentiability literature. Despite their complex derivation, the associated test statistics can be expressed rather simply as U-statistics. We study the asymptotic behavior of the proposed tests under the null hypothesis and under both fixed and local alternatives. We provide examples to which our tests can be applied and show that they perform well in a simulation study. As an important special case, our proposed tests can be used to determine whether an unknown function, such as the conditional average treatment effect, is equal to zero almost surely.

SUBMITTER: Luedtke AR

PROVIDER: S-EPMC6476331 | biostudies-literature | 2019 Feb

REPOSITORIES: biostudies-literature

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An omnibus non-parametric test of equality in distribution for unknown functions.

Luedtke Alexander R AR Carone Marco M van der Laan Mark J MJ

Journal of the Royal Statistical Society. Series B, Statistical methodology 20181102 1

We present a novel family of nonparametric omnibus tests of the hypothesis that two unknown but estimable functions are equal in distribution when applied to the observed data structure. We developed these tests, which represent a generalization of the maximum mean discrepancy tests described in Gretton et al. [2006], using recent developments from the higher-order pathwise differentiability literature. Despite their complex derivation, the associated test statistics can be expressed rather simp ...[more]

PMID: 31024219

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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.

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An omnibus non-parametric test of equality in distribution for unknown functions.

Publications

An omnibus non-parametric test of equality in distribution for unknown functions.

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