model is one of the key nonlinear regression models which may reflect the underlying The Emax biological response (Ting, 2006). In its 4-parameter form this model is usually written as: 3.6 where response is the response of interest, E0 is the basal effect or placebo response when Dose is equal to 0, is the maximum achievable effect a drug can have over the placebo response, Emax ED50 is the dose which produces 50% of the effect, and S is the slope. It is not uncommon to fix the slope as 1 in the analysis of model. Ting (2006) discussed the Emax model in (3.2) as a particular case of model in dose response modelling which is Emax Emax referred to as the hyperbolic model. The model with the slope factor (slope is not Emax Emax fixed at 1) is referred as sigmoidal model. The steepness of dose response relationship is Emax determined by the slope parameter in model. Although both models can be justified Emax biologically in the relationship of drug receptor, the use of hyperbolic model is primarily for empirical reasons. Both a hyperbolic and sigmoidal model can be used to fit dose response, the choice of hyperbolic is primarily for empirical reason. The study with hyperbolic model Emax (Slope =1) was designed prior to my joining the study team and was the protocol specified analysis. In the model fitting of proposed Bayesian model with the slope parameter (sigmoidal Emax Emax mode) from simulated data, computationally errors often occur in WinBUGS, regardless of the choices of non-informative or informative prior (for example the slope follows a uniform distribution between -2 and 2 or Normal distribution with mean of -1 and standard deviation of 0.5). While with the slope parameter fixed at 1, there were little computational errors. The bias of the model parameters ED90 were also small (the estimated ED90 is within 20% of true ED90).
The Emax model is one of the key nonlinear regression models which may reflect the underlying biological response (Ting, 2006). In its 4-parameter form this model is usually written as: 3.6 where response is the response of interest, E0 is the basal effect or placebo response when Dose is equal to 0, Emax is the maximum achievable effect a drug can have over the placebo response, ED50 is the dose which produces 50% of the effect, and S is the slope. It is not uncommon to fix the slope as 1 in the analysis of Emax model. Ting (2006) discussed the Emax model in (3.2) as a particular case of Emax model in dose response modelling which is referred to as the hyperbolic Emax model. The Emax model with the slope factor (slope is not fixed at 1) is referred as sigmoidal Emax model. The steepness of dose response relationship is determined by the slope parameter in Emax model. Although both models can be justified biologically in the relationship of drug receptor, the use of hyperbolic model is primarily for empirical reasons. Both a hyperbolic and sigmoidal model can be used to fit dose response, the choice of hyperbolic is primarily for empirical reason. The study with hyperbolic Emax model (Slope =1) was designed prior to my joining the study team and was the protocol specified analysis. In the model fitting of proposed Bayesian Emax model with the slope parameter (sigmoidal Emax mode) from simulated data, computationally errors often occur in WinBUGS, regardless of the choices of non-informative or informative prior (for example the slope follows a uniform distribution between -2 and 2 or Normal distribution with mean of -1 and standard deviation of 0.5). While with the slope parameter fixed at 1, there were little computational errors. The bias of the model parameters ED90 were also small (the estimated ED90 is within 20% of true ED90).
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