Modeling Rates and Effects of Drug X

As an additional comment on this problem: If you can model the concentrations of the drug then it should be possible to model the effect of the drug on either input or elimination of X as a function of the drug concentration. This would require specifying the problem with a differential equation defined model e.g. with ADVAN6. The use of drug concentration rather than dose would give you more information about the relationship of intensity of drug treatment to the effect on X kinetics and of course the model is more likely to represent reality by proposing a causal relationship via concentration rather than dose. This model has been studied a lot - warfarin pharmacodynamics would be the most classical case but other examples have been well described e.g. steroid dynamics (Bill Jusko's group in JPB within the last 12 months).