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

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.

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.

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.

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.