PharmD Xavier Delavenne
email: xavier.delavenne@chu-st-etienne.fr

MD, PhD Yesim Dargaud

Pr Xavier Delavenne

interpretation pitfalls, and use in the clinic

Keywords: Haemophilia A, Haemophilia B, recombinant human factor VIII, recombinant human factor IX, pharmacokinetic

INTRODUCTION

Haemophilia is a rare hereditary disease that has been known since antiquity. Paradoxically, a specific and effective anti-haemophilia treatment using a cryoprecipitate became available only in 1964 [START_REF] Key | Coagulation factor concentrates: past, present, and future[END_REF]. After the human immunodeficiency virus emergency in the 1980s, the improved safety of anti-haemophilia treatments, the arrival of recombinant factor concentrates and the patients' renewed confidence have allowed putting in place prophylaxis programmes for children that greatly limit joint damage and significantly reduce the occurrence of lifethreatening bleeding episodes [START_REF] Manco-Johnson | Prophylaxis versus episodic treatment to prevent joint disease in boys with severe hemophilia[END_REF][START_REF] Gringeri | de l'e tude ESPRIT. A randomized clinical trial of prophylaxis in children with hemophilia A (the ESPRIT Study)[END_REF]. Yet, just a single therapeutic approach is available: replacement therapy using plasma-derived or recombinant factor concentrates. Currently, patients with haemophilia are going through a real revolution and even haemophilia cure by gene therapy does not seem far away [START_REF] Skinner | Achieving the unimaginable: Health equity in haemophilia[END_REF]. The new non-substitutive therapeutic approaches, such as bispecific antibodies that mimic the function of activated factor VIII (FVIII), and the concept of modifying the haemostatic balance between pro-and anti-coagulant molecules allow addressing haemophilia treatment under a new angle with new therapeutic and laboratory tools.

Nevertheless, substitutive prophylaxis with concentrates of FVIII or factor IX (FIX) remains the gold standard for severe haemophilia management. The recent development and availability of clotting factor products with extended half-life (EHL) facilitate adherence, improve considerably the patients' quality of life, and simplify the management of breakthrough bleedings or surgery. These molecules have also brought to the limelight the concepts of optimization and personalization of anti-haemophilic prophylaxis. Previously, prophylaxis regimens were based on some historical protocols that were often very burdensome and expensive, for instance the Malmö protocol, or that did not avoid completely the appearance of joint damage, for instance the Canadian and Dutch protocols. Pharmacokinetics (PK) is one of the tools that can help haematologists to objectively and specifically adapt the prophylaxis regimen to each individual patient's specific needs. In the last 10 years, haematologists have become progressively more interested in this tool, as demonstrated by the increase in the number of publications concerning PK studies of antihaemophilic factors (PubMed data): about 1/year in the 1980s, 30/year in the 2010s, and 50 only in 2019! These PK studies are the mirror of the innovations that allowed producing improved recombinant products. Indeed, their development led to a considerable increase in the availability of more or less complex PK data. Consequently, many PK parameters, which were not part of the haematologists' habitual vocabulary, are now routinely used to describe and compare the features of the different anti-haemophilic products and also to personalize their administration. Indeed, for many years, haemophilia specialists have been using some simple PK parameters, such as recovery and residual level. However, recently, they have been confronted with many new PK parameters they were not familiar with, but that can be used to improve patient management. Due to the accumulation of PK data and their relative complexity, it is now necessary to analyse the relevance and limits of the different PK parameters relative to haemophilia specificities to better use them.

What is pharmacokinetics?

Pharmacokinetics is the study of the fate of a drug in the organism after its administration. This is the result of four processes: absorption, distribution, metabolism, and excretion (ADME). PK can be defined as the study of the time course of the drug concentration in plasma or serum. In the clinic, this knowledge is important for the effective and safe therapeutic management of a drug in each individual patient. Therapeutic drug monitoring is defined as the measurement of the drug concentrations in plasma or serum over time, and their interpretation to develop safe and effective drug regimens. This approach allows achieving therapeutic drug concentrations more rapidly and safely than by using empiric dose changes, and is recommended for drugs with large PK variability.

PK is a non-linear time process resulting from the increasing and decreasing phase of drug concentrations. Therefore, the drug concentration at a single time-point should not be considered. The drug concentration variations over time can be summarized using different PK parameters that are classified in two categories. The first category represents the basic or 'fundamental' PK parameters that describe the major steps of a drug in the organism (ADME).

For absorption, the absorption rate constant (ka) and bioavailability (F) are the most commonly used parameters. The drug distribution is described by the volume of distribution (Vd), whereas the drug elimination (metabolism and excretion) is defined by the elimination rate constant (ke), clearance (Cl), and half-life (t½). The estimation of these parameters requires a full PK analysis with a large number of samples. The second category corresponds to the parameters used in specific situations, for instance for therapeutic drug monitoring. These parameters should be easier to estimate and they need to be correlated with clinical events. The most used PK parameters in this category are the maximum concentration (Cmax) and the trough concentration (Ctrough). In special situations, more complex parameters can be used, such as the area under the curve (AUC), for instance for immunosuppressive agents, or the time spent above a threshold, for anti-haemophilic or antimicrobial agents (Figure 1) [START_REF] Dargaud | Individualized PK-based prophylaxis in severe haemophilia[END_REF].

Which parameters for which use?

The existence of different parameters to describe the same phenomenon brings some additional complexity. For example, the elimination of a drug can be evaluated with the half-life and also the clearance, the time above a threshold, or the mean residence time in the organism. It is essential to understand that some PK parameters are useful to describe the pharmacological characteristics of a new drug, whereas others are more suitable for tailoring the drug regimen.

Here, we will discuss the PK specificity of drugs used for haemophilia treatment.

PK parameters for regulatory studies

During the development of a new recombinant FVIII (rFVIII) product, its PK characteristics must be assessed in a bioequivalence study that typically has a crossover design and should include at least 12 patients. This is the simplest method to assess the therapeutic equivalence between medicinal products [START_REF]Comittee for medical products for human use, EMA, Guideline on the investigation of bioequivalence[END_REF][START_REF]Food and Drug Administration, Draft Guidance for Industry on Bioavailability and Bioequivalence Studies Submitted in NDAs or INDs--General Considerations[END_REF]. Briefly, bioequivalence is the comparison of the bioavailability of two drugs. As indicated by the U.S. Food and Drug Administration (FDA) guidelines, bioavailability is the extent and rate to which the active drug ingredient or active moiety from the drug product is absorbed and becomes available at the site of drug action [START_REF] Chow | Bioavailability and Bioequivalence in Drug Development[END_REF].

Therefore, in bioequivalence studies, AUC and Cmax are the key parameters for bioequivalence determination. The extent of the product bioavailability is estimated by quantifying the AUC of the blood concentration in function of time. The absorption rate is estimated by quantifying the maximum observed drug concentration (i.e. Cmax). However, according to the European Pharmacopoeia monograph for human clotting FVIII, the most important surrogate endpoints to assess the efficacy of a new FVIII product are AUC, incremental recovery, half-life, and clearance [START_REF]Comittee for medical products for human use, EMA, Guideline on the clinical investigation of recombinant and human plasma-derived factor VIII products[END_REF]. Incremental recovery is another way to explain the absorption rate. For additional information, the mean residence time also can be estimated. These PK parameters should be assessed using a non-compartmental analysis based on samples taken before the injection of 25-50 IU/kg of the FVIII product (baseline), and then at 10-15 minutes, 30 minutes, and 1, 3, 6, 9, 24, 28, and 32 hours after infusion completion. A sample at 48 hours may be collected if the patient received at least 50 IU/kg of drug [START_REF]Comittee for medical products for human use, EMA, Guideline on the clinical investigation of recombinant and human plasma-derived factor VIII products[END_REF]. Depending on the FVIII product type (e.g. EHL factor), the sampling time-points may be adjusted to cover the main parts of the activity time profile. FVIII activity must be measured using a chromogenic assay. For children younger than 12 years of age, PK sampling time-points can be reduced to baseline, and 1, 10, 24, and 48 hours after infusion completion [START_REF]Comittee for medical products for human use, EMA, Guideline on the clinical investigation of recombinant and human plasma-derived factor VIII products[END_REF]. For EHL factors further sampling time-points might be necessary. PK parameters should be calculated using model-independent analysis. AUC is frequently estimated using the linear trapezoidal rule. Tmax is the time required to reach the maximum concentration. The statistical method for testing bioequivalence is based on the 90% confidence interval (CI) of the test/reference ratio of the parameters under consideration using ANOVA. Data should be log transformed before analysis. This method is equivalent to the twoone-sided test with the null hypothesis of bioinequivalence at the 5% significance level. Two drugs are considered bioequivalent when the 90% CI for the PK parameter ratio ranges between 0.80 (80%) and 1.25 (125%) (Figure 2) [START_REF]Comittee for medical products for human use, EMA, Guideline on the investigation of bioequivalence[END_REF].

PK parameters for personalized dosing regimens

Historically, coagulation factor concentrate regimens are based on the notion that the PK characteristics of FVIII/FIX products are roughly similar in all patients. This theoretical model is not validated by clinical observations. Bjorkman et al were the first to highlight the huge inter-individual variability (2-4 times) concerning recovery and half-life [10,[START_REF] Björkman | Pharmacokinetics and dose requirements of factor VIII over the age range 3-74 years: a population analysis based on 50 patients with long-term prophylactic treatment for haemophilia A[END_REF]. PK data can help clinicians to personalize anti-haemophilic treatments particularly in two situations: surgery and prophylaxis.

Surgery

Patients with haemophilia undergoing surgery require one or several boluses or continuous infusion to reach and maintain a clinically efficient target level of circulating FVIII/FIX. The dose required is empirically calculated using the following formula: weight (kg) × desired factor level (%) × 0.5.

The target factor level is defined by the surgery type. However, the individual response may vary among patients. Therefore, the factor concentrate dosage should be personalized based on repeated measurements of the plasma clotting factor concentrate activity. In the 'classic' PK approach, the parameter used to reach a target concentration is the volume of distribution. This is defined as the theoretical volume (L) that would be necessary to contain the amount of administered drug at the same concentration as measured in the blood plasma. The volume of distribution is given by the following formula: amount of a drug/maximum observed drug concentration. In haemophilia, Incremental in Vivo Recovery (IVR) is a specific PK parameter used to tailor replacement therapy [START_REF] Prowse | In vivo recovery of factor VIII following transfusion, a survey of recent data and publications to assess the influence of standards used for potency assignment. On behalf of the Subcommittee on Factor VIII and IX of the Scientific and Standardization Committee of the ISTH[END_REF]. IVR gives a direct measure of the rise in coagulation activity in the plasma after administration of the dose (IU/dL/IU/kg). This parameter is defined as the ratio between the post-infusion peak (IU/dL) and the administered dose (IU/kg). It is easy to demonstrate that IVR is the inverse of the volume of distribution using different unities. However, it is not easy to predict the time to reach the maximum concentration (peak). Some protocols recommend using the extrapolated concentration based on three samples at 15, 30 and 60 minutes after infusion, or using only one sample at time 0. One of the limits of calculating dosages using IVR concerns patients with obesity. IVR takes into account the body weight but not the volume of distribution, although this does not change linearly with the patient weight [START_REF] Feldschuh | Prediction of the normal blood volume. Relation of blood volume to body habitus[END_REF]. Consequently, not adapted dosages (often in excess) are prescribed. More recently, Hazendonk et al proposed a Bayesian iterative approach to personalize the amount of drug administered during surgery based on a population PK model [START_REF] Hazendonk | OPTI-CLOT" study group. A population pharmacokinetic model for perioperative dosing of factor VIII in hemophilia A patients[END_REF].

Prophylaxis

Prophylaxis is considered the gold standard to prevent major bleeding episodes and joint damage in patients with severe haemophilia. A recent comparative study demonstrated a dose reduction by 7.2% and increasing dosing intervals for patients with personalized prophylaxis [START_REF] Lissitchkov | PK-guided personalized prophylaxis with Nuwiq(®) (human-cl rhFVIII) in adults with severe haemophilia A[END_REF]. The objective of dose tailoring is to maintain a FVIII/FIX level to avoid bleeding events using the minimum FVIII/FIX dose and the longest possible dosing interval. The key element of PK-based tailoring is the large inter-and intra-individual variability associated with all FVIII/FIX products (whatever the biotechnology). This PK variability is partly explained by age, body weight, blood group, von Willebrand factor (VWF) level, and assay method. Like for on-demand treatment (for surgery), prophylaxis uses specific PK parameters. The most important determinant of prophylaxis efficacy is the time spent below the threshold of 1%.

Collins et al demonstrated that this time is correlated with the rate of breakthrough bleeds and haemarthrosis [START_REF] Collins | Break-through bleed-ing in relation to predicted factor VIII levels in patients receiving prophylactic treatment for severe hemophilia A[END_REF]. The time above the 1% threshold (TAT1%) is relatively complex to estimate. It is the combination of the administered dose, which is known, and the half-life of the drug for a specific patient, which must be estimated using a PK analysis. This requires the collection of at least five or six blood samples for two or three days after the dose administration, which is a real challenge. Therefore, population PK analysis using a Bayesian approach has been proposed as an alternative approach to estimate complex PK parameters using only two or three samples [START_REF] Björkman | Population pharmacokinetics of recombinant factor VIII: the relationships of pharmacokinetics to age and body weight[END_REF][START_REF] Delavenne | Dose tailoring of human cell line-derived recombinant factor VIII simoctocog alfa: Using a limited sampling strategy in patients with severe haemophilia A[END_REF]. TAT1% is not the only determinant of prophylaxis effectiveness. Many other trough levels have been proposed. For example, Valentino et al demonstrated that longer times spent with FVIII level below 20% provide longer protection from bleeding [START_REF] Valentino | Association of peak factor VIII levels and area under the curve with bleeding in patients with haemophilia A on every third day pharmacokinetic-guided prophylaxis[END_REF]. They also showed that the peak FVIII activity and AUC could be interesting PK parameters. Adequate peak FVIII levels help to reduce the bleeding risk related to repetitive physical activity, and the AUC has been related to a lower risk of subclinical bleeding events.

Some considerations for the estimation of PK parameters

Regulatory bioequivalence studies only allow the direct comparison between FVIII/FIX products. Indirect comparisons are much more difficult to perform because many factors can influence the evaluation of PK parameters. A non-exhaustive list of the most important factors is presented in Table 1 & 2 and also their effect on the estimation of the PK parameters, particularly the time above a threshold value. The evaluation of the TAT1% is an essential element to determine the interval between FVIII administrations. This parameter depends on the administered dose and half-life in the patient. As the dose is predetermined, only the halflife must be estimated. The drug half-life is a hybrid parameter that depends on two basic PK parameters (clearance and volume of distribution) and that is difficult to estimate with precision because it is influenced by many factors.

Limit of quantification

The half-life is probably the PK parameter most influenced by the quantification methods, and particularly by the limit of quantification (LOQ) of the used technology. Toutain et al demonstrated in a theoretical example that the estimated half-life of a given drug increases by a factor of 10 when using a LOQ of 1 or 0.1, respectively (Figure 3) [START_REF] Toutain | Plasma terminal half-life[END_REF]. The continuous improvement of quantification methods allows decreasing the LOQ, and this influences the half-life. In the most recent studies, the LOQ has decreased from 1% to 0.5% and consequently, the estimated half-life has become progressively longer [START_REF] Powell | Safety and prolonged activity of recombinant factor VIII Fc fusion protein in hemophilia A patients[END_REF][START_REF] Powell | Phase 3 study of recombinant factor IX Fc fusion protein in hemophilia B[END_REF]. It is now time to question the clinical relevance of these longer half-life values calculated using methods with a LOQ smaller than 1%.

Missing data treatment

Another important factor in the estimation of PK parameters is the handling of missing data, particularly FVIII/FIX activity data below the LOQ. Data below the LOQ are frequent in PK studies and represent an issue for the estimation of PK parameters. Several approaches have been developed to handle this problem. The simplest one is to integrate a null value for these situations. Other methods consist in imputing the missing values using a fixed value, for instance half of the LOQ value (LOQ/2). It has been demonstrated that these methods are biased [START_REF] Samson | Extension of the SAEM algorithm to left-censored data in nonlinear mixed-effects model: application to HIV dynamics model[END_REF]. Specifically, Tiede et al compared the PK of N8-GP (turoctocog, Espereoct®) and of a standard rFVIII product [START_REF] Tiede | Enhancing the pharmacokinetic properties of recombinant factor VIII: first-in-human trial of glycoPEGylated recombinant factor VIII in patients with hemophilia A[END_REF]. In this study the TAT1% for 50 IU/kg of N8-GP was 6.53 days, a much higher value than that of other EHL products (Table 1). This overestimation might be explained by the use of a biased method for imputing missing data. Indeed, the first missing value was replaced by the LOQ/2 and the next one by 0. Currently, many statistical methods are available to input missing values during population PK analyses. Likelihood-based methods reduce the bias in the estimation of PK parameters and should be used [START_REF] Samson | Extension of the SAEM algorithm to left-censored data in nonlinear mixed-effects model: application to HIV dynamics model[END_REF].

Sampling

The sampling design also is important for estimating the PK parameters. The crucial question is how many samples should be collected to obtain robust half-life estimations. The minimum is three samples in the final slope of decrease (i.e. three times the half-life). The uncertainty of measurement also must be taken into account, particularly because the measured values are close to the LOQ (i.e. the value for which the uncertainty is 20%). Therefore, for comparing two products, the sampling design must be identical in the two arms of a crossover study. Yet, this is not always verified (Figure 4) [START_REF] Powell | Safety and prolonged activity of recombinant factor VIII Fc fusion protein in hemophilia A patients[END_REF][START_REF] Powell | Phase 3 study of recombinant factor IX Fc fusion protein in hemophilia B[END_REF].

Methods of quantification

FVIII activity can be quantified using different methods. Chromogenic and chronometric (onestage) methods are the most commonly used in laboratories. For PK studies, it is better to use the same quantification method to titrate the FVIII/FIX vials and also to measure FVIII/IX activity in plasma. The chromogenic method is recommended for FVIII and the chronometric method for FIX. However, the two techniques are not always available in the same laboratory.

Although these methods are well correlated, there are important differences that influence the estimation of PK parameters. Therefore, it is essential to know and to consider these elements in a PK analysis. For example, for the chronometric method, the activated partial thromboplastin time (aPTT) reagent, type of activator, and calibration range significantly affect the results. Moreover, the FVIII:C levels obtained with chronometric methods tend to be 15-20% lower compared with chromogenic methods [START_REF] Potgieter | One-stage vs. chromogenic assays in haemophilia A[END_REF]. Therefore, the IVR tends to be higher with the chromogenic method. The overestimation of low FVIII concentrations by the chronometric methods leads to an overestimation of the half-life. The uncertainty of measurement (accuracy, precision) also seems more important with the chronometric method [START_REF] Viuff | International comparative field study of N8 evaluating factor VIII assay performance[END_REF].

Population

Some of the factors that influence the PK variability of FVIII/FIX products are known. For example, patient's age, body weight, VWF level, and blood group significantly influence the PK of FVIII. Conversely, FIX PK is mainly influenced by the patient's body weight. Therefore, the indirect comparisons of PK parameters are possible only when populations are comparable.

Ideally, PK parameters should be compared in population sub-groups. As age and body weight explain most of the PK variability and are well correlated, a presentation in age sub-groups is relevant (<6 years, 6<12, >12 years). Indeed, for the same product, differences are important in these age sub-groups [START_REF] Delavenne | Dose tailoring of human cell line-derived recombinant factor VIII simoctocog alfa: Using a limited sampling strategy in patients with severe haemophilia A[END_REF].

Statistical analysis

There are two common strategies to estimate the PK parameters: the non-compartmental approach and the modelling or compartmental approach.

Non-compartmental approaches are recommended for PK parameter estimation in regulatory bioequivalence studies. It is a model-independent approach that uses minimal assumptions about the temporal kinetics of the drug concentration in the body. Non-compartmental analyses are fast and cost-efficient, especially compared with the more complex compartmental analyses (population PK analyses). The drawback is that a more structured sampling design and some approximations are necessary. For example, the design recommended by the Committee for Medicinal Products for Human Use of the European Medicines Agency (EMA) for bioequivalence studies requires more than ten samples taken during 48 hours for adults, and five samples for children [START_REF]Comittee for medical products for human use, EMA, Guideline on the clinical investigation of recombinant and human plasma-derived factor VIII products[END_REF]. The non-compartmental analysis approach is limited by all parameters listed in 3.1 to 3.6, and indirect comparisons should be avoided. This approach is also difficult to apply for dose tailoring in clinical practice, and population PK analysis should be preferred [START_REF] Iorio | Estimating and interpreting the pharmacokinetic profiles of individual patients with hemophilia A or B using a population pharmacokinetic approach: communication from the SSC of the ISTH[END_REF]. Population PK analysis can appear complex, but it is a well-established, quantitative method to quantify and explain drug variability (Figure 5). Drug concentrations can vary among individuals with the same dosing regimen. Population PK analyses are generally based on the use of non-linear mixed-effects models. This modelling technique can separate data variability to identify fixed effects (describing the concentration-time profile of a typical individual) and random effects (the variability between individuals or occasions as well as measurement errors). Population PK analysis is a powerful approach to estimate PK parameters even when sampling time-points are sparse (few observations per subject) and can take into account and handle data below the LOQ. It can quantitatively attribute variability to patient (i.e. age, weight, blood group, …) or extrinsic factors (assay method) and take into account the different quantification methods and their analytical performance. Moreover, Monte Carlo simulation studies can be developed to calculate the probability of achieving the desired target exposures with different dosing regimens or in different populations (using covariates). This approach is also less influenced by the parameters mentioned in 3.1 to 3.6 because they can be integrated in the model. Moreover, modelling and simulation actually play a large role in personalized medicine. This approach is now widely used in haemophilia for prophylaxis and surgery to estimate the TAT, half-life, and IVR for different recombinant FVIII products. Thanks to the Bayesian approach, an individual PK estimation and simulation are possible when only two or three samples are available [START_REF] Valentino | Association of peak factor VIII levels and area under the curve with bleeding in patients with haemophilia A on every third day pharmacokinetic-guided prophylaxis[END_REF][START_REF] Toutain | Plasma terminal half-life[END_REF]. There are several freely available Bayesian PK softwares which are currently used by hematologists and very helpful for developing the approach of personalized prophyalxis. Their principal characteristics are presented in Table 3.

Some considerations on extended half-life products

Recently, a holistic approach has been proposed to define EHL rFVIII products. An EHL product should meet three criteria: (i) fabricated using a technology designed to extend its halflife; (ii) lacking bioequivalence with a standard rFVIII comparator above the FDA/EMA cutoff of 125% for the 90% CI for the test/reference AUC ratio; and (iii) having an extended halflife ratio measured in a PK comparator crossover study [START_REF] Mahlangu | Defining extended half-life rFVIII-A critical review of the evidence[END_REF].

In this definition, it is not clear what 'a technology designed to extend half-life' (first criterion) really means. This could be a modification of the active moiety, a modification of the formulation, or a new route of administration, Nevertheless, EHL products should have a longer half-life, whatever the technology.

The second criterion concerns the evaluation of the PK parameters in a bioequivalence study.

By definition, and as discussed in paragraph 2.1, a bioequivalence study is not performed to demonstrate a biodifference. Indeed, some statistical considerations must be taken into account.

For example, a study with low statistical power (i.e. small sample size, Figure 2E) can conclude that there is no bioequivalence because the CI of the ratio is large, although the values of the tested PK parameters (AUC or Cmax) are identical or only slightly increased (clinically not relevant) (Figure 2). The opposite situation also can occur. Indeed, the ratio can be increased, but the CI is low (Figure 2B). This does not allow concluding about the absence of bioequivalence. Moreover, the AUC, a major criterion for bioequivalence evaluation, is not the most relevant for dose tailoring in haemophilia. It must be understood that theoretically, the AUC can be modified without any change in the terminal half-life of a drug. Therefore, it would be more relevant to use PK parameters that have shown a correlation with the clinical events, such as TAT1% and half-life.

The third criterion is the most important in clinical practice. To be recognized as EHL product, the half-life must be increased by 30%. The scientific basis of this value is debatable. Indeed, a clinically 'significant' half-life increase can be below this 30% threshold. For example, if octocog alfa is considered the reference product with its TAT1% of about 3 days for a dose of 50 IU/kg, then a product with a TAT1% of 4 days will correspond to a half-life increase of 25% for the same dose. Therefore, the threshold of 30% does not seem to be justified by a clinical benefit [START_REF] Hermans | Pharmacokinetic modelling and validation of the half-life extension needed to reduce the burden of infusions compared with standard factor VIII[END_REF]. FIX concentrates with a half-life increase by four or five times undeniably bring a clinical benefit. Conversely, the clinical benefit of FVIII concentrates for which the half-life gain is more modest (between 1.2 and 1.6 times) is less important. Indeed, in the clinical phase III studies on EHL rFVIII, only 1/3 of patients could switch to prophylaxis twice per week, whereas the others had shorter injection intervals [START_REF] Mahlangu | Defining extended half-life rFVIII-A critical review of the evidence[END_REF]. To justify the inclusion of a threshold for EHL definition, a criterion directly linked to the clinical benefit could be chosen rather than a percentage of increase. As already suggested by Mahlangu et al and Hermans et al [START_REF] Mahlangu | Defining extended half-life rFVIII-A critical review of the evidence[END_REF][START_REF] Hermans | Pharmacokinetic modelling and validation of the half-life extension needed to reduce the burden of infusions compared with standard factor VIII[END_REF], a EHL product could be defined as a product that allow increasing the interval between injections of at least one additional day relative to the reference treatment (e.g. from a prophylaxis every other day or four times per week to two injections per week). This would represent a real benefit with a yearly reduction of 52-104 injections for each patient. On the other hand, a hypothetical EHL product with a half-life increased by 30% (i.e. 1.2 to 1.3 times longer) might not necessarily lead, in most patients, to a reduction by 50% of the injections. Moreover, FVIII products with a lower half-life extension ratio (e.g. <1.3) will not provide the same level of coverage with reduced dosing frequency in most patients.

Discussion

An enormous quantity of PK data on anti-haemophilic factors is now available. This knowledge is needed to determine the pharmacological properties of these products, but they can also be a source of complications and confusion. It is crucial to distinguish the situations in which PK studies are performed. In regulatory studies, the methodology of which is precisely defined by different bodies (ISTH, FDA, EMA), the objective is to characterize the PK of a new compound by comparing it with the reference product in a bioequivalence study [START_REF]Comittee for medical products for human use, EMA, Guideline on the investigation of bioequivalence[END_REF][START_REF]Food and Drug Administration, Draft Guidance for Industry on Bioavailability and Bioequivalence Studies Submitted in NDAs or INDs--General Considerations[END_REF][START_REF]Comittee for medical products for human use, EMA, Guideline on the clinical investigation of recombinant and human plasma-derived factor VIII products[END_REF][START_REF] Lee | of the International Society for Thrombosis and Haemostasis. Scientific and Standardization Committee Communication. The Design and Analysis of Pharmacokinetic Studies of Coagulation Factors[END_REF]. Historically, bioequivalence studies were needed to ensure the therapeutic equivalence of recombinant and plasma-derived factors. The improvement of some PK properties, particularly the half-life, leads to question the use of bioequivalence studies not due to their design, but due to their statistical approaches and the choice of PK criteria (AUC, Cmax). It should be important to discuss this issue within the ISTH FVIII-FIX sub-committee and to modify the methodology to better adapt it to the challenges of the new EHL products.

On the other hand, in PK studies carried out to personalize treatment with an anti-haemophilic factor, the objective is not to characterize all PK parameters, but to precisely estimate the parameters that are best correlated with clinical bleeding events and that can be used to improve the patient management (i.e. the parameters that have shown a dose/concentration/clinical event correlation). In this case, according to the clinical context (surgery or prophylaxis), the incremental in vivo recovery and the time spent above a predefined FVIII threshold (possibly the half-life) seem to be the most relevant. Unlike regulatory studies, the methodology to estimate these parameters has not been defined. Here, we showed that many factors can influence the analysis of the PK parameters of interest and also bias the result interpretation.

Therefore, the PK parameters of products estimated using different methods must be interpreted with caution. This is particularly true when the time-points and the number of blood samples, the quantification method, and the LOQ, and finally the statistical analysis are different. This was recently illustrated by Carcao et al who compared the PK profiles of rFVIII-Fc (efmoroctocog alfa, Eloctate®/Elocta®) and BAX 855 (rurioctocog alfa pegol, Adynovate®/Adynovi®) in the same boys [START_REF] Carcao | Comparative pharmacokinetics of two extended half-life FVIII concentrates (Eloctate and Adynovate) in adolescents with hemophilia A: Is there a difference?[END_REF]. Using the same sampling time-points, FVIII measurement methods and statistical approach, the authors found that the PK parameters for rFVIII-Fc and BAX 855 are almost identical. Conversely, a previous study that compared the PK profiles of these EHL FVIIIs and of the standard half-life FVIII product in adolescents/adults reported mean half-lives of 19 hours and 14 hours for rFVIII-Fc and BAX 855, respectively [START_REF] Mahlangu | Phase 3 study of recombinant factor VIII Fc fusion protein in severe hemophilia A[END_REF][START_REF] Konkle | Pegylated, full-length, recombinant factor VIII for prophylactic and on-demand treatment of severe hemophilia A[END_REF]. In another study, Shah et al [START_REF] Shah | Direct comparison of two extended-half-life recombinant FVIII products: a randomized, crossover pharmacokinetic study in patients with severe hemophilia A[END_REF] directly compared rFVIII-Fc and BAY 94-9027 (damoctocog alfa pegol, Jivi®) using a population approach with the same sampling design, and found that the TAT1% for 60 IU/kg of rFVIII-Fc was lower than that determined by Solms et al and Coyle et al (4.87 hours versus 5.5 and 5.3 hours, respectively) [START_REF] Solms | Favorable Pharmacokinetic Characteristics of Extended-Half-Life Recombinant Factor VIII BAY 94-9027 Enable Robust Individual Profiling Using a Population Pharmacokinetic Approach[END_REF][START_REF] Coyle | Phase I study of BAY 94-9027, a PEGylated B-domain-deleted recombinant factor VIII with an extended half-life, in subjects with hemophilia A[END_REF].

Similarly, Escuriola-Ettinghausen et al. carried out a study in patients with haemophilia B to directly compare two EHL FIX products, N9-GP (nonacog beta pegol, Refixia®) and recombinant FIX-Fc fusion protein (eftrenonacog alfa, Alprolix®) [START_REF] Escuriola Ettingshausen | Favorable pharmacokinetics in hemophilia B for nonacog beta pegol versus recombinant factor IX-Fc fusion protein: A randomized trial[END_REF]. They obtained better PK profiles for N9-GP than rFIX-Fc, when similar sampling time-points and LOQ were used.

Conversely, the PK study was initially performed over 168 hours for N9-GP and 240 hours for rFIX-Fc. Surprisingly, the reference molecule nonacog alpha (Benefix®) had a half-life of 33.8 hours in the study on rFIX-Fc with sampling up to 240 hours, and of 19.34 hours in the study on N9-GP with sampling limited to 168 hours [START_REF] Iorio | Tailoring treatment of haemophilia B: accounting for the distribution and clearance of standard and extended half-life FIX concentrates[END_REF].

These results demonstrate the importance of the analytical method, statistical analysis and study design to estimate PK parameters. Well-designed comparative PK studies may help physicians to better manage switching between concentrates. Nevertheless, one should not forget that inter-individual variability is large, although population PK data can provide haemophilia clinicians with a more accurate prediction of the dosing regimen for their patients.

In patients on prophylaxis, a FVIII level of 1 IU/dL is often recommended as the minimum trough level. However, in some patients, targeting FVIII levels above 1 IU/dL is not sufficient to prevent bleeding. Clearance is an additional PK parameter with high clinical impact, but less frequently mentioned by haematologists when discussing personalized prophylaxis regimens.

After testing different prophylaxis regimens using the same total factor consumption, Berntorp et al [START_REF] Berntorp | Dosing regimens, FVIII levels and estimated haemostatic protection with special focus on rFVIIIFc[END_REF] showed that the lower clearance of rFVIII-Fc compared with conventional rFVIII might increase rFVIII-Fc potential of bleed prevention and reduce injection frequency for similar factor consumption.

Several improved therapeutic agents have recently arrived on the market, and haemophilia management is undergoing significant changes. A personalized choice of products and prophylaxis regimens (dose and intervals) is necessary to provide optimal therapy tailored to each patient's response to these agents and to their individual characteristics, such as bleeding phenotype, physical activity level, and joint status. Haematologists need to carefully choose the optimal treatment among these new products. PK parameters may help physicians to better understand the differences, risks and benefits of these new agents.

Like for regulatory studies, it should be useful to standardize the PK studies for parameter harmonization and better comparison. In 2018, Ragni et al published, on behalf of the ISTH FVIII/FIX sub-committee, the recommendations for switching from a standard factor concentrate to EHL products [START_REF] Ragni | Subcommittee on Factor VIII, Factor IX, and Rare Bleeding Disorders. Pharmacokinetics and the transition to extended halflife factor concentrates: communication from the SSC of the ISTH[END_REF]. We stress the need for a more precise definition of the PK methodology by the learned societies. This should include optimal sampling design, limiting the method LOQ to 1%, the use of a statistical method for inputting values below the LOQ, and especially the use of non-linear mixed effects models that have many advantages for assessing the PK parameters and facilitate comparing different studies. Note for figures: I would add a legend to each figure because figure should "stand alone" in a text. nr: not reported

Figure 1 :Figure 3 . 29 Figure 4 .Figure 5 .

 132945 Figure 1: Main pharmacokinetic parameters

Table 1 :

 1 Influence of different parameters on the estimation of the time above the threshold of 1% in adult patients with haemophilia

			TAT1%	Last
	Dosage (IU/kg)	Clotting factor	(med, or mean,	sampling time-	LOQ	Assay method	Reference
			day)	point
	20	rFVIII single-chain (Afstyla®)	4.3	96 h	1%	chromogenic	Zhang et al., 2017 [41]
		rFVIII-Fc (Eloctate®/Elocta®)	~ 4.5	240 h	0.5%	OS	Powell et al., 2012 [22]
		BAY 94-9027 (Jivi®)	~ 4.5	168 h	3%	chromogenic	Coyle et al., 2014 [36]
		BAY 94-9027 (Jivi®)	4.4	168 h	1.5% chromogenic Solms A [35]
	25	rFVIII (Advate®)	< 3	96 h	1%	OS	Powell et al., 2012 [22]
		rFVIII (Advate®)	2.6	48 h	1%	chromogenic	Shah et al., 2017 [42]
		BAY 81-8973 (Kovaltry®)	3.4	48 h	1%	chromogenic	Shah et al., 2017 [42]
		N8-GP (Esperoct®)	3.9	168 h	1%	chromogenic	Tiede et al., 2013 [25]
		BAY 94-9027 (Jivi®)	5.1	168 h	1.5% chromogenic	Solms 2019 [35]
		rFVIII-Fc (Elocta®)	4.9	72 h	0.5%	OS	Mahlangu et al., 2014 [32]
		rFVIII-Fc (Elocta®)	4.8	72 h	1%	chromogenic	Carcao,et al 2019 [31]
		rFVIII single-chain (Afstyla®)	5.1	96 h	1%	chromogenic	Zhang et al., 2017 [41]
	50	rFVIII (Advate®)	3.3	72 h	0.5%	OS	Mahlangu et al., 2014 [32]
		rFVIII (Advate®)	3.1	48 h	1%	chromogenic	Shah et al., 2017 [42]
		BAY 81-8973 (Kovaltry®)	3.9	48 h	1%	chromogenic	Shah et al., 2017 [42]
		rFVIII (Kogenate)	3.8	48 h	1%	chromogenic	Solms et al 2020 [43]

Table 2 :

 2 Influence of different parameters on the estimation of the time above the threshold of 1% in adult patients with haemophilia

	Dosage (IU/kg)	Clotting factor	TAT (med, or mean, day)	Last sampling time-point	LOQ	Assay method	Reference
	25	rFIXFc Alprolix®	1%, 7.34 d 3%, 3.81 d	240 h	1%	OS	Shapiro et al, 2012 [44]
	25	rIX-FP Idelvion®	1%, 16 d 3%, 10 d 5%, 7 d	336 h	nr	OS	Zhang et al 2016 [45]
	40	N9 GP Refixia	5%, 7d	168 h	nr	OS	Tiede et al 2017 [46]
	40	rIX-FP Idelvion®	1%, 20.5 d 3%, 13.5 d 5%, 10.5 d	336 h	nr	OS	Zhang et al 2016 [45]
	50	rIX-FP Idelvion®	5%, 14d	336 h	nr	OS	Santagostino et al. 2019 [47]
	50	rFIX Benefix®	5%, 2 d	336 h	nr	OS	Santagostino et al. 2019 [47]
	50	N9 GP Refixia®	1%, 22.5 d 3%, 16.2 d	168	nr	OS	Negrier C et al, 2011 [48]
	50	rFIXFc Alprolix®	1%, 10.1 d 3%, 6.28 d	240 h	1%	OS	Shapiro et al, 2012 [44]
	50	rFIX Benefix®	1%, 5.1 d 3%, 2.8 d	96 h	nr	OS	Powel et al 2013, [49]
	50	rFIXFc Alprolix®	1%, 11.2 d 3%, 5.8 d	96 h	nr	OS	Powel et 2013, [49]
	50	rIX-FP Idelvion®	1%, 23d 3%, 15.5d 5%, 12.5d	336 h	nr	OS	Zhang et al 2016 [45]
	75	rIX-FP Idelvion®	1%, 27.5 d 3%, 19.5d 5%, 16d	336 h	nr	OS	Zhang et al 2016 [45]
	100	rFIXFc Alprolix®	1%, 12.3 d 3%, 8.53 d	240 h	1%	OS	Shapiro et al, 2012 [44]

ACKNOWLEDGMENT

The authors thanks CSL Behring, for providing medical writing support, which is in accordance with Good Publication Practice (GPP3) guidelines (http://www.ismpp.org/gpp3).

CONFLICT OF INTEREST STATMENT

XD has received honoraria from Baxter, CSL Behring, Octapharma, Pfizer and Sobi.

YD has received grants/research support from Bayer, Baxter, Baxalta, Novo Nordisk, CSL Behring, LFB, Pfizer, LeoPharma, Octapharma and Stago; an educational grant from Takeda and honoraria from Bayer, Baxter, Novo Nordisk, CSL Behring, Sobi and Octapharma.


C Lebourgeois

D Delaugerre

M.-L Descamps

J Chaix

Ghosn

Benoit Visseaux

Stéphane Hué

Quentin Le Hingrat

Maud Salmona

Samuel Lebourgeois

Constance Delaugerre

Diane Descamps

Marie-Laure Chaix

Jade Ghosn

Phylogenetic investigation of HCV-4d epidemic in Paris MSM

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

The hepatitis C virus (HCV) epidemic has displayed several epidemiologic changes in the last decade in Europe with an increasing prevalence among men who have sex with men (MSM) infected with human immunodeficiency virus (HIV), from 0.42/100 person-years in 1991 to 1.34/100 in 2010 [START_REF] Hagan | Incidence of sexually transmitted hepatitis C virus infection in HIV-positive men who have sex with men[END_REF], but also among HIV-negative MSM, from 0.15/100 person-years to 1.2/100 person-years [START_REF] Yaphe | Incidence of acute hepatitis C virus infection among men who have sex with men with and without HIV infection: a systematic review[END_REF][START_REF] Cotte | Hepatitis C virus incidence in HIV-infected and in preexposure prophylaxis (PrEP)-using men having sex with men[END_REF]. The decreasing condoms use and ChemSex emergence including intravenous injections ("slam") and new biomedical prevention methods such as preexposure prophylaxis (PrEP) against HIV raise concerns about other sexually transmitted infections (STIs) in high-risk populations, including HCV [START_REF] Traeger | Effects of Pre-exposure Prophylaxis for the Prevention of Human Immunodeficiency Virus Infection on Sexual Risk Behavior in Men Who Have Sex With Men: A Systematic Review and Meta-analysis[END_REF]. HCV transmissions between HIVnegative and positive populations are increasingly reported [START_REF] Ramière | Patterns of HCV transmission in HIV-infected and HIV-negative men having sex with men[END_REF]. The use of new HCV directly acting agents (DAA), raising hope of an HCV eradication, is also associated with an increasing number reinfections in the absence of targeted interventions for at-risk behaviour populations [START_REF] Ingiliz | s HCV reinfection incidence among individuals treated for recent infection[END_REF].

The HCV global epidemiology has also been evolving since the last decades. HCV subtype 4, previously restricted to Central Africa and the Middle East, is now found in Western Europe at a low but increasing prevalence, estimated at 6% of HCV strains in early 2010's [START_REF] Gower | Global epidemiology and genotype distribution of the hepatitis C virus infection[END_REF]. An important outbreak of HCV subtype 4d, primarily associated with people who inject drugs, started in Paris in 2003 and illustrates these changes. This outbreak occurred between 2003 and 2007 among HIV-infected MSM without any traditional risk factor for HCV infection. The only factor associated with HCV acquisition at the time was highly at-risk sexual behaviour, including unprotected receptive anal intercourse with multiple casual partners, concomitant erosive STI (i.e. primary syphilis), group sex, fist-fucking, shared sex-toys, and use of recreational drugs [START_REF] Larsen | Gaining greater insight into HCV emergence in HIVinfected men who have sex with men: the HEPAIG Study[END_REF].

In this work, we performed a phylogenetic analysis of HCV strains from the French 2003-2007 outbreak to better understand the origin of this epidemic, its evolution and potential links with other countries.

Methods

Patients and sequences database

All partial NS5B gene (328 nucleotides) sequences from HIV-infected MSM diagnosed with HCV subtype 4d infection in Paris between 2003 and 2007 were included in this study (n=26) [START_REF] Larsen | Gaining greater insight into HCV emergence in HIVinfected men who have sex with men: the HEPAIG Study[END_REF]. All HCV-4d NS5B sequences available by the 30 th June of 2019 were retrieved from GenBank database (http://www.ncbi.nlm.nih.gov/genbank). We annotated all sequences with collection date and sampling location using data available in GenBank or related publications. Poor quality, clonal or iterative sequences were discarded resulting in a dataset of 530 sequences (184 from France, 68 from the Netherlands, 156 from other European countries, 107 from Africa, Middle-East or Turkey, 13 from Americas and 2 from Asia and India, cf. Supplementary table).

Phylogenetic analyses

Sequences were aligned using Clustal omega 1.2.4 and manually inspected in AliView 1.18.

The best fitting nucleotide substitution model was identified as GTR-G using ModelFinder implemented in IQ-Tree 1.6.1. A phylogenetic tree was inferred by maximum of likelihood reconstruction using IQ-Tree 1.6.1 with GTR-G model and ultrafast bootstrapping (1000 replicates). To check the potential clusters observed with French sequences, a lighter phylogenetic tree, only including sequences from the Northern countries, has also been inferred by Bayesian methods using MrBayes 3.2.7 with GTR-G model.

Results

The maximum likelihood phylogenetic reconstruction is shown in Figure 1. All but one of the 26 viruses from Paris during the 2003-2007 HCV outbreak formed a single monophyletic cluster, herein called cluster A. This cluster was strongly supported by maximum likelihood (branch support of 100%) and Bayesian (posterior probabilities of 100%) phylogenetic frameworks. It was also well separated from other HCV 4d strains with a genetic distance of 0.034 substitutions per nucleotide between the most recent common ancestor of cluster A and the previous node. Mean and maximal genetic distances within cluster A were 0.028 and 0.084 substitutions per nucleotide, respectively. Within cluster A, 73 other French sequences were also included. These sequences were sampled in Lyon from 2014 to 2017 (n=41) and Paris in 2016 (n=32), supporting the idea of a national outbreak rather than a localized one.

The cluster also included 28 sequences from the Netherlands sampled from 2001 to 2017 and interleaved in the whole cluster. Among all the French HCV 4d sequences, 54% are included in cluster A (98/184) and 41% of all Dutch sequences (28/68). Sequences from other countries were rare in cluster A: three sequences form United Kingdom, sampled

Discussion

The face of HCV infection amongst MSM is evolving quickly due to behaviour changes and new therapeutic strategies.

A few previous works have been conducted about the recent emergence of HCV-4d. A strong connection between Netherlands and Germany has already been observed as well as between Quebec and Europe [START_REF] Murphy | Molecular surveillance of hepatitis C virus genotypes identifies the emergence of a genotype 4d lineage among men in Quebec, 2001-2017[END_REF][START_REF] Vogel | Phylogenetic analysis of acute hepatitis C virus genotype 4 infections among human immunodeficiency virus-positive men who have sex with men in Germany[END_REF]. Our work highlights close links between the French and Netherlands MSM communities as emphasized by HCV transmission with several possible translocation events between these two countries within cluster A. The large representation of HCV 4d among French and Dutch sequences can be explained by local epidemics of this subtype but potentially also by sampling bias due the lack of systematic sequencing. As all HCV-4d sequences from Lyon have been sampled during the acute phase of the infection [START_REF] Ramière | Patterns of HCV transmission in HIV-infected and HIV-negative men having sex with men[END_REF],

we also evidence that this outbreak is still spreading a decade later and has reached Lyon, the second largest French city. Charre et al. also previously evidenced that it should have been transmitted to Lyon through HIV-negative MSM that have, later on, infected HIVpositive MSM, highlighting the new inter-relation between these two previously distinct population also observed in Netherlands [START_REF] Hoornenborg | MSM starting preexposure prophylaxis are at risk of hepatitis C virus infection[END_REF][START_REF] Charre | Hepatitis C virus spread from HIV-positive to HIVnegative men who have sex with men[END_REF]. This is in line with the recent French survey PREVAGAY, conducted in 2015 among MSM attending gay venues in 5 French metropolitan cities, were most HCV-positive patients with ongoing infections were infected with HCV-4d [START_REF] Vaux | Prevalence of hepatitis C infection, screening and associated factors among men who have sex with men attending gay venues: a crosssectional survey (PREVAGAY), France[END_REF]. The few sequences from United Kingdom, Italy and Germany included in cluster A suggest a low diffusion of this strain outside Netherlands and France. In our work, we also observed a tidy interconnection of all European sequences, strongly separated from Central Africa or Middle-East sequences, suggesting a pan-European network better explained by holiday resort of high-risk populations rather than global immigration.

As acute HCV infection is mostly asymptomatic, repeated screening, new screening approaches and behavioural interventions should be implemented in at-risk populations [14]. More systematic and standardized sequencing approaches, along with phylogenetic frameworks and epidemiological investigations, could allow contact tracing for targeted prevention and a deeper understanding of epidemiological shifts, as increasingly done worldwide for HIV surveillance. This is of peculiar importance as the globally decreasing HCV epidemic is increasingly driven by regular outbreaks in specific populations with international connections.

  between 2004 and 2007 (3 out of 93 English sequences), 3 from Italy sampled in 2014 and 2015 (3/14), and one from Germany (1/3) sampled in 2014. One sequence from the 2003 Paris outbreak was found in a second cluster, herein called cluster B. It is formed of 11 sequences, is strongly supported at 100% by both phylogenetic frameworks and well separated from other HCV 4d with a genetic distance of 0.036 substitutions per nucleotide between the ancestor of cluster B and the previous tree node. Mean and maximal genetic distances within cluster B were 0.026 and 0.049 substitutions per nucleotide, respectively. The Paris outbreak sequence, sampled in 2006, was the only French sequence in this cluster. Most of cluster B sequences were sampled in the United Kingdom from 2004 to 2014 (n=9). The last sequence of this cluster was sampled in Belgium in 2014.

14. Gras J, Mahjoub N, Charreau I, et al. Early diagnosis and risk factors of acute hepatitis c in high-risk men who have sex with men on pre-exposure prophylaxis. AIDS. 2019; .

Funding

This work was founded in part by the French ANRS (Agence Nationale de Recherche sur le SIDA et les hépatites virales).

Transparency declaration

Pr Descamps and Dr Ghosn report personal fees from ViiV Healthcare, personal fees from Gilead Science, personal fees from Janssen Cilag, personal fees from MSD, outside the submitted work. All the other authors have no conflict of interest to disclose.

Authors' contributions

JG, MLC, DD and CD conceived the study, provided expertise and contributed towards the review of the manuscript. BV and SH carried out data collection, analysis and initial drafting of the manuscript. QLH, SL and MS carried out data curation, assisted the analysis and critically reviewed the manuscript.