Extrapolation of a Brivaracetam Exposure–Response Model from Adults to Children with Focal Seizures

All clinical trials were conducted in accordance with the International Conference on Harmonization notes for Guidance on Good Clinical Practice and the Declaration of Helsinki. The study protocols were approved by the Institutional Review Boards at all study sites, and written informed consent was obtained from all patients, parents or legal guardians prior to enrollment.

The brivaracetam adult data originated from two placebo-controlled, phase II clinical studies and three placebo-controlled, phase III clinical studies with adjunctive brivaracetam in refractory adult patients with focal seizures [11]. Daily seizure count recordings were extracted from patient diaries. The brivaracetam pediatric data originated from an open-label, single-arm, multicenter, fixed three-step uptitration study evaluating the PK, safety, and efficacy of brivaracetam in children with refractory epilepsy syndromes or epilepsy, aged ≥1 month to <16 years [13]. In the absence of a placebo group, the absence of baseline seizure count assessments, and a wide range of epilepsy syndromes, available seizure count data were not subjected to modeling.

The levetiracetam adult data originated from four double-blind, placebo-controlled, parallel-group, phase III clinical studies with adjunctive levetiracetam in refractory adult patients with focal epilepsy [14‐17]. Seizure count recordings from patient diaries were aggregated over monthly between-visit periods. The levetiracetam pediatric data originated from a double-blind, placebo-controlled, multicenter study evaluating the efficacy and tolerability of levetiracetam as add-on treatment in refractory children (≥4 years to <16 years of age) with focal seizures [18]. Daily seizure count recordings were extracted from patient diaries. Details of the studies are provided in Table 1.

The levetiracetam PK data were obtained from a total of 101 pediatric and 799 adult patients receiving active treatment who contributed 415 and 3686 quantifiable levetiracetam concentrations, respectively. The pediatric levetiracetam PD data were obtained from a total of 211 patients receiving active or placebo treatment and who contributed 32,958 daily seizure-count records. The adult levetiracetam PD data were obtained from a total of 883 patients receiving active or placebo treatment and who contributed 6107 aggregated seizure-count records, corresponding to a total of 175,088 seizure-count assessment days. Patients with less than two focal seizures per 4 weeks prior to treatment administration were removed from the analysis. Descriptive statistics for demographic data are provided in Table 2.

The analyses were performed using NONMEM version 7.2.0 [19] software supplemented with the PsN toolkit [20]. PK data were analyzed using first-order conditional estimation with the interaction option, while seizure-count data were analyzed using Laplacian estimation. Data were further processed using 64-bit R version 3.1.2 software [21]. Simulations were performed using R and NONMEM.

The population PK model for levetiracetam was a one-compartment model with first-order absorption and elimination. The influence of body weight on clearance (CL) and volume (V) of distribution was estimated using the following allometric equation:where \(\varTheta_{1}\) is the population value of the estimated PK parameter, and WT_i is the individual body weight scaled to the population typical value of 70 kg. Interindividual variability (IIV) is described using η _i . The parameter \(\varTheta_{2}\) is the scaling parameter for the weight range, which can either be freely estimated or fixed to theoretical allometric values of ¾ and 1 for CL and V, respectively [22].

Exponential models were used to describe the IIV. Correlation between parameters was investigated by estimating a full or suitably reduced omega matrix. Both proportional and combined additive and proportional models were investigated to describe the residual variability.

The effects of the hepatic enzyme-inducer AEDs carbamazepine, phenytoin, and phenobarbital or primidone, or one or more of these AEDs (IND), were also investigated as potential covariates on CL. 95% confidence intervals (CIs) were calculated for the fixed effects parameters using the standard error of the estimates.

The empirical Bayes estimates (EBEs) from the final levetiracetam pediatric PK model were used to generate daily levetiracetam concentration profiles using recorded daily levetiracetam doses. Areas under the curve over 24 h were calculated using the simulated profiles and divided by 24 h, resulting in daily average concentration values (C _av) that were then used to drive the PK/PD model. This procedure allowed changes in daily dose to result in gradual changes of predicted concentrations without having to assume steady state. For the adult data, the EBEs for CL were used to simulate C _av values using the median dose during the assessment period.

A population PK/PD model using daily seizure counts has been previously developed [11]. In short, the brivaracetam PK/PD model was developed using a count model with a negative binomial distribution [23], to describe daily seizures where seizure rates were a function of both placebo and drug effects. The negative binomial distribution is an extension of the Poisson distribution that uses an overdispersion parameter to allow an increase in variability of seizure counts. Clustering of seizures was described using a Markovian component [24] by influencing the seizure rate on a particular day by seizures on the previous day [25]. Significant decreases in seizure frequency were observed under placebo treatment. Some of the patients receiving active treatment were best described by the placebo-response distribution, while the remaining patients displayed a decrease in seizure frequency following brivaracetam administration. This was implemented by assuming two populations: the ‘mixture-model responder population’ where a concentration-dependent decrease in seizure frequency was added onto the placebo distribution, and the ‘mixture-model placebo-like population’, with a response governed only by the placebo model parameter. Seizure rates were modeled on the log scale, and the model for the two populations was described using Eqs. 2 and 3: where λ is the modeled seizure rate, Q ₂ = 0 for baseline and 1 for post-baseline, and C _av is the average daily concentration. Basal seizure rates (S _0ij ) are seizure rates in the absence of placebo and drug effects, while placebo and E _max describe the individual specific change due to the placebo effect and the maximum brivaracetam effect, and are estimated with IIV (η _3i and η _4i). Finally, EC₅₀ is the typical population C _av associated with reaching 50% of the maximum effect. NONMEM estimated the probability of a patient ending up in one of the two populations.

The structure of the PK/PD model for levetiracetam in adults and children aimed to match the existing PK/PD model structure for brivaracetam in adults [11] as closely as possible. The daily seizure-count model was modified to describe total seizure counts over specified periods for the adult levetiracetam PD data; expected values for total counts per period were given by λ times number of days counted. For the daily counts in children, the number of days counted was 1 for every record.

The following equation was used to describe the basal seizure rate:

The pediatric population marker (PED) was 0 for adults and 1 for children. The basal seizure rate for adult patients was given by the population value (S ₀) with added IIV (η _1i ), and, for children, this was combined with an E _max function depending on the observed number of seizures on the preceding day (DPDV_ij), the maximum increase in seizure rate (S _max ) with IIV (η _2i), and the number of preceding-day seizures associated with 50% of the maximum increase (ES₅₀). Basal seizure rates were transformed using a Box–Cox transformation [26] to correct for marked skewness.

Parameter values for levetiracetam in Eqs. 2, 3, and 4 for adult patients, and multiplication factors from adults to children, were estimated for S ₀, placebo, E _max, EC₅₀, and the mixing fraction. These multiplication factors (if significant) were used to scale the existing adult brivaracetam PK/PD model to predict concentration-dependent seizure reduction for children receiving brivaracetam.

A visual predictive check (VPC) [27] was performed to evaluate the predictive performance of the levetiracetam adult and pediatric population PK/PD model. The VPC examines the model’s ability to simulate back the data that has been used for the model development. Seizure counts were simulated 500 times using the levetiracetam dose and covariate data from the patients who were included in the analysis at the same sampling times. Mean seizure frequencies were calculated for every patient during baseline and during treatment, and normalized to 28-day seizure frequencies. The log(x + 1) values of the mean 28-day seizure frequencies (to allow log transformation of seizure frequencies of zero) of the baseline and treatment values were taken, and the differences between log-baseline and log-treatment values were calculated to quantify change from baseline. These log differences were then back-transformed, yielding percentage change estimates from baseline.

Posterior predictive checks were performed by calculating the median percentage change from baseline for the raw data and the simulated studies by randomized treatment dose; the raw data median percentage change from baseline values were compared with the simulated distributions arising from the 500 simulated studies. Additionally, the proportion of 50% responders for each randomized treatment dose was calculated, defined as the proportion of patients with a decrease from baseline seizure frequency of at least 50%.

The 50% responders (both simulated and observed) should not be confused with the mixture-model responder population: the 50% responders are the patients who demonstrate an actual seizure frequency reduction of at least 50%, possibly due to both placebo effect and drug effect, while the mixture-model responder population identifies the patients who show a decrease in seizure frequency that can be attributed to levetiracetam C _av. At low doses, patients can still be assigned to the mixture-model responder population even though maximum effect has not been reached, and, conversely, patients can be considered 50% responders during placebo treatment if they have a sufficient decrease in seizure frequency from baseline.

The previously derived pediatric brivaracetam population PK model [12] used lean body weight (LBW) to allometrically scale CL and V. The National Health and Nutrition Examination Survey (NHANES) Dual X-ray Absorptiometry (DXA) database [28] was used to provide LBW values for children 4–16 years of age to drive the simulations; corresponding age and WT values were used to categorize the simulated responses. Primidone, carbamazepine, and valproate coadministration, identified as significant covariates in the pediatric brivaracetam population PK model, was sampled from the brivaracetam pediatric dataset, where the combination, within a patient, of primidone, carbamazepine, and valproate coadministration was kept intact. Brivaracetam concentrations for milligrams/kilogram body weight doses of 1, 2, 3, 4, 5, and 6 mg/kg/day, with a maximum dose of 200 mg/day, were simulated. The simulated brivaracetam concentrations were then used to simulate individual daily seizure-count profiles using the scaled adult-to-pediatric brivaracetam PK/PD population model. The simulations were used to generate a sequence of 8 weeks at baseline, followed by 12 weeks of brivaracetam treatment at the simulated C _av value. Change from baseline was calculated as described above, and summarized using the median and the interquartile range.