. Author manuscript; available in PMC: 2012 Aug 1.

Published in final edited form as: Bone. 2011 Mar 31;49(2):250–256. doi: 10.1016/j.bone.2011.03.770

Table 1.

Conceptual Pharmacodynamic (PD) Models

Model	Equations
Linear Model	E= E₀ + S * C
Simple E_max Model	E= (E_max * C)/(C+ED₅₀)
Simple E_max Model with E₀	E=E₀+ (E_max-E₀)* (C/(C+ED₅₀))
Sigmoid E_max Model	E=(E_max * C ^γ )/(C ^γ +ED₅₀ ^γ)
Sigmoid E_max Model with E₀	E=E₀ + (E_max -E0)*( C ^γ /( C ^γ + ED₅₀ ^γ))
Weibull	E = E_max * (1-exp(-(C/ ED₅₀)^S))
Makoid-Banakar	E = E_max (C/Cmax)^Sexp(S*(1-C/Cmax)), when C≤ Cmax, E = E_max, when C > C_max

E= effects, C= Dose, S= Slope, γ= sigmoidicity factor, C_max = maximal dose, E_max= maximal effects, E₀= baseline effects at C=0, ED₅₀= dose that induced 50% of E_max