Pharmacodynamics exponential

The consequence of moving consciously toward this model will be the provision of a robust and scalable IT infrastructure and systems able to cope with exponentially growing data mountains that will need to be integrated and shared, accessed and mined in the most effective way. It will also require formidable computing power and sophisticated algorithms to be able to simulate both organs and whole body systems to reduce expensive failures in the clinic and predict much earlier the pharmacokinetic and pharmacodynamic properties and toxicological and efficacy profiles of molecules in pharmaceu-... 

Once the health-effect endpoint and data points describing the exposure concentration-duration relationship have been selected, the values are plotted and fit to a mathematical equation from which the AEGL values are developed. There may be issues regarding the placement of the exponential function in the equation describing the concentration-duration relationship (e.g., C x t = k vs C X t = k2 vs X E = k3>. It is clear that the exposure concentration-duration relationship for a given chemical is directly related to its pharmacokinetic and pharmacodynamic properties. Hence, the use and proper placement of an exponent or exponents to describe these properties quantitatively is highly complex and not completely understood for all materials of concern. 

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. 

In contrast to pharmacokinetic model parameters which are often modeled assuming an exponential scale, model parameters from a pharmacodynamic model are sometimes modeled on an arithmetic scale... 

Whether to model a pharmacodynamic model parameter using an arithmetic or exponential scale is largely up to the analyst. Ideally, theory would help guide the choice, but there are certainly cases when an arithmetic scale is more appropriate than an exponential scale, such as when the baseline pharmacodynamic parameter has no constraint on individual values. However, more often than not the choice is left to the analyst and is somewhat arbitrarily made. In a data rich situation where each subject could be fit individually, one could examine the distribution of the fitted parameter estimates and see whether a histogram of the model parameter follows an approximate normal or log-normal distribution. If the distribution is approximately normal then an arithmetic scale seems more appropriate, whereas if the distribution is approximately log-normal then an exponential scale seems more appropriate. In the sparse data situation, one may fit both an arithmetic and exponential scale model and examine the objective function values. The model with the smallest objective function value is the scale that is used. 

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