Emax model relationship

There was a direct relationship between the effect and the plasma concentration in the rat pharmacodynamic data and it was well described by a simple Emax model. Based on preclinical models for efficacy, a 90% effect was considered as the target for therapeutic effect. Finally the human C90 (human concentration corresponding to 90% effect, C90 man) was estimated by accounting for the different affinities and unbound fractions of each compound for the rat and human receptors as follows ... 

Fig. 3. Concentration-effect relationship for the sigmoid Emax model with 5 = 0.5, 1, 3 and 5, respectively, (a) Linear concentration scale, (b) logarithmic concentration scale.

In the simplest case, drug effects are directly related to plasma concentrations, but this does not necessarily mean that effects simply parallel the time course of concentrations. Because the relationship between drug concentration and effect is not linear (recall the Emax model described in Chapter 2 Drug Receptors Pharmacodynamics), the effect will not usually be linearly proportional to the concentration. 

Fig. 15.10 Concentration-effect relationship of pegfilgrastim based on a simple Emax model. The average concentrations of pegfilgrastim from patients with breast cancer at doses of 30, 60, and 100 pg/kg are indicated ( ).

Population pharmacodynamic data, i.e., observed 24-hour efficacy scores were modeled as a function of individual predicted 24-hour steady state AUCs. Various pharmacodynamic models were explored including linear, Emax, and sigmoidal Emax models. Fixed and random-effect parameters were used to describe the PK/PD relationship. The results of the model development are presented in Table 7. 

In Figure 18.16, the Emax model is used to quantify the relationship between theophylline serum level and improvement in pulmonary function as measured by the increase in forced expiratory volume in 1 second (FEVi) in six patients who were treated with placebo and three incremental doses of theophylline (14). 

The linear-effect model defines this relationship adequately as long as biophase drug concentrations/ [B], are substantially less than is the EC50. However/ the decision to use an Emax rather than a linear model is usually determined by the available data rather than by theoretical considerations. For example/ in one study of QT interval prolongation by an anti-arrhythmic drug/ a linear-effect model was satisfactory for analyzing the response of four patients but an Emax model was required to analyze the exaggerated response of a fifth patient (15). 

Emax Model, ftmax model was originally derived from the classic drug-receptor occupancy theory. It is an empirical function for describing a non-linear concentration-effect relationship with the general form ... 

The PK-PD relationship for G-CSF following IV and SC administration was well characterized in healthy volunteers (53). The PK model was a two-compartment PK model with bisegmental absorption from the site of SC administration, parallel first-order and saturable elimination pathways, and an indirect effect PD model describing the time course of neutrophils. A sigmoidal Emax model was applied for the stimulation of the neutrophil input rate. In addition, a time-variant scahng factor for absolute neutrophil count (ANC) observations was introduced to account for the early transient depression of ANC. 

Several of the PK/PD models described in Chapter 19 have been employed to explore the relationship between circulating protein concentrations and pharmacodynamic endpoints. For example, a dog model of hemophilia was used to study the activity of recombinant FIX (79). Activity was determined in a bioassay, a modified one-stage partial thromboplastin time assay with pooled human plasma as the internal standard. As shown in Figure 32.14, the relationship between activity and recombinant FIX (BeneFIX) concentration was linear (r = 0.86), suggesting that for every 34.5 ng/mL of FIX, there would be a corresponding 1% increase in FIX activity. In 11 males with hemophilia B, it was necessary to use a sigmoid Emax... 

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