We have read with great interest the letter published in this Journal by Rubio et al.,1 and we would like to expound briefly our ideas on his comments.
Upon observing the value of HCO3, Rubio et al., calculated the expected value of pCO2 by using the famous Winters’ formula,2 which consists of a linear regression with a slope of 1.5 and an interception of 8.3. Although still widely used, the Winters’ formula was proposed in the sixties. There is a more recent formula, which is a contribution made by Bushinsky et al.,3 who argued that the decrease in pCO2 should be predicted by multiplying the decrease in HCO3 by the factor 1.2. The relationship between pCO2 and HCO3 proposed by Bushinsky et al., may be found in many current textbooks; see, for example, Du Bose.4,5
Nevertheless, these two formulas are not necessarily in conflict. In order to prove this, let us consider the normal values of HCO3, pCO2, namely 24mEq/L, 40mmHg, respectively. By introducing these numbers into the formula of Bushinsky et al., the formula reduces to the equation pCO2=1.2* HCO3+ 11.2, that is to say, a linear regression with a slope of 1.2, an intersection of 11.2, which is not that different from Winters’ regression.
Moreover, the Winters’ formula was derived from a population where the value of HCO3 was close to 9.9 mEq/L, while Bushinsky et al., analysed a wider range of HCO3 values. Thanks to a more detailed statistical analysis, Bushinsky et al.3 show that, by restricting the range of HCO3 values to a maximum of 10 mEq/L, the slope of the linear regression acquires a value of 1.5 (exactly the same slope reported by Winters), while the slope reaches 1.2 for values of HCO3 between 10.1 and 25mEq/L.
To summarise, in our opinion, the more accurate way to predict the expected value of pCO2 in chronic metabolic acidosis, and hence to correctly deduce the presence of mixed acid-base disorders, is by using different formulae according to the range of HCO3 values. Therefore, if the value of HCO3 is greater than 10mEq/L, as it usually happens, Bushinsky's formula should be considered. The use of Winters’ formula seems appropriate only for lower values of HCO3.
For these reasons, in the cases reported by Rubio et al., where the value of HCO3 is much greater than 10mEq/L, although the use of Winters’ formula leads to the correct diagnosis (i.e., mixed acidosis), we conclude that a more orthodox approach would be to resort to the formulae of Bushinsky et al.
Please cite this article as: Marano M. Sobre el uso de la fórmula de Winters en la acidosis metabólica crónica. Rev Psiquiatr Salud Ment (Barc.). 2015;8:45–46.