Pharmacodynamics sigmoid Emax model

Pharmacokinetics. Figure 2 Sigmoid Emax model of pharmacodynamics with Hill coefficient (H), concentration producing half-maximum effect (CE50), threshold concentration (CE05), and ceiling concentration (CE95). 

Under the assumptions of the direct-link model, neither a counterclockwise (Figure 10.2) nor a clockwise hysteresis loop (Figure 10.4) will be recorded in an effect vs. concentration plot. In principle, the shape of the effect vs. concentration plot for an ideal direct-link model will be a curve identical to the specific pharmacodynamic model, relating effect with concentration, e.g., linear for a linear pharmacodynamic model, sigmoid for the sigmoid Emax model (cf. Table 10.1 and following paragraphs and sections), etc. 

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. 

Sigmoid Emax Model Jonkers and colleagues [80] studied the pharmacodynamics of racemic metoprolol, a cardioselective beta-blocker, and the active S-isomer in extensive metabolizers (EMs) and poor metabolizers (PMs). The drug effect studied was the antagonism by metoprolol of terbutaline-induced hypokalemia (abnormally low potassium concentration in the blood). The pharmacodynamic interaction was described by a sigmoidal function for competitive antagonism based on the earlier work of Holford and Sheiner [81] ... 

What this equation shows is that the F-test and AIC are not independent and that given one of them the other can be determined. These equations also show that sometimes the two criteria can lead to different conclusions. Suppose a modeler fit an Emax model with two estimable parameters and a sigmoid Emax model with three estimable parameters to a data set with 14 observations, such as might be the case when fitting a pharmacodynamic model to individual data. In this case, an F-test greater than 3.84 is required to declare the sigmoid Emax model the superior model at the 0.05 level, which is equivalent to a AAIC of —2.19. An F-test value less than 3.84 is considered to be not statistically significant at the 0.05 level and the reduced model is chosen as the superior model. However, any AAIC less than 0, even values between 0 and —2.19, is still considered to be indicative that the full model is the superior model. Hence, the possibility exists for the two criteria to reach different conclusions. 

Pharmacodynamic models mathematically relate a drug s pharmacological effect to its concentration at the effect site. Examples of the types of pharmacodynamic models that have been employed include the fixed-effect model/ maximum-effect models (Emax and sigmoid Emax)/ and linear and log-linear models (11). Unlike pharmacokinetic modelS/ pharmacodynamic models are time independent. However these models can be linked to pharmacokinetic modelS/ as discussed in Chapter 19. 

FIGURE 18.15 Sigmoid Emax pharmacodynamic model relating drug effect to the drug concentration at the effect site. The three curves show the effect of the exponential Hill (H) constant n on the slope of the sigmoid curves. 

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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