D-optimal Adaptive Bridging Studies in Pharmacokinetics
Lee-Kien Foo, Stephen Duffull
University of Otago, New Zealand
Background:
Bridging studies are a method for extrapolating information gathered from clinical study in an original region (prior population), e.g. an adult patient population, to a new region (target population), e.g. a paediatric patient population. Since the PK profile of the prior and target populations may be different then optimally designed studies based solely on the prior population may be suboptimal when applied to the target population. Optimal adaptive design can be used to address this issue which the design phase and estimation phase is updated in the experiment, where the parameter estimates obtained in the current iteration are used to design the experiment for the next iteration. This approach can provide reliable estimates of PK parameters under uncertainty and sampling restrictions [1]. Here we propose a new method for applying optimal adaptive design to bridging studies.
Objective:
To develop a D-optimal adaptive bridging study (D-optimal ABS) that has general applicability to pharmacokinetics.
Methods:
Our proposed D-optimal ABS starts with collecting sample data from all prior population patients enrolled following an initial (arbitrary) study design. Patients of the target population will be divided into B batches. The prior population sample data will be modelled and the estimated parameter values from the best model used to locate a D-optimal sampling schedule (D1) that will be applied to the first batch target population patients. The first batch of target population patients will be enrolled and data collected according to D1 will be pooled with a reduced data set arising from the prior population, where the prior population data is reduced by an amount proportional to the size of the batch of the target population. The pooled data will be modelled and the D-optimal design (D2) is located for the new model. Subsequently a second batch of target population patients is enrolled and data collected according to D2. The iterative process of estimation and design was repeated until all batches of the target population patients have been enrolled. The size of batches will also be considered for optimization.
Simulation Study:
The D-optimal ABS was designed and assessed using simulations under two different scenarios. In scenario 1, the PK profile of prior and target populations are similar where the design optimized based on prior population PK profile is a good but not optimal design for target population. In scenario 2, the PK profile of the prior and target populations are different and a design optimized based on prior population PK profile will perform poorly for the target population. The simulations are carried out in MATLAB and NONMEM, called from MATLAB, is used for estimation. For each scenario, 100 adaptive bridging studies were simulated. The relative percentage difference of the estimated parameter values from the empirical (true) parameter values were used to assess performance of the adaptive bridging study.
Scenario 1: {adult to paediatric}
In this scenario the D-optimal ABS is for an adult (prior) to paediatric (target) patients for a small molecule drug. The drug is taken orally and assumed to follow a Bateman PK model. Two hundred adult patients and twenty five paediatric patients were simulated and the paediatric patients were divided into five enrolment batches with five patients in each batch. The nominal parameter mean of adult patients were CL = 4Lh-1, V = 20L, Ka = 1h-1 and dose = 100 mg. The nominal parameter mean of CL and V for paediatric patients are scaled allometrically to CL = 1.56Lh-1, V = 5.71L. Ka is assumed to be the same as adult patients and dose = 29 mg. The variance of the log-normal between subject variability was 0.1 for both populations. A combined residual error model was assumed. The two hundred adult patients each provided 6 blood samples following an arbitrary sampling schedule.
Scenario 2: {normal weight to obese adult}
In this scenario, the D-optimal ABS is for a normal weight (prior) to obese (target) adult patients for a large molecule drug which is given subcutaneously. We assumed the disposition phase to follow a 1-compartment model. In both populations the absorption profile followed a transit compartment model, with the obese patients having significantly greater mean transit time. The populations consisted of 60 normal weight and 60 obese adult patients. The obese patients were divided into five batches with twelve patients in each batch. The nominal parameter mean of normal weight patients were CL = 4Lh-1, V = 20L, MTT (mean transit time) = 3h, N (number of transit compartment) = 2 and dose = 100mg. The nominal parameter mean of obese patients were CL = 5.2Lh-1, V = 30L, MTT = 20h, N = 20 and same dose is given. The variance of the log-normal between subject variability for CL, V and MTT are assumed to be the same for both populations with value 0.2. We assumed there is no between subject variability for N in both populations. A combined residual error model was assumed. The 60 normal weight patients each provided 8 blood samples following a D-optimal sampling schedule.
Results and Discussion:
Scenario 1:
Two hundred adult patients with 6 samples per patient provided precise parameter estimates for the adult population. The adaptive design with fixed reduction rate of adult patient data (20% per iteration) provided precise parameter estimates for the paediatric population at the 5th (final) iteration. Results from scenario 1 showed that D-optimal ABS was not inferior compared to the study design optimized on prior population used directly in the target population.
Scenario 2:
Sixty normal weight adult patients with 8 D-optimal samples per patient provided precise parameter estimates for the normal weight adult population. The D-optimal ABS with fixed reduction rate of normal weight adult patient data (20% per iteration) provided acceptable parameter estimates for the obese adult population at the 5th (final) iteration. In this setting a D-optimal ABS design performed better than when a D-optimal design from the prior population was applied to the target population.
Conclusions:
Optimal adaptive designs for bridging studies are a potentially useful method for learning about new populations. The proposed design method for bridging studies provided reasonable parameter estimates for the target population even when the PK profile of the prior and target populations were widely divergent.
References:
[1] Boulanger B, Jullion A, Jaeger J, Lovern M and Otoul C. Developtment of a Bayesian Adaptive Sampling Time Strategy for PK studies with constrained number of samples to ensure accurate estimates. PAGE 17 (2008) Abstr 1310 (http://www.page-meeting.org/?abstract=1310)