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The empirical likelihood prior applied to bias reduction of general estimating equations.

ABSTRACT: The practice of employing empirical likelihood (EL) components in place of parametric likelihood functions in the construction of Bayesian-type procedures has been well-addressed in the modern statistical literature. The EL prior, a Jeffreys-type prior, which asymptotically maximizes the Shannon mutual information between data and the parameters of interest, is rigorously derived. The focus of the proposed approach is on an integrated Kullback-Leibler distance between the EL-based posterior and prior density functions. The EL prior density is the density function for which the corresponding posterior form is asymptotically negligibly different from the EL. The proposed result can be used to develop a methodology for reducing the asymptotic bias of solutions of general estimating equations and M-estimation schemes by removing the first-order term. This technique is developed in a similar manner to methods employed to reduce the asymptotic bias of maximum likelihood estimates via penalizing the underlying parametric likelihoods by their Jeffreys invariant priors. A real data example related to a study of myocardial infarction illustrates the attractiveness of the proposed technique in practical aspects.

SUBMITTER: Vexler A

PROVIDER: S-EPMC6481956 | biostudies-literature | 2019 Oct

REPOSITORIES: biostudies-literature

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The empirical likelihood prior applied to bias reduction of general estimating equations.

Vexler Albert A Zou Li L Hutson Alan D AD

Computational statistics & data analysis 20190411

The practice of employing empirical likelihood (EL) components in place of parametric likelihood functions in the construction of Bayesian-type procedures has been well-addressed in the modern statistical literature. The EL prior, a Jeffreys-type prior, which asymptotically maximizes the Shannon mutual information between data and the parameters of interest, is rigorously derived. The focus of the proposed approach is on an integrated Kullback-Leibler distance between the EL-based posterior and ...[more]

PMID: 31031458

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Project description:ImportanceThere is increasing concern that continued use of a glomerular filtration rate (GFR) estimating equation adjusted for a single racial group could exacerbate chronic kidney disease-related disparities and inequalities.ObjectiveTo assess the performance of GFR estimating equations across varied patient populations.Data sourcesPubMed, Embase, Web of Science, ClinicalTrials.gov, and Scopus databases were systematically searched from January 2012 to February 2023.Study selectionInclusion criteria were studies that compared measured GFR with estimated GFR in adults using established reference standards and methods. A total of 6663 studies were initially identified for screening and review.Data extraction and synthesisFollowing Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines, 2 authors independently extracted data on studies that examined the bias and accuracy of GFR estimating equations. For each outcome, a random-effects model was used to calculate pooled estimates. Data analysis was conducted from March to December 2023.Main outcomes and measuresThe primary outcomes were bias and accuracy of estimated GFRs in Black vs non-Black patients, as well as in individuals with chronic conditions. Bias was defined as the median difference between the measured GFR and the estimated GFR. Accuracy was assessed with P30 (the proportion of persons in a data set whose estimated GFR values were within 30% of measured GFR values) and measures of heterogeneity.ResultsA total of 12 studies with a combined 44 721 patients were included. Significant heterogeneity was found in the bias of various GFR estimation equations. Race-corrected equations and creatinine-based equations tended to overestimate GFR in Black populations and showed mixed results in non-Black populations. For creatinine-based equations, the mean bias in subgroup analysis was 2.1 mL/min/1.73 m2 (95% CI, -0.2 mL/min/1.73 m2 to 4.4 mL/min/1.73 m2) in Black persons and 1.3 mL/min/1.73 m2 (95% CI, 0.0 mL/min/1.73 m2 to 2.5 mL/min/1.73 m2) in non-Black persons. Equations using only cystatin C had small biases. Regarding accuracy, heterogeneity was high in both groups. The overall P30 was 84.5% in Black persons and 87.8% in non-Black persons. Creatinine-based equations were more accurate in non-Black persons than in Black persons. For creatinine-cystatin C equations, the P30 was higher in non-Black persons. There was no significant P30 difference in cystatin C-only equations between the 2 groups. In patients with chronic conditions, P30 values were generally less than 85%, and the biases varied widely.Conclusions and relevanceThis systematic review and meta-analysis of GFR estimating equations suggests that there is bias in race-based GFR estimating equations, which exacerbates kidney disease disparities. Development of a GFR equation independent of race is a crucial starting point, but not the sole solution. Addressing the disproportionate burden of kidney failure on Black individuals in the US requires an enduring, multifaceted approach that should include improving diagnostics, tackling social determinants of health, confronting systemic racism, and using effective disease prevention and management strategies.

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The empirical likelihood prior applied to bias reduction of general estimating equations.

Publications

The empirical likelihood prior applied to bias reduction of general estimating equations.

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