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Clinical Chemistry and Laboratory Medicine (CCLM)

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‘Likelihood-ratio’ and ‘odds’ applied to monitoring of patients as a supplement to ‘reference change value’ (RCV)

Per Hyltoft Petersen1 / Sverre Sandberg2 / Natàlia Iglesias3 / György Sölétormos4 / Aasne Karine Aarsand5 / Ivan Brandslund6 / Lone G.M. Jørgensen7

1NOKLUS, Norwegian Quality Improvement of Primary Care Laboratories, Division for General Practice, University of Bergen, Bergen, Norway

2NOKLUS, Norwegian Quality Improvement of Primary Care Laboratories, Division for General Practice, University of Bergen, Bergen, Norway and Laboratory of Clinical Biochemistry, Haukeland University Hospital, Bergen, Norway

3Department of Pharmacy, City Hospital, Birmingham, UK

4Department of Clinical Biochemistry, Hillerød Hospital, Hillerød, Denmark

5Laboratory of Clinical Biochemistry, Haukeland University Hospital, Bergen, Norway

6Regional Health Research, University of Southern Denmark, Odense, Denmark

7The Research Unit for General Practice in Copenhagen, Centre for Health and Society, Copenhagen, Denmark

Corresponding author: Per Hyltoft Petersen, NOKLUS, Norwegian Quality Improvement of Primary Care Laboratories, Division for General Practice, University of Bergen, Bergen, Norway, Postal address: Flittig Lise Vej 20, 5250 Odense SV, Denmark Phone: +45-65-962565,

Citation Information: Clinical Chemical Laboratory Medicine. Volume 46, Issue 2, Pages 157–164, ISSN (Online) 14374331, ISSN (Print) 14346621, DOI: 10.1515/CCLM.2008.042, December 2007

Publication History

Received:
2007-08-08
Accepted:
2007-10-14
Published Online:
2007-12-13

Abstract

Background: Interpretation of serial data in monitoring of patients is usually performed by use of the ‘reference change value’ (RCV). While this tool for interpretation of measured differences is simple and clear, there are a number of drawbacks attached to the uncritical use of this concept. It is a dichotomised interpretation of continuous data using a fixed probability without any counter hypothesis. Therefore, a tool for better understanding and interpretation of measured differences in monitoring is needed.

Theory: The concept of sensitivity, specificity, likelihood ratios and odds used for diagnostic test evaluations is applied to monitoring by substituting measured concentrations with measured differences. Thus, two frequency distributions of differences are assumed, one for a stable, steady-state, situation and one for a certain change. Values exceeding a measured difference will thus represent ‘false change’ for the stable and ‘true change’ for the change and the ratio between these will define the likelihood. By making the hypothesis of change variable and equal to the actual difference, the distribution corresponding to the true changes for the measured difference varies with this. Consequently, the likelihood ratio for change increases with growing measured difference and when used together with the pre-test odds or pre-test probability, the post-test odds and post-test probability, related to the clinical situation, can be calculated.

Results: One example is acute intermittent porphyria, where increasing excretion of porphobilinogen is characteristic for an attack. The within-subject biological variation is estimated to 25%, which for two measurements gives a variation of 35% for measured differences. Three pre-test probabilities are assumed and illustrate that post-test odds and probability depends on both the pre-test probability and the measured difference. A second example is monitoring women in a follow-up after treatment of breast cancer, using the tumour marker CA 15-3. The within-subject biological variation is estimated to 14.9% and for differences 21% (2½×14.9 due to two measurements). Here, the monitoring is totally scheduled and the frequency of progression depends on the time after treatment. Thus, the pre-test probability varies with time so that a certain measured difference with a given likelihood ratio will result in varying post-test odds depending on time.

Conclusions: The concept presented here expands the earlier concept of RCVs by making it possible to have an estimate of the post-test odds for a certain difference to occur based on likelihood ratios and pre-test odds.

Clin Chem Lab Med 2008;46:157–64.

Keywords: post-test odds (a posteriori odds); post-test probability; pre-test odds (a priori odds); pre-test probability; within-subject biological variation for porphobilinogen and tumour markers

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