Correspondence: Measurement of erythrocyte transketolase activity

CorreSpondence Measurement of erythrocyte transketolase activity Correspondence from Donald E. King C. R. Milner et al.'s recent paper compared automated versus manual procedures for the 'Measurement of erythrocyte trans-ketolase activity on a discrete analyser' (Journal of Automatic Chemistry, Vol. 4, No. 4, pp. 183-185). In it the author uses regression analysis to evaluate the similarity of results. It is a common error on the part ofall ofus to ignore the basic premise in linear regression that the x variable is taken to be the independent variable. As long as the correlation coefficient (r) is close to 1.00 the effect on the slope estimate bl is small. However, when r =0.9 the slope b of the equation obtained by choosing y to be the independent variable, rather than x, is 19% steeper than bl .In fact b is equal to bl/r 2. Thus, since both lines pass.through the point defined by the average of the two data-sets, the intercepts are affected as well. So on the assumption that the manual method is the independent variable the author determined that the automated procedure yields results according to the equation: y=0"90x+0.14 (r=0"87). But if the more likely assumption had been made that the automated procedure was the independent variable, it can be calculated that the corresponding equation would have been: y 1-19x-0.10. The new slope and intercept are calculated from the correlation coefficient and the mean values of the two methods as stated in the paper. Thus 1.19 =0"90/r (=b2) and 0.10 =-1.192 where .P 0'86 and 2 0. 81. When one realizes that these two equations differ in slope by almost 30%, because of their dependence on the correlation coefficient, one begins to question the validity of conclusions drawn from the use of linear regression. In the absence ofany proofthat one ofthe two methods is the independent variable, one must appreciate that the probable relationship lies somewhere between these two extreme positions. Since they both depend on r it is interesting to speculate that this central equation is given by: y l'03x + 0"02 where 1"03 =0"90/0.87 and 0"02 y 1.032 note: bo =bl/r=(b b2) (=bo)