Taylor Series Approximation for Accurate Generalized Confidence Intervals of Ratios of Log-Normal Standard Deviations for Meta-Analysis Using Means and Standard Deviations in Time Scale

Pei-Fu Chen; Franklin Dexter

doi:10.1002/pst.2467

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Taylor Series Approximation for Accurate Generalized Confidence Intervals of Ratios of Log-Normal Standard Deviations for Meta-Analysis Using Means and Standard Deviations in Time Scale

Journal article

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Peer reviewed

Taylor Series Approximation for Accurate Generalized Confidence Intervals of Ratios of Log-Normal Standard Deviations for Meta-Analysis Using Means and Standard Deviations in Time Scale

Pei-Fu Chen and Franklin Dexter

Pharmaceutical statistics : the journal of the pharmaceutical industry, Vol.24(1), e2467

01/2025

DOI: 10.1002/pst.2467

PMCID: PMC11755222

PMID: 39846155

Appears in UI Libraries Support Open Access

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Abstract

With contemporary anesthetic drugs, the efficacy of general anesthesia is assured. Health-economic and clinical objectives are related to reductions in the variability in dosing, variability in recovery, etc. Consequently, meta-analyses for anesthesiology research would benefit from quantification of ratios of standard deviations of log-normally distributed variables (e.g., surgical duration). Generalized confidence intervals can be used, once sample means and standard deviations in the raw, time, scale, for each study and group have been used to estimate the mean and standard deviation of the logarithms of the times (i.e., "log-scale"). We examine the matching of the first two moments versus also using higher-order terms, following Higgins et al. 2008 and Friedrich et al. 2012. Monte Carlo simulations revealed that using the first two moments 95% confidence intervals had coverage 92%-95%, with small bias. Use of higher-order moments worsened confidence interval coverage for the log ratios, especially for coefficients of variation in the time scale of 50% and for larger sample sizes per group, resulting in 88% coverage. We recommend that for calculating confidence intervals for ratios of standard deviations based on generalized pivotal quantities and log-normal distributions, when relying on transformation of sample statistics from time to log scale, use the first two moments, not the higher order terms.

Anesthesiology - methods

Anesthesiology - statistics & numerical data

Anesthetics

Computer Simulation

Confidence Intervals

Data Interpretation, Statistical

Humans

Meta-Analysis as Topic

Models, Statistical

Monte Carlo Method

Time Factors

UIOWA OA Agreement

Details

Title: Subtitle: Taylor Series Approximation for Accurate Generalized Confidence Intervals of Ratios of Log-Normal Standard Deviations for Meta-Analysis Using Means and Standard Deviations in Time Scale
Creators: Pei-Fu Chen - Yuan Ze University
Franklin Dexter - University of Iowa
Resource Type: Journal article
Publication Details: Pharmaceutical statistics : the journal of the pharmaceutical industry, Vol.24(1), e2467
DOI: 10.1002/pst.2467
PMID: 39846155
PMCID: PMC11755222
NLM abbreviation: Pharm Stat
ISSN: 1539-1612
eISSN: 1539-1612
Publisher: Wiley
Grant note: Departmental
Language: English
Date published: 01/2025
Academic Unit: Anesthesia
Record Identifier: 9984775019602771

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