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Dear Sir,
I analysed 9-timepoint PK profiles of 20 kidney transplantation recipients with concomitant cyclosporine. Plasma mycophenolic acid (MPA) concentrations were measured using HPLC with UV detector. The best model of MPA AUC0-12 was 0, 30 minutes and 2 hours. Because of lacking of the another validated dataset, how do I validate this model? or should I the model of other previous studies by using my full PK profile to validate these other equation?
Best Regards,
Wanarat Anusornsangiam
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Dear Wanarat:
I am not clear what you are doing. Are you trying to validate a limited sampling strategy for estimating AUC? If so, I am most interested, and have several questions to ask you.
1. Let us first agree that AUC is a very useful index of exposure to a drug. This AUC can be in that of the serum concentrations, or it can also be an AUC in an unobservable peripheral compartment, as for digoxin, for example. Let us start with the serum AUC.
2. Let us suppose that you have estimates of the AUC. You might wish to validate it by examining its ability to predict the AUC based another prospective data set. How does one take into account the inevitable variation that occurs between patients due to body weight, renal function, and differences in dosage between subjects? How does one specify the relationships between these things and AUC? And if the AUC is not the one you want for the patient, how do you determine the dose to achieve the desired AUC with maximal precision?
3. Many workers have used population PK/PD modeling, to describe these relationships, and MAP Bayesian adaptive control to then achieve the desired AUC. In this case, the AUC is computed by adding up the concentrations by simulating the behavior of the patient's Bayesian posterior model,, and one can use model mean or median parameter values to find the dose that is this case is designed to hit the target AUC exactly. However, using such parametric population models, in which the parameter distributions are assumes to be normal, or lognormal, for example, one has only single point estimates of the distributions. Because of this, there is no way to evaluate in advance just how precisely the regimen is likely to hit the target AUG or other goal. One simply assumes that the goal will be hit exactly. However, if that were really so, we certainly would not to do any TDM.
4. Another way to do this is to use nonparametric (NP) population PK/PD models. In these models, the parameter distributions are no longer continuous, but are actually discrete. Several important theorems (Caratheodory, Lindsay, and Mallet, for example) have shown that the most likely distribution given the data is just such a discrete one, supported at up to N points for N subjects studied. Also, the likelihoods are exact, and statistically consistent behavior (study more subjects, parameter estimates more closely approach the true ones) is guaranteed. The big advantage of the nonparametric approach is that it estimates the ENTIRE parameter distribution, not just a point estimate of it, as the parametric methods do.
5. The separation principle states that whenever one separates the control of a system or model into first, getting point estimates for parameter distributions, and next, developing a control (dosage regimen) based on these point parameter estimates, then the job of the control is done suboptimally. This is the problem with control (dosage regimens) based on maximum aposteriori probability (MAP) Bayesian adaptive control. The problem here is that since the underlying full parameter distributions are not known, there is no way to optimize the control using this approach.
6. The way around the separation principle is to use nonparametric approaches in which the entire population or Bayesian posterior parameter distributions are estimated, and then to use that entire distribution to develop the dosage regimen. This is done using multiple model (MM) dosage design. This comes not from the PK/PD community, but rather from the aerospace community. This is the method used for maximally precise control of aircraft, spacecraft, etc. Here, this is done by least squares curve fitting in reverse. A candidate regimen is given to each support point of the nonparametric population model. The multiple predictions, each weighted by the probability of that support point in the population, are compared with the target goal (or AUC) and the weighted squared error of the failure of that regimen to hit the target is calculated. Then, in the same way, the regimen that specifically minimizes the weighted squared error of target achievement is found. In this way one now has the ma
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