Manon Tauzin
email: manon.tauzin@gmail.com

Jean-Marc Tréluyer

Rima Nabbout

Nicole Chemaly

Thierry Billette De Villemeur

Isabelle Desguerre

Gabrielle Lui

Ines Gana

Sana Boujaafar

Yi Zheng

Sihem Benaboud

Naim Bouazza

Camille Chenevier-Gobeaux

Cécile Freihuber

Déborah Hirt

Predictive Performance of Population Pharmacokinetic Models of Levetiracetam in Children and Evaluation of Dosing Regimen Q1

Keywords: epilepsy, neurology, pediatrics, pharmacokinetics, therapeutic drug monitoring

Levetiracetam is a broad-spectrum antiepileptic drug that exhibits high interindividual variability in serum concentrations in children. A population pharmacokinetic approach can be used to explain this variability and optimize dosing schemes. The objectives are to identify the best predictive population pharmacokinetic model for children and to evaluate recommended doses using simulations and Bayesian forecasting. A validation cohort included children treated with levetiracetam who had a serum drug concentration assayed during therapeutic drug monitoring. We assessed the predictive performance of all the population pharmacokinetic models published in the literature using mean prediction errors, root mean squared errors, and visual predictive checks. A population model was finally constructed on the data, and dose simulations were performed to evaluate doses. We included 267 levetiracetam concentrations ranging from 2 to 69 mg/L from 194 children in the validation cohort. Six published models were externally evaluated. Most of the models underestimated the variability of our population. A 1-compartment model with first-order absorption and elimination with allometric scaling was finally fitted on our data. In our cohort, 57% of patients had a trough concentration <12 mg/L and 12% <5 mg/L. To reach a trough concentration >5 mg/L, doses ≥30 mg/kg/d for patients ≤50 kg and ≥2000 mg/d for patients >50 kg are required. In our population, a high percentage of children had low trough concentrations. Our population pharmacokinetic model could be used for therapeutic drug monitoring of levetiracetam in children.

Levetiracetam is a new generation antiepileptic drug (AED) frequently used to treat children with epilepsy. It has a broad-spectrum activity on focal and generalized seizures as first-line treatment or adjunctive therapy. [START_REF]The Epilepsies: the diagnosis and management of the epilepsies in adults and children in primary and secondary care: pharmacological update of Clinical Guideline 20[END_REF] Levetiracetam exhibits a good tolerability profile. Some adverse effects are reported: behavioral abnormalities such as aggression, irritability, or psychotic symptoms; headache; somnolence; ataxia; and seizures. [START_REF] Tan | Levetiracetam clinical pharmacokinetic monitoring in pediatric patients with epilepsy[END_REF] Levetiracetam demonstrates linear pharmacokinetics with high interindividual variability in serum concentrations with same doses. [START_REF] Tan | Levetiracetam clinical pharmacokinetic monitoring in pediatric patients with epilepsy[END_REF] It is rapidly absorbed (time to maximum concentration, 1-2 hours) and has very low protein binding (<10%). [START_REF] Jacob | An updated overview on therapeutic drug monitoring of recent antiepileptic drugs[END_REF][START_REF] Johannessen | Pharmacokinetic variability of newer antiepileptic drugs: when is monitoring needed?[END_REF] Half-life for pediatric patients is estimated between 4 and 6 hours, [START_REF] Glauser | Pharmacokinetics of levetiracetam in infants and young children with epilepsy[END_REF][START_REF] Fountain | Prospective assessment of levetiracetam pharmacokinetics during dose escalation in 4-to 12-year-old children with partial-onset seizures on concomitant carbamazepine or valproate[END_REF][START_REF] Pellock | Pharmacokinetic study of levetiracetam in children[END_REF] and clearance per kilogram decreases with increasing age. Levetiracetam is mainly excreted unmetabolized by the kidney (70%), explaining that glomerular filtration rate is often included in pharmacokinetic models and that dose adjustments are needed for patients with renal impairment; only one-third of levetiracetam undergoes hepatic metabolism by hydrolysis. Clearance per kilogram in children is 30% to 40% higher than in adults, so children necessitate higher doses in milligrams per kilogram per day. [START_REF] Fountain | Prospective assessment of levetiracetam pharmacokinetics during dose escalation in 4-to 12-year-old children with partial-onset seizures on concomitant carbamazepine or valproate[END_REF][START_REF] Pellock | Pharmacokinetic study of levetiracetam in children[END_REF] Drug-drug interactions between levetiracetam and other AEDs seem to be minor because of its minimal hepatic metabolism. However, lower concentrations and exposure to levetiracetam are reported by several studies for patients treated concomitantly with an enzyme inducer (carbamazepine, phenobarbital, or phenytoin). Studies do not report any effect of enzyme inhibitors such as valproate on levetiracetam clearance. [START_REF] Tan | Levetiracetam clinical pharmacokinetic monitoring in pediatric patients with epilepsy[END_REF][START_REF] Dahlin | Age and comedications influence levetiracetam pharmacokinetics in children[END_REF][START_REF] May | Serum concentrations of Levetiracetam in epileptic patients: the influence of dose and comedication[END_REF] One-third of patients with epilepsy remain nonresponsive to antiepileptic therapy. [START_REF] Van Dijkman | Individualized dosing algorithms and therapeutic monitoring for antiepileptic drugs[END_REF] To deal with those patients, we need to rationalize AED use, and a population pharmacokinetic approach might be a key to manage it. Model-based dosing algorithms have been proven effective to reduce the variability of concentrations and to individualize treatments with therapeutic drug monitoring (TDM) of AEDs. [START_REF] Van Dijkman | Individualized dosing algorithms and therapeutic monitoring for antiepileptic drugs[END_REF] However, several population pharmacokinetic models for levetiracetam on different populations have been published in the literature. The issue is to choose the appropriate model to use on our pediatric population to optimize dosing schemes. External validation of population pharmacokinetic models is the most robust form of evaluation of predictive performance of models and will be used in our study. [START_REF] Brendel | Are population pharmacokinetic and/or pharmacodynamic models adequately evaluated? A survey of the literature from 2002 to 2004[END_REF] This study reviews all population pharmacokinetic models of levetiracetam in children and assesses their predictive performance on an external validation cohort. The objectives were (1) to externally evaluate the predictive performance of published population pharmacokinetic models, (2) to construct a model with our monitoring data, and (3) to evaluate doses using simulations.

Methods

Population and Treatment

We extracted data for the validation data set from the pharmacology laboratory database of Hôpital Cochin, Paris, France. We included all patients ≤18 years old who had at least 1 levetiracetam serum concentration assay at steady state for routine therapeutic monitoring between 2007 and 2019. The ethics committee of Hôpital Necker Enfants-Malades approved the anonymous use of these data and their publication. Levetiracetam treatment and doses were conducted according to clinicians' expertise. We collected data on dosing regimen, time of last intake, sampling time, age, weight, serum creatinine (SCr), and comedication by valproate or an enzyme-inducing AED (phenobarbital, phenytoin, or carbamazepine). SCr was measured by the enzymatic method. We treated missing data for weight and height by taking the median weight or height for age and sex according to the Centers for Disease Control and Prevention clinical growth charts for the pediatric population. Missing SCr values were calculated according to age with the following formula [START_REF] Ceriotti | Reference intervals for serum creatinine concentrations: assessment of available data for global application[END_REF] : mean creatinine (μmol/L) = -2.37330 -12.91367 × ln(age) + 23.93581 × (age) 0.5 . Glomerular filtration rate was calculated using the Schwartz formula. [START_REF] Schwartz | New equations to estimate GFR in children with CKD[END_REF] We excluded patients with missing comedication data, unknown dosing regimen, or unclear delay between dose and sampling and patients for whom a lack of compliance was clearly suspected.

Levetiracetam Serum Concentration Assay

Levetiracetam serum concentrations were measured in the pharmacology laboratory of Hôpital Cochin, Paris, France, by high-pressure liquid chromatography with ultraviolet detection, with a calibration range from 2 to 80 mg/L. Coefficients of variation of intra-and interassay for this method were <15%. The lower limit of quantification (LLOQ) was 2 mg/L.

Population Pharmacokinetic Models Used

A literature review was performed using the PubMed database to identify all published population pharmacokinetic models of levetiracetam. The search was conducted in April 2020 with associations of the following terms ("levetiracetam" AND ("children" OR "infants" OR "pediatric") AND ("population pharmacokinetic" OR "nonlinear mixed effects" OR "NONMEM"). The studies were included if they fulfilled the following criteria: (1) They were in the English language, (2) they contained data on pediatric patients, and (3) a population pharmacokinetic model was developed on oral levetiracetam.

Five studies presenting six different population pharmacokinetic models were published between 2008 and 2016. [START_REF] Toublanc | Retrospective population pharmacokinetic analysis of levetiracetam in children and adolescents with epilepsy: dosing recommendations[END_REF][START_REF] Chhun | Population pharmacokinetics of levetiracetam and dosing recommendation in children with epilepsy[END_REF][START_REF] Wang | Population pharmacokinetics modeling of levetiracetam in Chinese children with epilepsy[END_REF][START_REF] Toublanc | Development of an integrated population pharmacokinetic model for oral levetiracetam in populations of various ages and ethnicities[END_REF][START_REF] Ito | Population pharmacokinetic modeling of levetiracetam in pediatric and adult patients with epilepsy by using routinely monitored data[END_REF] A summary of the main characteristics of those studies is presented in Table 1. A 1-compartment model and a first-order absorption described levetiracetam pharmacokinetics in all studies. Only model 2 described a lag time. [START_REF] Chhun | Population pharmacokinetics of levetiracetam and dosing recommendation in children with epilepsy[END_REF] Models 4 and 5 were developed on both child and adult data. [START_REF] Toublanc | Development of an integrated population pharmacokinetic model for oral levetiracetam in populations of various ages and ethnicities[END_REF][START_REF] Ito | Population pharmacokinetic modeling of levetiracetam in pediatric and adult patients with epilepsy by using routinely monitored data[END_REF] Models 1a, 1b, and 2 were developed with data from trials. [START_REF] Toublanc | Retrospective population pharmacokinetic analysis of levetiracetam in children and adolescents with epilepsy: dosing recommendations[END_REF][START_REF] Chhun | Population pharmacokinetics of levetiracetam and dosing recommendation in children with epilepsy[END_REF] The covariates explaining interindividual variability were body weight (all models), comedication by an inducer (3 models), glomerular filtration rate (GFR; 2 models), dose (2 models), and age (1 model). In model 1, two different models were proposed: a full model (1a) including weight, inducer comedication, GFR, and dose as covariates of clearance; and a reduced model (1b) with only body weight and inducer comedication as covariates of clearance. Validation methods varied between articles: Goodness-of-fit plots were used for all the models; model 1 used the jackknife method; model 2 used normalized predictive distribution errors; models 2, 4, and 5 used visual predictive checks; and models 3 and 4 used an external validation. ALAG, lag-time (h); BW, body weight (kg); CBZ, carbamazepine; CL, clearance (L/h); covCL-V, covariance between clearance and volume; DD, total daily dose; DOSE, dose of last intake; GFR, glomerular filtration rate (mL/min/1,73m 2 ); IIV, interindividual variability expressed as the square root of the variance of the eta-distribution (ω); IND, enzyme inducer; INH, enzyme inhibitor; IOVka, interoccasion variability on ka; ka, absorption constant (h -1 ); LAMO, lamotrigine; MHD, oxcarbazepine; proportional RV, proportional residual variability expressed as square root of the variance of the epsilon-distribution (σ ); TOPI, topiramate; V, volume of distribution (L); VPA, valproic acid . Age, BW, and dose are expressed as median (range).

External Validation

We applied each population pharmacokinetic model to our validation cohort by implementing them one by one into Monolix software version 2018R1 (Lixoft, Antony, France) with the parameters described in the original article. We used R software version 3.3.2 (R Foundation for Statistical Computing, Vienna, Austria) for statistics and graphics. Population predictions were made according to dose, sampling time, and covariate characteristics of our validation data set.

To assess predictive performance of each model, we first compared goodness-of-fit plots of the population predicted concentrations and the observed concentrations. To assess bias and precision of the models, we calculated mean prediction error (MPE) (1) and root mean squared prediction error (2) between population predicted concentrations of each model and observed concentrations of the validation data set. [START_REF] Sheiner | Some suggestions for measuring predictive performance[END_REF]

MPE =

1

n n i = 1 (C pred i -Cobs i ) (1) MPE = 1 n n i = 1 (C pred i -Cobs i ) (2)
Predictive performance was also assessed with prediction corrected-visual predictive check (pc-VPC) on 1000 simulations. We plotted observed concentrations of the validation data set along with the 5th, 50th, and 95th percentiles of the simulated concentrations to evaluate population predictions visually.

Modeling of the Data With a New Model Data were analyzed using the nonlinear mixed effect modelling software Monolix. A 1-compartment model with first-order absorption and elimination best described the data. Several error models were investigated (ie, proportional, additive, or combined error models) to describe residual variability. Interindividual variability was defined by an exponential error model. Continuous covariates were integrated as follows:

θ i = θ pop × ( Cov i median(Cov) )
β where θ pop is the typical value of clearance for a patient with the median covariate value and β is the estimated influential factor for the continuous covariate estimated by the modeling software. For body weight, according to the allometric rule, the power was fixed at 0.75 for clearance parameters and 1 for volume of distribution parameters. Categorical covariates were tested as follows:

θ i = θ pop × β COV i , COV i equals 0 or 1.
A covariate was finally retained in the model if its effect was biologically plausible, if it produced a reduction in the variability of the pharmacokinetic parameter interindividual variability, and if the OFV was decreased by at least 3.84 (χ 2 with 1 df; P < .05) in the upward phase and was increased by >6.63 (χ 2 with 1 df; P < .01) in the backward phase.

For evaluation of the goodness-of-fit, the following graphs were performed: observed concentrations vs population predictions and vs individual predictions, and normalized predictive distribution errors vs time and vs predictions.

From the final model, Monte Carlo simulations were performed to compute the pc-VPC. The 5th, 50th, and 95th percentiles of the simulated concentrations at each time were then overlaid on the observed concentration data, and a visual inspection was performed.

Evaluation of Dose Recommendations

Using our final model, we estimated trough levels for our patients. We determined the proportion of patients reaching target concentrations (between 12 and 46 mg/L according to the International League Against Epilepsy) [START_REF] Patsalos | Therapeutic drug monitoring of antiepileptic drugs in epilepsy: a 2018 update[END_REF] and the proportion of trough concentrations <5 mg/L. [START_REF] Reimers | Reference ranges for antiepileptic drugs revisited: a practical approach to establish national guidelines[END_REF]

Results

Population and Treatment

We included data from 194 patients and 267 levetiracetam serum concentrations. The median age was 8.9 years (range, 0.04-18.9 years), and the median weight was 26.8 kg (range, 2.8-95 kg). The main characteristics of the validation data set are described in Table 2. Serum concentrations ranged from the LLOQ (2 mg/L) to 69 mg/L. We had 9 concentrations (3.4%) under the LLOQ for which we used the LLOQ/2. Covariates were missing in 9% of the patients and replaced as indicated in the method. To avoid imprecision in the data, we excluded patients with missing comedication data, unknown dosing regimen, or unclear delay between dose and sampling and patients for whom a lack of compliance was clearly suspected. Since we did not have that much missing data, we did not try to use only complete cases for the external validation.

External Validation

Graphically in Figure 1, models 1a, 1b, 2, and 4 seemed to have the best adequacy between predicted and observed concentrations. These 4 models showed the least bias, with an MPE between -0.14 and 1.6 mg/L, and the highest precision, with a root mean squared prediction error between 11.6 and 12.3 mg/L. Models 3 and 5, respectively, largely overpredicted and underpredicted our observed concentrations. The results of the external validation are presented in Table 3.

On the pc-VPC (Figure 2), most of the models seemed to underestimate the variability observed in our population, for example, lines representing the 5th and 95th percentiles of the observations are often outside the blue areas representing 95% confidence intervals of the 5th and 95th simulated percentiles. Models 1a and 1b seemed to best represent our population with very similar predictive performance graphically and numerically. Because model 1b was a reduced version of model 1a, it appeared to be easier to apply in clinical practice, particularly because no GFR calculation is needed.

Modeling of the Data With a New Model

A 1-compartment model with first-order absorption and elimination, with an allometric model, best described the data. Due to the lack of samples in the first hour after drug intake, the absorption constant rate could not be estimated and was fixed to a value of the literature. The median value of 2.56/h was chosen, although all the other values produced similar estimates for apparent clearance and volume. A proportional error model was used to describe residual variability. Final pharmacokinetic parameter estimates are summarized in Table 4 and diagnostic graphs are shown in Figure 3.

Evaluation of Dose Recommendations

We used our pharmacokinetic model to predict trough concentrations using Bayesian forecasting. The median predicted trough concentration was 11.0 mg/L (range, 0.2-44.1 mg/L). In our population, 146 predicted trough concentrations (55%) were <12 mg/L (lower limit of the reference range), 34 values (13%) <5 mg/L, and none were >46 mg/L (higher limit of the reference range). Predicted trough concentrations according to daily dose, weight, and comedications for our patients are represented in Figure 4. For patients from 10 to 30 kg, 76% (55/72) of patients treated with a dose <40 mg/kg/d had a trough concentration below 12 mg/L vs 35% (17/49) for patients with a dose ≥40 mg/kg/d. For patients from 30 to 50 kg, 76% (29/38) of patients treated with a dose <40 mg/kg/d had a trough concentration <12 mg/L vs 12% (3/25) for patients with a dose ≥40 mg/kg/d. For patients >50 kg, 86% (18/21) of patients treated with a dose <2000 mg/d had a trough concentration <12 mg/L vs 17% (4/24) for patients with a dose ≥2000 mg/d. When looking at trough concentrations with a lower threshold at 5 mg/L, for patients from 10 to 30 kg, 40% (14/35) of patients treated with a dose <30 mg/kg/d had a trough concentration <5 mg/L vs 7% (6/86) for patients with a dose ≥30 mg/kg/d. For patients from 30 to 50 kg, 21% (5/24) of patients treated with a dose <30 mg/kg/d had a trough concentration below 5 mg/L vs 8% (3/39) for patients with a dose ≥30 mg/kg/d. For patients >50 kg, 14% (3/21) of patients treated with a dose <2000 mg/d had a trough concentration <5 mg/L vs 0% (0/24) for patients with a dose ≥2000 mg/d.

The results of doses simulations are presented in Figure 5 for patients ≤10, 10 to 30, 30 to 50 and >50 kg. To reach a trough concentration above 5 mg/L, simulations suggested the following dosing regimen: a dose between 30 and 60 mg/kg/d for patients ≤50 kg and between 2000 and 3000 mg/d for adolescents >50 kg.

Discussion

To our knowledge, this study is the first to review and assess all population pharmacokinetic models for levetiracetam in children. Our validation cohort was representative of the pediatric population treated by levetiracetam with large ranges of weights, ages, doses, and comedications. We identified suitable models to represent our population, but most of them could not describe the high variability of our patients. A new model was done that could be used for a personalized dosing regimen and dose individualization by Bayesian forecasting in clinical practice.

We conducted an external evaluation of predictive performance of all the population pharmacokinetic models of levetiracetam published for pediatric patients. Models 1a, 1b, 2, and 4 had good predictive

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performance in our analysis. [START_REF] Toublanc | Retrospective population pharmacokinetic analysis of levetiracetam in children and adolescents with epilepsy: dosing recommendations[END_REF][START_REF] Chhun | Population pharmacokinetics of levetiracetam and dosing recommendation in children with epilepsy[END_REF] All 4 models were developed on trial data, on a large number of children and samples. The reduced model from Toublanc et al 14 (1b) performed as well as the full model (1a) in our population. First, the coefficients on the covariates "DOSE" and "GFR" in model 1a are very low (0.0443 and 0.111, respectively), resulting in a small effect on clearance. Moreover, few patients had renal impairment (GFR <60 mL/min/1.73 m 2 ). Thus, the reduced model (1b) would be easier to apply in routine clinical practice. Graphically, both models 1a and 1b demonstrated good predictive performance in our analysis. Since models 1a and 1b had similar predictive performance as our model, we also conducted dose simulations with these models that confirmed our results. Model 5 also performed well but with less precision and more bias, probably because it was developed on both adults and children. [START_REF] Toublanc | Development of an integrated population pharmacokinetic model for oral levetiracetam in populations of various ages and ethnicities[END_REF][START_REF] Ito | Population pharmacokinetic modeling of levetiracetam in pediatric and adult patients with epilepsy by using routinely monitored data[END_REF] Indeed, their development data set contained a larger proportion of adults, and the calculation included an effect of the dose on clearance; children receive higher doses in milligrams per kilogram per day than adults, which might explain the lower performances of this model on our patients. [START_REF] Ito | Population pharmacokinetic modeling of levetiracetam in pediatric and adult patients with epilepsy by using routinely monitored data[END_REF] Model 3 reported a 50% lower clearance than the others, explaining the bias found with this model for our population. [START_REF] Wang | Population pharmacokinetics modeling of levetiracetam in Chinese children with epilepsy[END_REF] In their article, the hypothesis for this difference was the existence of ethnical differences between White and Chinese children. This difference was not reported for other populations. For instance, in the study by Toublanc et al published in 2014, [START_REF] Toublanc | Development of an integrated population pharmacokinetic model for oral levetiracetam in populations of various ages and ethnicities[END_REF] there was no difference between a Japanese and a North American population of adults and children. Another study conducted on healthy Chinese adults reported similar pharmacokinetics as White subjects. [START_REF] Zhao | Single-dose pharmacokinetics of levetiracetam in healthy Chinese male subjects[END_REF] This difference of pharmacokinetics in Chinese children should be further studied. This raises the question of transferability of models. The studied models demonstrated little bias (as shown by small values of MPE). However, the evaluation by the pc-VPC showed that none of the studied models were validated by our data because of underestimation of variability or due to structural model misspecification.

The difference between data from trials and data from routine monitoring could explain these large differences in variability. Another hypothesis for this increased variability is that patients who need TDM during their levetiracetam treatment might have different underlying conditions or different characteristics or can have more severe forms of epilepsy. All this could induce bias in our data compared to trial data, for example. However, our study adds a "routine practice" point of view and exhibits the variability in concentrations experienced in clinical practice. For these reasons, we decided to build a new model to describe this variability.

In clinical practice, the first interest of a population pharmacokinetic model is to propose an initial dosing regimen knowing the patient's characteristics (weight and comedication): This estimation of doses is indicative for a population but is not as precise as individual predictions. Indeed, the second interest is at an individual level: A population pharmacokinetic model can be useful to individualize treatment using Bayesian forecasting when we have a serum concentration assayed during TDM. [START_REF] Al-Metwali | Personalised dosing of medicines for children[END_REF][START_REF] Admiraal | Towards evidence-based dosing regimens in children on the basis of population pharmacokinetic pharmacodynamic modelling[END_REF] The reference range for levetiracetam serum concentrations relies on reported concentrations and retrospective database and is not consensual. Indeed, clear efficacy or toxicity thresholds have not been described yet. Different ranges of trough concentrations have been reported: 12 to 46 mg/L for the International League Against Epilepsy, [START_REF] Patsalos | Therapeutic drug monitoring of antiepileptic drugs in epilepsy: a 2018 update[END_REF] but other authors reported a lower threshold of 8, 6, or even 5 mg/L. [START_REF] Reimers | Reference ranges for antiepileptic drugs revisited: a practical approach to establish national guidelines[END_REF][START_REF] Leppik | Effective levetiracetam doses and serum concentrations: age effects[END_REF][START_REF] Neels | Therapeutic drug monitoring of old and newer anti-epileptic drugs[END_REF] The target 12 to 46 mg/L is extracted from an abstract published in 2002 on 371 samples from adults and 29 children with no precision on the time of sampling. [START_REF] Leppik | Effective levetiracetam doses and serum concentrations: age effects[END_REF] In 2003, May et al 9 reported trough concentrations of 16 ± 9.7 mg/L for 363 adults and children. Similarly, Johannessen et al [START_REF] Johannessen | Therapeutic drug monitoring of the newer antiepileptic drugs[END_REF] proposed a target between 8 and 26 mg/L. In our study, 12% of our patients had a predicted trough concentration <5 mg/L and 57% were <12 mg/L. From these results, an efficacy threshold at 12 mg/L seems quite high, and an efficacy on seizures with lower trough concentrations is highly possible. A very high number of patients had predicted trough concentrations below the lower threshold. We can see in Figure 4 that these patients were mainly patients with low doses. According to our simulations, following doses would be required to reach a trough concentration >5 mg/L: ≥30 mg/kg/d for patients ≤50 kg and ≥2000 mg/d for patients >50 kg. Regarding the uncertainty of the efficacy threshold for levetiracetam, clinical evaluation should remain the major way to judge efficacy. Levetiracetam doses should be increased gradually to reach the lower efficient dose, and TDM could be useful in these cases to search for individual therapeutic levels. However, in case of nonresponse, our study suggests to increase doses to reach therapeutic levels before changing molecules. We could not evidence an effect of inducer comedications on levetiracetam pharmacokinetics, although several studies exhibit this effect. This might be due to a small proportion of patients with concomitant treatment by an inducer in our cohort (28/267; 10.5%). The mechanism of this induction on levetiracetam is not properly elucidated since levetiracetam is mainly excreted by the kidney and its hepatic metabolism is mainly due to noncytochrome P-dependent hydrolysis. [START_REF] Tan | Levetiracetam clinical pharmacokinetic monitoring in pediatric patients with epilepsy[END_REF][START_REF] Fountain | Prospective assessment of levetiracetam pharmacokinetics during dose escalation in 4-to 12-year-old children with partial-onset seizures on concomitant carbamazepine or valproate[END_REF][START_REF] Patsalos | Antiepileptic drugs best practice guidelines for therapeutic drug monitoring: a position paper by the subcommission on therapeutic drug monitoring, ILAE Commission on Therapeutic Strategies[END_REF] Since there is no clear target for serum concentrations, TDM of levetiracetam serum concentration is not currently conducted for all patients, and clinical evaluation remains the best way to judge the efficacy of this molecule. However, TDM might be beneficial, especially in some circumstances such as polytherapies, suspicion of toxicity, uncontrolled epilepsy with patients switching molecules, compliance assessment, or patient with an individual therapeutic concentration. [START_REF] Tan | Levetiracetam clinical pharmacokinetic monitoring in pediatric patients with epilepsy[END_REF][START_REF] Jacob | An updated overview on therapeutic drug monitoring of recent antiepileptic drugs[END_REF][START_REF] Johannessen | Pharmacokinetic variability of newer antiepileptic drugs: when is monitoring needed?[END_REF] This study presents some limitations. First, retrospective collection of routine data implies a degree of uncertainty. However, it reflects the use of population pharmacokinetics in clinical practice. Second, we had 9% of missing data on covariates that we imputed as described in the Methods section. Another way could have been to take only complete cases for the validation, but it would have reduced our population. Third, we did not have clinical data on the control of epilepsy and potential adverse events in our population. Hence, we could not conclude on a relationship between serum levetiracetam levels and the efficacy or toxicity of the molecule and on the relevance of the reference range used. Fourth, all our patients had normal renal function, probably preventing us from including the impact of GFR in our final model. However, impaired renal function is a rare condition in a pediatric population, and TDM should be carried out in those patients.

Conclusion

After a systematic evaluation of predictive performance of published population pharmacokinetic models of levetiracetam in children, we identified a model suitable for our population. Our population exhibits more variability than most of the models tested. This study highlights the need to evaluate population pharmacokinetic models published and raises the question of transferability of models and their utility in clinical practice. It also highlights the need to characterize more properly a reference range for levetiracetam to enable us to rationalize its use in children.

  CL = 2.1 × (BW/32) 0.75 × 1.22 IND V = 20.4 × (BW/32) ωka = 0.858 ωCL = 0.199 ωV = 0.122 covCL-V = 0CL = 4.33 × (BW/70) 0.75 × (GFR/100) 0.638 × (1 + 0.175 × ((DD/(BW 0.75 ))/59.3)) V = 0.753 × BW ωka = 0.638 ωCL = ka = 2.56 (fixed) CL = 2.4 × (BW/26.8) 0.75 V = 80 × (BW/26.8) ωCL = 0.434 ωV = 0.758 σ = 0.43

Figure 1 .

 1 Figure 1. Population predicted concentrations (milligrams per liter) vs observed levetiracetam serum concentrations (milligrams per liter) for the 6 population pharmacokinetic models evaluated. Identity line is represented as a dashed line.

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  Journal of Clinical Pharmacology / Vol 0 No 0 2021

Figure 2 .

 2 Figure 2. Prediction-corrected visual predictive checks for the 6 levetiracetam models. Colored areas represent 95% confidence intervals of 5th, 50th, and 95th simulated percentiles. Lines are empirical (observed) 5th, 50th, and 95th percentiles. Dots are observed data.

Figure 3 .

 3 Figure 3. Performance of our model: Population (upper left) and individual (upper middle) predicted concentrations (milligrams per liter) vs observed levetiracetam serum concentrations (milligrams per liter), normalized prediction distribution error metrics vs time after dose (upper right) and vs predictions (lower left) and predicted-corrected visual predictive check (lower middle).

Figure 4 .

 4 Figure 4. Predicted trough concentrations (cc) in our population (milligrams per liter) according to recommended daily dose in milligrams per kilogram per day for patients ≤10 kg (upper left), patients from 10 to 30 kg (upper right), patients from 30 to 50 kg (lower left) and recommended daily dose in milligrams per day for patients >50 kg (lower right). Monotherapy and neutral comedication are represented with circles (•), enzyme inducer comedication with dots (•), and valproate comedication with triangles ( ).

Figure 5 .

 5 Figure 5. Boxplots of simulated trough concentrations according to daily dose for patients ≤10 kg (upper left), patients from 10 to 30 kg (upper right), patients from 30 to 50 kg (lower left), and patients >50 kg (lower right). Horizontal lines correspond to the target concentration range of 12 and 46 mg/L and dotted lines to a 5 mg/L trough concentration.

Table 1 .

 1 Summary of Key Information of Published Population Pharmacokinetic Models of Levetiracetam in Children

	Q4

Table 2 .

 2 Demographic and Treatment Characteristics of the Validation Cohort

	Number of patients	194
	Number of concentrations	267
	Number of male/female subjects	109/85
	Age, N (%)
	0-1 y	13 (6.7)
	1-2 y	8 (4.1)
	2-6 y	41 (21.1)
	6-10 y	49 (25.3)
	10-18 y	83 (42.8)
	Median (range)	8.9 (0.04-18.9)
	Body weight, kg, a	26.8 (2.8-95)
	Serum creatinine, μmol/L a	37 (13-99)
	Glomerular filtration rate, mL/min/1.73m 2a	123 (53-350)
	Daily dose, mg/d a	900 (100-3000)
	Daily dose, mg/kg/d a	35.1 (5-66.7)
	Comedication, N (%)
	Monotherapy or neutral comedication	171 (64.0)
	Valproate	65 (24.3)
	Inducer	28 (10.5)
	Inducer + valproate	3 (1.2)

a Median (range)

Table 3 .

 3 Results of Assessment of Predictive Performance for the 6 Levetiracetam Models: Evaluation of Prediction Error

			Bias and Precision
	Model	Mean Prediction	Root Mean Squared
		Error (mg/L)	Prediction Error (mg/L)
	1a	-1.6	11.7
	1b	-1.0	11.6
	2	--1.1	12.3
	3	12.8	20.9
	4	-0.14	12.3
	5	-5.9	12.8

Table 4 .

 4 Pharmacokinetic Parameter Estimates From the Final Model Built

	Q6
	Fixed Population Effects	Estimates	RSE (%)
	Ka(L.h -1 )	2 . 5 6	F I X
	CL = θ CL × (BW/26.8) 0.75
	θ CL L/h	2.4	5
	V = θ V × (BW/26.8) 1
	θ V L	8 0	2 1
	Interindividual variability
	ω CL	0.434	11
	ω V	0.758	34
	Residual proportional
	variability	0.43	8
	σ prop
	ω

CL , ; ω V , ; σ prop , ; BW, body weight (kg); CL, clearance; ka, absorption constant; RSE, relative standard error; V, .

Funding

This work was funded by a research grant from the Fondation pour la Recherche Médicale (code DEA 41304).

Data Availability

Data are available, upon reasonable request, by contacting the corresponding author (manon.tauzin@gmail.com).

Conflicts of Interest

The authors declare no conflicts of interest.


Olivier Steichen
email: olivier.steichen@aphp.fr

MD Phd Affiliations

How to intensify treatment in older hypertensive patients: is there a single answer?

Randomized trials show that half-dose antihypertensive bitherapies reduce blood pressure (BP) more than full-dose monotherapies, with no more adverse effects [START_REF] Salam | Efficacy and safety of dual combination therapy of blood pressure-lowering drugs as initial treatment for hypertension: a systematic review and meta-analysis of randomized controlled trials[END_REF]. Indeed, combining two drugs has an additive effect on BP reduction whereas increasing the dose of a drug is less than additive (2): a half dose is only 25% less potent than a full dose. Under these assumptions, the expected potency of antihypertensive drug combinations can be approximated (Table 1). For example, the combination of two drugs at half dose is expected to be 50% more potent than a single drug at full dose. Using half doses also reduces the adverse effects of thiazide diuretics and calcium-channel blockers (2); and combination with a renin-angiotensin system blocker further reduces some of them, such as thiazide induced hypokalemia and calcium channel blockers induced peripheral edema.

The main drawback of bitherapies is the number of pills needed. However, many can be prescribed as single-pill combinations (SPC), with improved adherence and persistence compared to free-equivalent combinations [START_REF] Parati | Adherence to Single-Pill Versus Free-Equivalent Combination Therapy in Hypertension: A Systematic Review and Meta-Analysis[END_REF]. Large cohorts of real-life patients have shown that initiating hypertension treatment with a drug combination (usually as SPC), rather than a single drug, is associated with fewer treatment discontinuation (4), better BP control [START_REF] Egan | Initial monotherapy and combination therapy and hypertension control the first year[END_REF], and ultimately a lower risk of cardiovascular events [START_REF] Gradman | Initial combination therapy reduces the risk of cardiovascular events in hypertensive patients: a matched cohort study[END_REF][START_REF] Rea | Early cardiovascular protection by initial two-drug fixeddose combination treatment vs. monotherapy in hypertension[END_REF].

The evidence available to guide intensification when treated patients do not reach their BP goal is more limited. When all existing drugs are already at full dose, we add a new drug. But when at least one drug is not at full dose, should we add a new drug or first maximize existing drugs? The pharmacological rationale suggests that adding a half-dose new drug is more potent with fewer adverse effects but the use of SPC is not always possible in this case, and more pills can lead to poorer adherence and treatment discontinuation.

A study published in this issue addresses the question of treatment intensification in hypertensive patients [START_REF] Aubert | Adding a new medication versus maximizing dose to intensify hypertension treatment in older adults: a prospective observational study[END_REF]. No less than 178,562 veterans with systolic BP > 130 mmHg and at least one antihypertensive drug not at full dose had their antihypertensive regimen intensified: 45,575 (26%) by drug addition and 132,987 (74%) by dose maximization. Outcomes were then compared after adjustment for baseline characteristics. Drug addition was less frequently sustained at three months than dose maximization (49.8% versus 65.0%) but the 12-month mean systolic BP decrease was nonetheless 1.1 mmHg larger (5.6 versus 4.5 mmHg).

This study includes a vast number of elderly patients, who are underrepresented in clinical trials. Sophisticated statistical methods intend to emulate a clinical trial from this observational cohort but the results remain vulnerable to bias and confounding. For example, the assessment of BP relied on unstandardized office measurements. This adds noise to the outcome data and might bias the results in unpredictable ways, especially since white-coat hypertension is common in this age group [START_REF] Conen | Age-specific differences between conventional and ambulatory daytime blood pressure values[END_REF]. However, the main shortcoming of the study lies in the broad spectrum of baseline situations. The logic of treatment intensification differs with the baseline number and doses of antihypertensive drugs, number of pills per day, BP level, and clinical condition including comorbidities and fitness (especially in older patients). Encompassing such a heterogeneous case-mix prevents definitive conclusions on how best to intensify treatment in uncontrolled hypertensive patients, in general or in any given situation. Consider a patient not at his BP goal while on a SPC with two half-dose drugs (combination potency 150 in one pill, see Table 1). We could favor maximizing the dose of the two drugs of the SPC (potency 200 in one pill) rather than adding a third drug at half dose (potency 225 but two pills). Staying with a single pill offsets the more limited potency increase (+50 instead of +75) and warrants an attempt. Now consider the same patient not at his goal while on a SPC with one full-dose and one half-dose drug (potency 175 in one pill). Here we could first favor adding a third drug at half dose (two pills but potency 250) rather than maximizing the second drug of the existing SPC (one pill but potency 200). The larger potency increase (+75 instead of +25) is worth the burden of adding one pill, provided the patient agrees with this strategy. These two oversimplified examples only scratch the surface of diverse situations requiring individualized and shared decision-making.

Nonetheless, two results must be stressed. First, whatever the chosen strategy, treatment intensification leads to large BP decreases in patients who need it the most. Figure 2 of the paper shows that the mean 12-month systolic BP decrease is about 8 mmHg in patients with baseline systolic BP between 140 and 160 mmHg and about 20 mmHg in those with baseline systolic BP over 160 mmHg.

Second, both intensification strategies are associated with roughly similar 12-month BP decreases in the emulated intention-to-treat analysis. In this analysis, mean BP decrease is the compound result of persistence and BP-lowering potency. Similar mean BP decrease despite lower persistence is, therefore, confirmatory evidence that drug addition is more potent than dose maximization in those who persist. When a large BP decrease is needed, drug addition should be preferred together with promoting persistence, for example with SPC and patient education [START_REF] Parati | Adherence to Single-Pill Versus Free-Equivalent Combination Therapy in Hypertension: A Systematic Review and Meta-Analysis[END_REF][START_REF] Gwadry-Sridhar | Impact of interventions on medication adherence and blood pressure control in patients with essential hypertension: a systematic review by the ISPOR medication adherence and persistence special interest group[END_REF].

In practice, this study provides support to several general principles of antihypertensive drug prescription. When intensification is indicated, we should not waste time with elaborate reasoning, either add a drug or maximize the dose of existing drugs, whichever seems to fit best with the patient current treatment, clinical state, and preferences. We must try to keep the treatment as simple as possible but remember that increasing the dose of a single drug has a limited effect on the overall potency of a combination. We should use SPC whenever it simplifies the treatment and explain any unavoidable complexification with the patient. A follow-up visit must be planned about one month later to assess adherence, tolerance and effectiveness, and perform further adjustments if needed. Table 1. Expected approximate potency of antihypertensive combinations according to the number of drugs (from different classes) and their doses.

Monotherapy Bitherapy Tritherapy

Half-dose 75 150 225

Full-dose 100 200 300

Potencies are expressed as a percentage of the BP decrease expected from a single full-dose drug.

The potency of any combination can be approximated by adding the potency of all its component drugs. For example, a bitherapy with one full-dose drug and one half-dose drug will have a 100 + 75 = 175 potency.