The median-effect equation of chou

The Median-Effect Principle The Median-effect Equation of Chou A general equation for dose-effect relationship was derived by Chou (1,2) through mathematical induction using hundreds of enzyme kinetic models. It correlates the “Dose” and the “Effect” in the simplest possible form: fa/fu = (D/Dm)m [Eq. 1] where D: the dose of drug Dm: the median-effect dose signifying the potency. It is determined from the x-intercept of the median-effect plot. fa: the fraction affected by the dose fu: the fraction unaffected, fu=1-fa m: an exponent signifying the sigmoidicity (shape) of the dose effect curve. It is determined by the slope of the median-effect plot.] The alternative forms of the median-effect equation are: fa = 1/[1+ (Dm/D)m] [Eq. 2] D = Dm[fa/(1-fa)]1/m [Eq. 3] From Eq. 2, if Dm and m are known, the effect (fa) can be determined for any dose (D). From Eq. 3, if Dm and m are known, the dose (D) or (Dx) can be determined for any effect (fa). Thus, Dm and m parameters representing the potency and shape, respectively, determine the entire dose-effect curve. The Median-effect Plot and Parameters The median-effect plot is a plot of x = log (D) vs y = log (fa/fu) introduced by Chou in 1976 (2,14). It is based on the logarithmic form of Chou’s median-effect equation [Eq. 1]: log (fa/fu) = m log (D) - m log (Dm) [Eq. 4] Eq. 4 has the form of a straight line, y = mx+b. Thus, the slope yields m value and the x-intercept yields log (Dm) value, and thus, the Dm value. The Dm can also be determined by: Dm = 10-(y-intercept)/m)