Re: VPC appropriateness in complex PK

Yaning, I am not understanding something in your example which you use to assert that adaptive dosing should not be used in simulations for a VPC. if you used adaptive dosing and the correct PK structural and random effects model (as you seem to describe) then if there was no error in the measured conc/timing then of course the simulated concs would exactly match the observed concs in each subject. What is wrong with that? Your example uses the correct simulation model for prediction of the original data distribution and so the predictive check should of course confirm the model. That is what a predictive check is about. It checks that the model is adequate (i.e. good enough to to be the true model). In reality adaptive designs based on measured concs will always have errors in the measured conc or timing of concs in addition to the between subject variability in PK parameters so using the nominal adaptive design algorithm would always add some additional noise to the predicted distribution. Another real life feature is that clinical study staff dont follow the protocol (or there may not even be a protocol!). If one can devise a clinically reasonable adaptive design protocol then this is a useful step in trying to perform a predictive check of a trial with an unfollowed or unknown protocol. If the adaptive design protocol matches the data using a VPC then one can have some confidence in using the PK model and the adaptive design algorithm to simulate future trials which are not expected to have a strictly followed adaptive protocol. The need for this kind of auxiliary model to account for real life variations in design has been recognized for dropouts due to informative missingness mechanisms. It not only allows a predictive check to evaluate the adequacy of the model but also gives a mechanism for future clinical trial simulation. With regard to your second point -- it has made me think more carefully about the assumptions of the SPC method and I think I can now convince myself that you are correct that the original dosing design needs to be used for simulation. Here is my rationale which I hope you will be willing to try to follow and see if the logic is reasonable. If this logic is OK then I will retract my previous statement that SPCs would fail if they did not simulate with an adaptive design. My understanding of how SPCs work involves the basic idea of comparing a measured conc to a distribution of simulated concs that arise from the structural and random effects model under the original design that gave rise to the measured conc. If the original design (i.e. "CRF" dosing regimen) that gave rise to the measured concs is used then the distribution of simulated concs will depend on the structural and random effects model conditional on the original design. It is clear that the mean simulated concentration for an individual will not match the observed concentration in a particular individual because the random PK parameters for that individual will be randomly different from the actual PK parameters. This is why the CRF dose cannot be used for the VPC (unless both the predictions and observations are 'normalized' so that the actual dosing regimen does not matter as is done in the PC-VPC). But it is plausible that the discrepancy of a single observed concentration from the simulated distribution of concs at that time for that individual will be random across individuals and thus the prediction discrepancy would be uniform (if the PK structural and random effects model is correct). However, the within subject correlation of these discrepancies due to the PK parameter between subject differences (which will affect all concentrations in that individual) will violate the assumption of independent discrepancies and this is what the NPDE method tries to achieve by removing the within subject correlation. Thus I think we should not rely on PDE methods for SPC unless there is only one observation per subject. The technology for doing uncorrelated PDEs (e.g. NPDE) is now freely available ( http://www.npde.biostat.fr/index.php ) so there is really no justification to use correlated PDEs . Nick Wang, Yaning wrote: > In my opinion, the concentration data after dose adaptation should not > be simulated based on the adaptive algorithm implemented in the original > design. Using the simple but extreme case proposed by Leonid, i.e. all > patients were targeting a common concentration level with no or small > residual variability and no or small inter-occasion variability. For > example, under iv infusion, the target is Css of 100ng/ml. All patients > start with the same infusion rate and the infusion rate will be adjusted > after steady state is achieved. For patient A, if the Css under the > initial infusion rate is 50ng/ml, then double the infusion rate. For > patient B, if the Css under the initial infusion rate is 200ng/ml, > reduce the infusion rate by half. After dose adaption, every one should > hit 100ng/ml. Then no matter what the model is, all the simulated > concentrations after dose adaptation will hit the same target (matching > exactly the observed data) if the original adaptive algorithm is used in > simulation. In this case, there is no way the structure model can be > wrong because it is very simple (R/CLi). But imagine we fit an > exponential between-subject variability model to a log-normally > distributed CLi. Then using the exponential distribution to simulate CLi > and then adjust individual infusion rate accordingly. All patients will > still hit 100ng/ml after dose adjustment. Of course, one can argue the > pre-adaptation concentration should pick up the mis-specification. The > point is that post-adaption data cannot be simulated based on the > adaptive algorithm. > > On the other hand, simulation can be done based on original adapted > doses ("obtained from the CRF") assuming the whole set of simulated > individuals will also take the exact dose sequence that was taken by one > specific individual in the trial. The only difference among these > individuals will be due to the random between-subject variation on PK > parameters. SVPC or PDE should still show uniform distribution even for > > those post-adaption data (even if all observed data are 100ng/ml). > > Yaning Wang, Ph.D. Team Leader, Pharmacometrics Office of Clinical Pharmacology Office of Translational Science Center for Drug Evaluation and Research U.S. Food and Drug Administration Phone: 301-796-1624 Email: [email protected] > > "The contents of this message are mine personally and do not necessarily > reflect any position of the Government or the Food and Drug > Administration." >