Pharsight

Case Study of Clinical Pharmacology

Title: PK/PD Modeling of MMF in Renal Transplants

Mycophenolate mofetil (MMF), a pro-drug for mycophenolic acid, reduces the likelihood of allograft rejection (Hale 1998) after renal transplantation. A randomized concentration-controlled study (RCCT) (Endrenyi and Zha, 1994) was proposed since a causative PD relationship was desired to support an NDA. In this case study, we discuss the analyses (Hale and Reeve, 1994) and how one would use Pharsight® modeling products to support the analyses.

In planning the RCCT, several questions needed to be answered:

What is the appropriate PK parameter to measure and control?
What is the PK variability among patients and within repeated determinations on the same patient?
What is the relationship between dose and the PK parameter?

The analysis described below answers these questions.

The data to generate the models can be obtained from previous clinical or preclinical studies. The data analyzed was from a pilot study. In the pilot study, patients received either 0.5, 1, or 1.5 grams of oral MMF capsules administered bid. 31 of the 32 patients in this trial had one or more 12 hour plasma profiles.

Which PK Parameter

Several pharmacokinetic summary measures can be used. The parameter to be used is that which best discriminates between responders and nonresponders. This is easily assessed via a received operating characteristic (ROC) curve (e.g., Zweig, Mark and Gregory Campbell 1993). Many PK summary measures can be computed in WinNonlin® via noncompartmental modeling. Looking at AUC0-12, Cmax, and trough concentration, we see that AUC0-12 is best at discriminating responders versus nonresponders (Fig. 1). We will now concentrate on AUC as the PK measure of interest.

Variability of AUC

We need an estimate of the intra- and inter-subject variability in AUC. This can easily be computed in WinNonlin 3.2 using LinMix or in WinNonlin 3.1 or older using ANOVA. Using ANOVA, one must compute the variance components from the mean squares using the expected mean squares method; using LinMix, this is done automatically. The linear model included terms for the dose group and patient within group; ln(AUC) was the dependent variable. The variance components came to 0.080 and 0.145 for inter- and intra-subject variance, or 28% and 38% coefficient of variation. In previous studies involving healthy, normal male subjects, the intra-subject CV had been estimated to be in the range 10% to 15%.

The relationship of dose to AUC was also needed. This is easily accomplished by modifying the model above so that ln(AUC) is a function of ln(daily dose), and refitting the model. From this model, it is easy to estimate an initial dose for each subject given the target AUC since one merely backsolve the linear model. Nonlinear relationships can also be looked at using WinNonMix®. Indeed, body weight was also included in the model in several models, but was not found to be a useful covariate.

PK/PD Relationship

The PD response of interest was rejection (1=rejection, 0=no rejection). The model fit was a classical logit model regressing rejection onto ln(AUC). These models can be fit using WinNonMix. After several fittings, it was determined that the upper asymptote should not be 1, but a parameter of some lower value. Also, reparameterization (Bates and Watts, 1988) of the model was used to improve convergence. Because binary models are inherently difficult to compute, several iterations and attempts should be expected before success. One need to watch out for local minima and flat regions of the likelihood that can lead the model fitting astray. For these reasons, one should always attempt the problem using several different starting values, as well as utilize graphical display of the data to guide the modeling process. Both WinNonlin and WinNonMix allow the user to generate custom graphics from their data.

Model parameters were found, and the -2 log likelihood was compared to the -2 log likelihood of the null model of no PK/PD relationship. Because there were 2 additional parameters in the alternative model than the null, the difference in -2 log likelihood was compared to the chi-squared distribution with 2 degrees of freedom. A p-value of 0.004 was found, indicating a strong relationship between ln(AUC) and rejection rate. These analyses were considered exploratory because (a) ln(AUC) was not controlled in the pilot study and hence a causative relationship cannot be inferred, (b) the analysis was guided by the data and not prespecified in the protocol. The full study will prespecify the statistical analysis and the ln(AUC) values will be controlled by customizing the dose of each patient in the full study, but the small p-value is encouraging.

Study Simulation

Powering such a study is impossible using conventional statistical methodologies. As such, computer simulation was used to estimate the power of several proposed designs and to optimize trial characteristics, including the size of the dose adjustment, the maximum dose allowed in the study, sample size for each AUC target group and other parameters (Reeve and Hale 1994). But computer simulation had other benefits as well. For example, it was determined how many of each configuration of large and small capsules to be packaged to minimize material waste and packaging effort. And the statistical analysis was scrutinized to ensure that the Type I error rate conformed to expectations. In this particular example, the chi-squared test was shown to not follow the naïve degrees of freedom, but instead degrees of freedom of 1.5 was more appropriate to describe the null distribution. The Pharsight Trial Simulator can be used to answer these and additional questions that may arise in the trial design phase.

Conclusion

The modeling used to construct a randomized concentration-controlled trial was described and results presented. These models included linear and nonlinear mixed effect models and noncompartmental models. The modeling can be performed using Pharsight tools, including WinNonlin and WinNonMix. The simulation necessary to complete the planning can be accomplished using the Pharsight Trial Simulator.

The trial was successfully completed, and the analysis of the trial is presented in Hale et al (1998).

References

Endrenyi, Laszlo, and Jiuhong Zha (1994) Coparative efficiencies of randomized concentration- and dose-controlled clinical trials, Clin Pharmaco Ther, 56, pp. 331-338

Hale, Michael D, et al (1998) The pharmacokinetic-pharmacodynamic relationship for mycophenoalte mofetil in renal transplant, Clin Pharmaco Ther, 64, pp. 672-683

Hale, Michael D, and Russell Reeve (1994) Planning a randomized concentration controlled trial with a binary response, Proceedings of the Biopharmaceutical Section, 1994 Joint Statistical Meetings

Reeve, Russell and Michael D Hale (1994) Results and efficiency of Bayesian dose adjustment in a clinical trial with binary endpoint, Proceedings of the Biopharmaceutical Section, 1994 Joint Statistical Meetings

Zweig, Mark H and Gregory Campbell (1993) Receiver-operating characteristic (ROC) plots: a fundamental evaluation tool in clinical medicine, Clin. Chem, Vol 39, No. 4, pp. 561-577