Optimal screening for patients with hyperparathyroidism with use of serum calcium observations. A decision-theoretical analysis

Abstract

The conventional upper 95 percentile reference limit of serum calcium does not necessarily constitute an optimal decision limit in screening for patients with hyperparathyroidism. The design of optimal screening procedures has to consider (a) the prevalence of disease; (b) the relative importance of making correct classifications of patients; and (c) the influence of analytical imprecision and inaccuracy. Based on serum calcium determinations from three reference sample groups (healthy individuals, patients with hyperparathyroidism, and patients with hypercalcaemia due to malignant disease) optimal decision limits were calculated for different screening situations. Optimum was defined in terms of estimated ‘costs’ due to misclassification. Different values for disease prevalence were used, as well as different weighting factors reflecting the importance related to correct classification of healthy and pathological patients.

For a disease prevalence of 5% the optimal decision limit varies between 2.59 and 2.65 mmol/l for a weighting ratio false positives to false negatives of between 1:5 to 5:1. For a prevalence of 0.1% the corresponding range was 2.67–2.72 mmol/l. Compared to classification on the basis of the conventional upper reference limit, the application of optimal decision limits means significantly lower costs due to misclassification. Analytical bias then has to be kept stable within ± 0.01 mmol/l.

Inter-laboratory analytical variation also has to be reduced to the same level in order to make it possible to transfer reference values, decision limits and single patient values to other laboratories.

Key-words:

• decision theory
• hyperparathyroidism
• screening
• serum calcium
• simulation