Nonlinear Mixed Effect Modeling과 $Na\ddot{i}ve$ Pooled Data 방법에 의한 Barnidipine Dose-Titration Trial의 분석

Analysis of Dose-Titration Trial for Barnidipine with Nonlinear Mixed Effect Modeling and $na\ddot{i}ve$ Pooled Data Method

Background : naive pooled data(NPD) or two-stage method, the two traditional population approaches in pharmacokinetic/pharmacodynamic(PK/PD) analysis, have much limitation in their application. Nonlinear mixed-effect modeling approach has many advantages over the traditional approaches. It provides a solution for analysis of nonexperimetntal or observational data, such as those from clinical situations, which have characteristics of sparseness, unbalancedness, and fragmentariness and so on. In addition, it can be also adopted as a method for estimation of PK/PD parameters in clinical trial of less stringent and restrictive design condition and by doing so we can design clinical trial more flexibly, which will be helpful especially if PK/PD are to be investigated in patients. We analyzed a dose-titration trial for barnidipine, an antihypertensive agent, with nonlinear mixed effect modeling and naive pooled data method and based on the actual trial we simulated dose-titration trials of various conditions with Monte-Carlo method and analyzed with both nonlinear mixed effect modeling and naive pooled data method and compared the results. Methods : A dose-titration trial 'Blood-pressure lowering effect of barnidipine HCI in renal parenchymal hypertension' which was performed in three general hospitals of Seoul, was analyzed with nonlinear mixed effect modeling and naive pooled data method And based on the actual trial, we simulated dose-titration trials of various conditions for barnidipine with Trial Simulator $2.1l^{\circledR}(Pharsight)$ which uses Monte-Carlo method in simulation. We designed and simulated a total of 6 trials adopting linear model and Emax model with conditions of drop-outs of study subjects or high BSV/BOV. The simulated outcomes were analyzed with nonlinear mixed effect modeling and naive pooled data method respectively using $NONMEM^{\circledR}$. We used $NONMEM^{\circledR}$, a computer software for the analyses. Results : When we analyzed the actual dose-titration trial, linear model was superior with regard to model building criteria and serum creatinine level was found to be the sole covariate. When we analyzed the simulated data, 18 out of 21(85.7%) population parameters (6 out of 9 in linear model, 12 out of 12 in Emax model) estimated with nonlinear mixed effect modeling or naive pooled data method were statistically different from each other. And 16 of them (88.9%) showed values closer to the true values(those introduced for simulation), which suggested the superiority of nonlinear mixed effect modeling to naive pooled data method in the analysis of parameters. But, when we tested with ANOVA$({\alpha}=0.05)$, parameter sets from base designs, those with drop-outs and those with high variability grouped by nonlinear mixed effect modeling and naive pooled data method combinated with linear and Emax model, only 3 out of 7(43 %) population parameters(1 out of 3 in linear model and 2 out of 4 in Emax model) showed no difference in parameters. Conclusion : In the simulation of dose-response of barnidipine with the parameter estimates from actual clinical data, the results showed a propensity of the lower responses at higher dosages with parameter estimates from naive pooled data method than with those from nonlinear mixed effect modeling in both linear and Emax model. And these are due to the dose-titration design in itself, in which at higher dosage, only poor responders will remain to be administered the higher dosage. Thus, naive pooled data method is not appropriate for the analysis, but nonlinear mixed effect modeling, which reflects the individual differences in analysis, is required for accurate parameter estimation in this kind of trials. When estimated parameters from simulated data, we can confirm that parameters can be estimated more accurately with nonlinear mixed effect modeling than with naive pooled data method in various conditions.