Exact parametric confidence intervals for Bland-Altman limits of agreement

Carkeet, Andrew (2015) Exact parametric confidence intervals for Bland-Altman limits of agreement. Optometry and Vision Science, 92(3), e71-e80.

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Abstract

Purpose

The previous literature on Bland-Altman analysis only describes approximate methods for calculating confidence intervals for 95% Limits of Agreement (LoAs). This paper describes exact methods for calculating such confidence intervals, based on the assumption that differences in measurement pairs are normally distributed.

Methods

Two basic situations are considered for calculating LoA confidence intervals: the first where LoAs are considered individually (i.e. using one-sided tolerance factors for a normal distribution); and the second, where LoAs are considered as a pair (i.e. using two-sided tolerance factors for a normal distribution). Equations underlying the calculation of exact confidence limits are briefly outlined.

Results

To assist in determining confidence intervals for LoAs (considered individually and as a pair) tables of coefficients have been included for degrees of freedom between 1 and 1000. Numerical examples, showing the use of the tables for calculating confidence limits for Bland-Altman LoAs, have been provided.

Conclusions

Exact confidence intervals for LoAs can differ considerably from Bland and Altman’s approximate method, especially for sample sizes that are not large. There are better, more precise methods for calculating confidence intervals for LoAs than Bland and Altman’s approximate method, although even an approximate calculation of confidence intervals for LoAs is likely to be better than none at all. Reporting confidence limits for LoAs considered as a pair is appropriate for most situations, however there may be circumstances where it is appropriate to report confidence limits for LoAs considered individually.

Impact and interest:

3 citations in Scopus
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7 citations in Web of Science®

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ID Code: 79116
Item Type: Journal Article
Refereed: Yes
Keywords: exact confidence limits, Bland-Altman limits of agreement, two sided tolerance factors, one sided tolerance factors
DOI: 10.1097/OPX.0000000000000513
ISSN: 1538-9235
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000)
Australian and New Zealand Standard Research Classification > MEDICAL AND HEALTH SCIENCES (110000) > OPTOMETRY AND OPHTHALMOLOGY (111300)
Divisions: Current > QUT Faculties and Divisions > Faculty of Health
Current > Institutes > Institute of Health and Biomedical Innovation
Current > Schools > School of Optometry & Vision Science
Copyright Owner: Copyright 2015 American Academy of Optometry
Copyright Statement: This is a non-final version of an article published in final form in (provide complete journal citation)
Deposited On: 09 Feb 2015 23:41
Last Modified: 06 Apr 2016 07:16

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