Evaluations of Dose-effect Curves and Half-maximal Effective Doses Using the Four-parameter Logistic Model: When are Results Reliable?

INTRODUCTION/OBJECTIVE: The four-parameter logistic model is widely used to evaluate a dose-death rate curve to determine the half-maximal effective dose (ED50). However, misinterpreting ED50 is frequently noted. METHODS: ED50 under each typical condition is calculated using the four-parameter model, and then compared with the real ED50. RESULTS: ED50 from the four-parameter model is the nominal ED50, which actually is the effective dose at %[50×(top+bottom)]. The nominal ED50 is equal to, lower than, or higher than the real ED50 when (top+bottom)/2 is 0.5, <0.5, or >0.5, respectively. The real ED50 is unavailable when the death rates ε(0, 0.5) or ε(0.5, 1). DISCUSSION: The nominal ED50 overestimates the effect when (top+bottom)/2 is <0.5, but underes-timates the effect when it is >0.5. Errors noted in released trails are mainly due to the neglect of the premise of the four-parameter model (i.e., minimal death rate = 0, and maximal death rate = 1). CONCLUSION: ED50 from the four-parameter model is the nominal ED50, being with a risk of leading to inconsistencies in a trial when nominal ED50 ≠ real ED50. The real ED50 can be deduced when 0.5ε(minimal death rate, maximal death rate). Each curve should be considered as a whole when comparing multiple dose-death rate curves in a drug combination. Absorbance is not a rational substitute for the death rate.