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当效应数据为连续值并且在暴露量范围内观察到平台时，可考虑 Emax模型 或者 Sigmoid Emax模型 （式1）。如果随着暴露量的变化未观察到平台时，可考虑线性模型（式2）。

The Emax model (Equation 2) is the most fundamental description of the concentration effect relationship. It has strong theoretical support from the physicochemical principles governing binding of drug to a receptor (the law of mass action).

The E max model is a nonlinear model frequently used in dose–response analyses. The model is shown in Eq. (9.1)

Salient features of the model are: The E max model has four parameters: E 0, E max, ED 50, and N. The E max model predicts the maximum effect a drug can have (E max). The E max model predicts a zero-dose effect (E 0) when no drug is present. The E max model follows the “law of diminishing returns” at higher doses. The E max model parameters ...

Our paper compares three different models (independent, EMAX, and hierarchical EMAX) and two different design strategies. The first design considered is Bayesian with a fixed trial design, it has a fixed schedule for randomization. The second design is Bayesian but adaptive, it uses response adaptive randomization.

2024年8月14日 · This study formulates an extended Emax (eEmax) model designed to overcome these limitations. The eEmax model generates multiple DRCs from a single dataset by using various estimated $${\alpha }^{\prime}\text{s}\in \left[\text{0,100}\right]$$ , while keeping $$E{D}_{\alpha }$$ fixed, rather than estimating an $$E{D}_{50}$$ value as in the Emax ...

2015年12月3日 · For continuous response data, one of the most common parametric model is Emax model. There is a 3-parameter Emax model by fitting the dose response function g(D) where E0 is the response Y at baseline (absence of dose), Emax is the asymptotic maximum dose effect (maximum effect attributable to the drug) and ED50 is the dose which produces 50% ...

Sigmoid E max models, also known as Hill equations, have successfully explained pharmacodynamics of many drugs with Hill coefficients determining sigmoidicity or sensitivity between exposure and response. [9] .

The Emax model is well-characterized in the literature and widely used in a va- riety of fields including clinical trials, biochemistry, agriculture and environmental experiments (e.g., Bretz et al., 2010; Baker, 2010; Baker et al., 2016; Han et al.,