Reference range: which statistical intervals to use?
Reference range: which statistical intervals to use?
Reference ranges, which are data-based intervals aiming to contain a pre-specified large proportion of the population values, are powerful tools to analyse observations in clinical laboratories. Their main point is to classify any future observations from the population which fall outside them as atypical and thus may warrant further investigation. As a reference range is constructed from a random sample from the population, the event ‘a reference range contains (100 P)% of the population’ is also random. Hence, all we can hope for is that such event has a large occurrence probability. In this paper we argue that some intervals, including the P prediction interval, are not suitable as reference ranges since there is a substantial probability that these intervals contain less than (100 P)% of the population, especially when the sample size is large. In contrast, a (P,γ) tolerance interval is designed to contain (100 P)% of the population with a pre-specified large confidence γ so it is eminently adequate as a reference range. An example based on real data illustrates the paper’s key points.
Nonparametric prediction interval, Nonparametric tolerance interval, Prediction interval, Reference range, Tolerance interval
1-12
Liu, Wei
b64150aa-d935-4209-804d-24c1b97e024a
Bretz, Frank
aada8c67-05d5-4a06-ad97-92a24c6f1d6a
Cortina-Borja, Mario
028ebae2-003d-413b-95cc-47d76914b006
Liu, Wei
b64150aa-d935-4209-804d-24c1b97e024a
Bretz, Frank
aada8c67-05d5-4a06-ad97-92a24c6f1d6a
Cortina-Borja, Mario
028ebae2-003d-413b-95cc-47d76914b006
Liu, Wei, Bretz, Frank and Cortina-Borja, Mario
(2020)
Reference range: which statistical intervals to use?
Statistical Methods in Medical Research, .
(doi:10.1177/0962280220961793).
Abstract
Reference ranges, which are data-based intervals aiming to contain a pre-specified large proportion of the population values, are powerful tools to analyse observations in clinical laboratories. Their main point is to classify any future observations from the population which fall outside them as atypical and thus may warrant further investigation. As a reference range is constructed from a random sample from the population, the event ‘a reference range contains (100 P)% of the population’ is also random. Hence, all we can hope for is that such event has a large occurrence probability. In this paper we argue that some intervals, including the P prediction interval, are not suitable as reference ranges since there is a substantial probability that these intervals contain less than (100 P)% of the population, especially when the sample size is large. In contrast, a (P,γ) tolerance interval is designed to contain (100 P)% of the population with a pre-specified large confidence γ so it is eminently adequate as a reference range. An example based on real data illustrates the paper’s key points.
Text
0962280220961793
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More information
Accepted/In Press date: 8 September 2020
e-pub ahead of print date: 14 October 2020
Keywords:
Nonparametric prediction interval, Nonparametric tolerance interval, Prediction interval, Reference range, Tolerance interval
Identifiers
Local EPrints ID: 444875
URI: http://eprints.soton.ac.uk/id/eprint/444875
ISSN: 0962-2802
PURE UUID: de408098-a5e9-4fb6-b692-55d3e9235426
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Date deposited: 09 Nov 2020 17:30
Last modified: 17 Mar 2024 02:37
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Author:
Frank Bretz
Author:
Mario Cortina-Borja
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