Critical evaluation of equations for serum osmolality: Proposals for effective clinical utility

Background: Many studies have assessed the predictive accuracy of serum osmolality equations. Different approaches for selecting a usable equation were compared using thirty published equations and patient data from a regional hospital laboratory. Methods: Laboratory records were extracted with same-sample results for measured serum osmolality, sodium, potassium, urea and glucose analysed in a regional hospital laboratory between 1/1/2017-31/12/2018. Differences were analysed using Passing-Bablok and difference (Bland-Altman) analysis. Three approaches were compared: the shotgun approach, adjusting for bias, and deriving a novel equation using multivariate analysis. The criteria for success included bias <= 0.7%, a 230 - 400 mOsm/kg range, and osmolal gap (OG) 95% reference limits within +/- 10 mOsm/kg. Results: The majority of equations produced proportionally negative-biased results. The shotgun approach identified two equations (EQ19, EQ6) with bias <= 0.7% but unworkable OG reference limits. The bias adjustment approach produced several equations with bias <= 0.7% and OG reference limits within or equivalent to +/- 10 mOsm/kg. A novel equation generated by us (1.89Na(+) 1.71 K+ 1.08 Urea + 1.08 Glucose + 13.7) improved with the adjustment of bias and was not superior to the adjusted published equations. Conclusion: Few published equations are immediately usable. Adjustment of bias derives several usable equations of which the best had OG ranges < 20 mOsm/kg. We conclude that adjustment of bias can generate equations of equal or superior performance to that of novel equations.