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Mathematical Modeling: Assumptions Affect Results

¹ St. Paul’s Hospital, Department of Laboratory Medicine, and the Department of Pathology, University of British Columbia, Vancouver, BC, Canada
² Department of Mathematics, University of British Columbia, Vancouver, BC, Canada

^aAddress correspondence to this author at: St. Paul’s Hospital Department of Laboratory Medicine and the University of British Columbia Department of Pathology. 1081 Burrard Street, Vancouver, BC, Canada, V6Z 1Y6. Fax 604-806h8815; e-mail dtholmes@interchange.ubc.ca.

The first 20% of the full text of this article appears below.

To the Editor:

Apple et al. (1) recently presented an analysis of the effect of imprecision (CV) on false positive cardiac troponin I (cTnI) results. After examining their methodology, we have identified problems with the model and arguments.

Key mathematical details are omitted, and some assumptions appear unrealistic. The authors model the plasma cTnI concentrations in a healthy reference population by an exponential distribution and the analytical error as gaussian using 2 assumed CV profiles: a baseline profile and the same scaled by a factor of 0.40. We observe 2 difficulties.

First, the baseline profile is incompletely specified, and the points provided (CVs of 37.5%, 25.0%, and 9.4% at true cTnIs of 0.05, 0.07, and 0.14 µg/L) imply SDs that decrease with increasing cTnI, which does not reflect reality (2)(3). Further, the "SD of the blank" (cTnI = 0 µg/L) is entirely unspecified. To contrast, we constructed empirical profiles using mean concentration data and CVs from a recent paper comparing 15 cTnI assays (4). Fig. 1a compares the 5 cTnI assays whose data overlap the concentration range 0.05–0.14 µg/L to those used by Apple et al. . . . [Full Text of this Article]