Validation of an equation for free calcium estimation: accuracy improves after adjustment for phosphate and CO.

Purpose: Free calcium is the gold standard for diagnosis of calcium disorders, although calcium assessment is routinely performed by albumin-adjusted calcium. Our objective was to develop a novel-specific correction equation for free calcium employing serum total calcium and other analytes.

Methods: Retrospective single-center cohort study. A new equation for free calcium assessment was formulated from data of hospitalized patients (n = 3481, measurements = 7157) and tested in a validation cohort (n = 3218, measurements = 6911). All measurements were performed simultaneously from the same blood draw.

Results: Total CO and phosphate, in addition to albumin, were the principal factors associated to calcium misdiagnosis. A novel laboratory-specific prediction equation was developed: free calcium (mmol/L) = 0.541 + (total calcium [mmol/L] *0.441) - (serum albumin [g/L] *0.0067) - (serum phosphate [mmol/L] *0.0425) - (CO [mmol/L] *0.003). This new equation substantially improved adjusted R to 0.67 (95% CI 0.78-0.82, p < 0.001; Kendall's c-tau: 0.28, p < 0.001). Bland-Altman plots of estimated free calcium and free calcium showed a mean difference of - 0.0006 mmol/L (LOA + 0.126 to - 0.124). In validation cohort, the AUC-ROC curves for hypercalcemia and hypocalcemia diagnosis deploying the new equation were 0.88 (95% CI 0.86-0.89, p < 0.001) and 0.98 (95% CI 0.97-99, p < 0.001), respectively, which were superior to historical formulas for calcium. In univariate models, eGFR was associated with Ca-status misdiagnosis, yet this association disappeared when analysis was adjusted to phosphate and CO.

Conclusions: The novel equation proposed for prediction of free calcium could be useful when free calcium is not available. The conventional formulas misclassify many patients, in particular when phosphate or bicarbonate disturbances are present.