Choice of the best equation for plasma osmolality calculation: Comparison of fourteen formulae

• We compare fourteen equations to elucidate which provides the least osmolal gap.
• The gold standard was crioscopically measured osmolality.
• We do not recommend the use of the famous Dorwart and Chalmers equation.
• The best result was determined from OSMc = 1.86(Na + K) + 1.15(Glu / 18) + (Urea / 6) + 14.
• A reasonable alternative is the simple equation 2(Na + K) + (Glu / 18) + (Urea / 6).

BackgroundMany different equations have been previously described to estimate plasma osmolality. The aim of this study is to compare 14 of these equations, in order to determine which results agree best with measured osmolality.ObjectivesOur aim is to elucidate which is the most accurate equation for osmolality calculation among the fourteen that were previously described.MethodsWe measured osmolality by the freezing point depression method, and glucose, urea, sodium, potassium, calcium and magnesium concentrations with Unicell DXC 800 analyzer. Goodness-of-fit rates were calculated using the Passing–Bablok regression model and the t-paired sample test. In addition, we used survival curves in order to find the percentage of cases in which the difference between measured and calculated osmolality was under 10 mOsm/kg. Data were plotted using the Bland–Altman graphical approach.ResultsThe equation that provides the best fit between measured and calculated osmolality is 1.86(Na + K) + 1.15(Glu / 18) + (Urea / 6) + 14, followed by 2Na + 1.15(Glu / 18) + (Urea / 6).ConclusionsAccording to our results, the Dorwart–Chalmer's equation should not be used for osmolality calculations. The equation 1.86(Na + K) + 1.15(Glu / 18) + (Urea / 6) + 14 is the most accurate. The widespread use of the equation 2(Na + K) + (Glu / 18) + (Urea / 6) is also acceptable.