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Global identifiability of latent class models with applications to diagnostic test accuracy studies: A Grobner basis approach.

ABSTRACT: Identifiability of statistical models is a fundamental regularity condition that is required for valid statistical inference. Investigation of model identifiability is mathematically challenging for complex models such as latent class models. Jones et al. used Goodman's technique to investigate the identifiability of latent class models with applications to diagnostic tests in the absence of a gold standard test. The tool they used was based on examining the singularity of the Jacobian or the Fisher information matrix, in order to obtain insights into local identifiability (ie, there exists a neighborhood of a parameter such that no other parameter in the neighborhood leads to the same probability distribution as the parameter). In this paper, we investigate a stronger condition: global identifiability (ie, no two parameters in the parameter space give rise to the same probability distribution), by introducing a powerful mathematical tool from computational algebra: the Gröbner basis. With several existing well-known examples, we argue that the Gröbner basis method is easy to implement and powerful to study global identifiability of latent class models, and is an attractive alternative to the information matrix analysis by Rothenberg and the Jacobian analysis by Goodman and Jones et al.

SUBMITTER: Duan R

PROVIDER: S-EPMC7036323 | biostudies-literature | 2020 Mar

REPOSITORIES: biostudies-literature

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Global identifiability of latent class models with applications to diagnostic test accuracy studies: A Gröbner basis approach.

Duan Rui R Cao Ming M Ning Yang Y Zhu Mingfu M Zhang Bin B McDermott Aidan A Chu Haitao H Zhou Xiaohua X Moore Jason H JH Ibrahim Joseph G JG Scharfstein Daniel O DO Chen Yong Y

Biometrics 20191106 1

Identifiability of statistical models is a fundamental regularity condition that is required for valid statistical inference. Investigation of model identifiability is mathematically challenging for complex models such as latent class models. Jones et al. used Goodman's technique to investigate the identifiability of latent class models with applications to diagnostic tests in the absence of a gold standard test. The tool they used was based on examining the singularity of the Jacobian or the Fi ...[more]

PMID: 31444807

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Project description:BackgroundTyphoid fevers are infections caused by the bacteria Salmonella enterica serovar Typhi (Salmonella Typhi) and Paratyphi A, B and C (Salmonella Paratyphi). Approximately 17.8 million incident cases of typhoid fever occur annually, and incidence is highest in children. The accuracy of current diagnostic tests of typhoid fever is poorly understood. We aimed to determine the comparative accuracy of available tests for the pediatric population.MethodsWe first conducted a systematic literature review to identify studies that compared diagnostic tests for typhoid fever in children (aged ≤15 years) to blood culture results. We applied a Bayesian latent-class extension to a network meta-analysis model. We modelled known diagnostic properties of bone marrow culture and the relationship between bone marrow and blood culture as informative priors in a Bayesian framework. We tested sensitivities for the proportion of negative blood samples that were false as well as bone marrow sensitivity and specificity.ResultsWe found 510 comparisons from 196 studies and 57 specific to the pediatric population. IgM-based tests outperformed their IgG-based counterparts for ELISA and Typhidot tests. The lateral flow IgG test performed comparatively well with 92% sensitivity (72% to 98% across scenario analyses) and 94% specificity. The most sensitive test of those investigated for the South Asian pediatric population was the Reverse Passive Hemagglutination Assay with 99% sensitivity (98% - 100% across scenario analyses). Adding a Widal slide test to other typhoid diagnostics did not substantially improve diagnostic performance beyond the single test alone, however, a lateral flow-based IgG rapid test combined with the typhoid/paratyphoid (TPT) assay yielded improvements in sensitivity without substantial declines in specificity and was the best performing combination test in this setting.ConclusionIn the pediatric population, lateral-flow IgG, TPT and Reverse Passive Hemagglutination tests had high diagnostic accuracy compared to other diagnostics. Combinations of tests may provide a feasible option to increase diagnostic sensitivity. South Asia has the most informed set of data on typhoid diagnostic testing accuracy, and the evidence base in other important regions needs to be expanded.

Dataset Information

Global identifiability of latent class models with applications to diagnostic test accuracy studies: A Grobner basis approach.

Publications

Global identifiability of latent class models with applications to diagnostic test accuracy studies: A Gröbner basis approach.

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