Pharmacometric Models for Individualisation of Warfarin in Adults and Children

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UNIVERSITATISACTA

Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Medicine 897

Pharmacometric Models for Individualisation of Warfarin in Adults and Children

ANNA-KARIN HAMBERG

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Dissertation presented at Uppsala University to be publicly examined in Auditorium Minus, Gustavianum, Akademigatan 3, Uppsala, Saturday, May 25, 2013 at 13:00 for the degree of Doctor of Philosophy (Faculty of Medicine). The examination will be conducted in English.

Abstract

Hamberg, A-K. 2013. Pharmacometric Models for Individualisation of Warfarin in Adults and Children. Acta Universitatis Upsaliensis. Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Medicine 897. 80 pp. Uppsala. ISBN 978-91-554-8653-2.

Warfarin is one of the most widely used anticoagulants. Therapy is complicated by warfarin’s narrow therapeutic range and pronounced variability in individual dose requirements. Although warfarin therapy is uncommon in children, it is crucial for children with certain congenital or acquired heart diseases. Treatment in children is especially difficult due to the lack of i) a decision support tool for efficient and consistent dose adjustments, and ii) a flexible warfarin formulation for accurate and reproducible dosing.

The overall aim of this thesis was to develop a PKPD-based pharmacometric model for warfarin that describes the dose-response relationship over time, and to identify important predictors that influence individual dose requirements both in adults and children. Special emphasis was placed on investigating the contribution of genetic factors to the observed variability.

A clinically useful pharmacometric model for warfarin has been developed using NONMEM.

The model has been successfully reformulated into a KPD-model that describes the relationship between warfarin dose and INR response, and that is applicable to both adults and children.

From a clinical perspective, this is a very important change since it allows the use of information on dose and INR that is available routinely. The model incorporates both patient and clinical characteristics, such as age, weight, CYP2C9 and VKORC1 genotype, and baseline and target INR, for the prediction of an individualised starting dose. It also enables the use of information from previous doses and INR observations to further individualise the dose a posteriori using a Bayesian forecasting method.

The NONMEM model has been transferred to a user-friendly, platform independent tool to aid use in clinical practice. The tool can be used for a priori and a posteriori individualisation of warfarin therapy in both adults and children. The tool should ensure consistent dose adjustment practices, and provide more efficient individualisation of warfarin dosing in all patients, irrespective of age, body weight, CYP2C9 or VKORC1 genotype, baseline or target INR. The expected outcome is improved warfarin therapy compared with empirical dosing, with patients achieving a therapeutic and stable INR faster and avoiding high INRs that increase the risk of bleeding.

Keywords: warfarin, pharmacokinetics, pharmacodynamics, pharmacometrics, pharmacogenetics, dose individualisation, children

Anna-Karin Hamberg, Uppsala University, Department of Medical Sciences, Clinical pharmacogenomics and osteoporosis, Akademiska sjukhuset, SE-751 85 Uppsala, Sweden.

ISBN 978-91-554-8653-2

urn:nbn:se:uu:diva-197599 (http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-197599)

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“Remember that all models are wrong; the practical question is how wrong do they have to be to not be useful."

George E P Box (1919-2013) Professor of Statistics University of Wisconsin

In memory of my Mother

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List of Papers

This thesis is based on the following papers, which are referred to in the text by their Roman numerals.

I Hamberg AK, Dahl ML, Barban M, Scordo MG, Wadelius M, Pengo V, Padrini R, Jonsson EN. (2007) PK-PD model for pre- dicting the impact of age, CYP2C9, and VKORC1 genotype on individualization of warfarin therapy. Clinical Pharmacology and Therapeutics, 81(4): 529–38

II Hamberg AK, Wadelius M, Lindh JD, Dahl ML, Padrini R, De- loukas P, Rane A, Jonsson EN. (2010) A pharmacometric model describing the relationship between warfarin dose and INR response with respect to variation in CYP2C9, VKORC1, and age. Clinical Pharmacology and Therapeutics, 87(6): 727–34 III Hamberg AK, Friberg LE, Hanséus K, Ekman-Joelsson B-M,

Sunnegårdh J, Jonzon A, Lundell B, Jonsson EN, Wadelius M.

(2013) Warfarin dose prediction in children using pharmacometric bridging – comparison with published pharmacogenetic dosing algorithms. European Journal of Clinical Pharmacolo- gy. Published online 11 January 2013

IV Hamberg AK, Hellman J, Dahlberg J, Jonsson EN, Wadelius M. A decision support tool for individualized warfarin therapy in adults and children. [In manuscript]

V Hamberg AK, Wadelius M, Friberg LE, Biss TT, Kamali F, Jonsson EN. Predicting the relative importance of genetic, clinical and demographic factors on warfarin dose in children using pharmacometric modelling. [Submitted]

Reprints were made with permission from the respective publishers.

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Abbreviations

A drug amount in body

ADME absorption, distribution, metabolism and excretion

CL clearance

CV coefficient of variation

CYP2C9 cytochrome P-450 enzyme (family 2, subfamily C, polypeptide 9)

CYP2C9 the gene coding for the CYP2C9 enzyme

DR dose rate

DVT deep vein thrombosis

EC50 concentration to produce 50% of the maximum effect EDK50 dose rate to produce 50% of the maximum effect

EMAX maximum effect

FOCE first-order conditional estimation method GAM

h

generalised additive modelling hours

HT height

IIV interindividual variability INR international normalized ratio IOV inter occasion variability

IWPC International Warfarin Pharmacogenetics Consortium

ka absorption rate constant

KDE elimination rate constant ke elimination rate constant k10 elimination rate constant

KPD kinetic-pharmacodynamic

MAE mean absolute error

MPE MTT

mean prediction error mean transit time OFV objective function value

pc-VPC prediction corrected visual predictive check

PD pharmacodynamic

PE pulmonary embolism

PK pharmacokinetic

PKPD pharmacokinetic-pharmacodynamic PT

Q

prothrombin time

inter-compartmental clearance

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RMSE root mean square error RSE relative standard error

TV typical value

V volume of distribution

VKORC1 the enzyme vitamin K epoxide reductase, subunit C1 VKORC1 the gene coding for the VKORC1 enzyme

VPC visual predictive check

WARG the Warfarin Genetics study

WT weight

ε (epsilon) difference between individual prediction and observation (residual error)

η (eta) difference between population and individual parameter estimate

γ (gamma) Hill factor (slope in EMAX-model) λ (lambda) slope factor in PD-model

Ω (Omega) variance-covariance matrix of η:s ω (omega) standard deviation of η:s

σ (sigma) standard deviation of ε:s

θ (theta) fixed-effect parameter (typical value)

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Introduction

Warfarin

Warfarin is the most widely prescribed anticoagulant for prevention and treatment of thromboembolic events. Although highly effective, the use of warfarin is limited by a narrow therapeutic range combined with a large difference in the dose required for adequate anticoagulation. To achieve a fa- vourable balance between the wanted antithrombotic effect and the risk of bleeding, it is important to identify the right dose for individual patients. The challenge is to know beforehand what the right dose should be, but also how to adjust the dose once treatment has started to achieve and maintain the desired therapeutic effect, and at the same time minimise the risk of adverse bleeding events.

Growing amount of data support that a large part of the variability in warfarin maintenance dose requirement can be explained by a combination of clinical and genetic factors. There are several dosing algorithms available that include both clinical (e.g. age, bodyweight) and genetic factors (VKORC1 and CYP2C9 genotype) [e.g. 1-3], and which can be used to pre- dict a more individualised warfarin maintenance dose in adults. In other words, there is a certain degree of understanding of the effect of clinical, demographic and genetic factors on the variability in warfarin maintenance dose in adults, but not how these factors influences dose requirements in children or how they influences the response to warfarin over time. Exam- ples of temporal outcomes of interest in warfarin therapy include the time delay between dose administration and INR response, extent and rate of drug accumulation, and time to stable treatment response.

Pharmacometric models, which are based on mathematical and statistical models, can provide a better understanding of the dose-response relationship over time for a drug, and help identify and quantify factors that influences variability in drug response. With a better understanding of the dose-effect relationship, therapy can be truly individualised.

In this thesis, pharmacometric models have been developed to describe the relationship between warfarin dose and anticoagulant effect over time for both adults and children. This type of models have the potential to provide individualised start doses, but more importantly, improve dose adjustment practices and provide more efficient individualisation of warfarin by integra- tion of modelling and simulation into clinical decision support systems.

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History

In the early 1920s, there was an outbreak of a previously unrecognized cattle disease in northern USA and Canada, with cattle bleeding uncontrollably after minor procedures: 21 out of 22 cows died after dehorning, and 12 out of 25 bulls died after castration, all deaths caused by massive haemorrhage [4]. In 1921, a Canadian veterinary pathologist concluded that the disease was caused by feeding the cattle spoiled hay made from sweet clover [5,6].

In 1933 the chemist Karl Link and his colleagues at the University of Wis- consin set out to isolate and characterize the agent causing haemorrhages. It took seven years before two of Link's students had identified the cause as being 3,3'-methylenebis-(4-hydroxycoumarin), which they named dicoumarol [4].

Dicoumarol is formed from coumarin, which is present in many plants and gives the sweet smell to freshly cut grass or hay. Coumarin itself does not have any anticoagulant properties. It must first be metabolised by various fungi into 4-hydroxycoumarin and then further into dicoumarol to influence coagulation. Over the next few years, numerous similar chemicals (4- hydroxy-coumarins with a large aromatic substituent at the 3' position) were synthesised and found to also have anticoagulant properties. The first to be used as a pharmaceutical was dicoumarol. Karl Link continued working on synthesising more potent coumarin-based anticoagulants for use as a rodent poison, and this work resulted in the discovery of warfarin in 1948 [4]. The structural formula of coumarin and warfarin are shown in Figure 1.

Figure 1. The structural formula of coumarin and its chiral derivative warfarin.

The name "warfarin" stems from the acronym WARF, for Wisconsin Alum- ni Research Foundation, with the ending -arin alluding to its link to coumarin. Warfarin was first registered as a rodenticide in 1948. However, after an incident a few years later, where a US soldier attempted suicide with a large dose of warfarin but fully recovered after being treated with the antidote vitamin K, clinical development of warfarin as an anticoagulant began, and in 1954 it was first approved for medical use in humans. In 1955, the former US president Eisenhower was prescribed warfarin following a heart attack, and within a year it was considered “the anticoagulant of choice” in US hospitals [4]. Like Duxbury and Poller said “After all, what was good for a war

!

Coumarin Warfarin (*chiral center)

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hero and the President of the United States must be good for all, despite being a rat poison” [6]. However, everything has it drawbacks, and in 2003, a group of Russian and American historians presented a new theory that the sudden death of the former Soviet leader Joseph Stalin in 1953 from a cere- bral haemorrhage may have been caused by warfarin poisoning [7].

The cases described above illustrate one of the major challenges associated with warfarin therapy even today, and that is to find the dose for the individual patient that will best balance between prevention of clot formation and the risk for serious bleeding.

Clinical pharmacology

Warfarin is essentially completely absorbed after oral administration with peak concentration generally attained within the first four hours. It consists of a racemic mixture of two enantiomers, R- and S-warfarin, each of which is cleared by different pathways. The S-form is metabolized by the polymor- phic cytochrome P-450 enzyme CYP2C9, whereas several enzymes including CYP1A2 and CYP3A4 clear the R-form. The half-life of R-warfarin is reported to range from 37 to 89 hours, while that of S-warfarin is reported to range from 21 to 43 hours [8].

Warfarin influences blood coagulation by inhibiting the enzyme vitamin K epoxide reductase, subunit C1 (VKORC1) in the vitamin K cycle (see Figure 2).

Figure 2. The vitamin K cycle. Reduced vitamin K is necessary for activation of several clotting factors. Vitamin K epoxide reductase (VKORC1) is involved in regenerating reduced vitamin K. Warfarin inhibits VKORC1, thereby impairing recycling of vitamin K and the synthesis of new functional clotting factors.

The enzyme VKORC1 is involved in the recycling of oxidized vitamin K to its reduced form, which is required for formation of functioning coagulation

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factors II, VII, IX and X and the anticoagulant proteins C, S and Z [9]. S- warfarin is claimed to be three to five times more potent than the R-form with respect to inhibition of the vitamin K cycle [10]. The anticoagulant effect of warfarin is not seen instantly since it only inhibits the formation of new functioning coagulation factors, and has no effect on their elimination.

Hence, the appearance of the anticoagulant effect will reflect the elimination of functional coagulation factors from the circulation, and that is governed by the half-lives of the individual coagulation factors. Changes in anticoagulant effect, as measured by the prothrombin time (PT) are typically noted 24- 36 hours after start of treatment and reflect the decrease in total activity of factors II, VII and X. The earliest changes reflect the disappearance of factor VII, which has the shortest half-life (~6h). The antithrombotic effect of warfarin, on the other hand, is not seen until the circulating level of factor II is reduced. Due to its long half-life of ~50-90 h, this does not occur until the fourth to fifth day of therapy [9].

Clinical use in adults and children

Warfarin is the most widely used oral anticoagulant for the prevention and treatment of thromboembolic events. Duration of treatment varies, from weeks to months for venous thrombosis, to life for some cardiac indications or recurrent thrombosis. The most common indications in adults are prevention of arterial thromboembolism in patients with atrial fibrillation and/or mechanical heart valves, and treatment and prevention of deep vein thrombosis (DVT) and pulmonary embolism (PE) [9]. Although anticoagulant therapy is not common in children, it is crucial for specific patient groups, such as children with certain congenital or acquired heart diseases [11]. War- farin is also the most commonly prescribed anticoagulant in children [12].

A major challenge in warfarin therapy is its narrow therapeutic range, which requires frequent monitoring of the anticoagulant effect coupled with appropriate dose adjustments to maintain the desired therapeutic effect and minimise the risk of adverse bleeding events. Too low doses can result in thrombosis, which can be life threatening, while too high doses can result in haemorrhage, which can also be fatal. Even a mild degree of over- anticoagulation may lead to haemorrhagic complications, with average year- ly bleeding rates in adults reported to be in the range 0.1-1% for fatal bleeding, 0.5-6.5% for major bleeding, and 6.2-21.8% for minor bleeding [13].

Warfarin therapy is further complicated by a pronounced interindividual variability in the dose required to reach a therapeutic response. Variability in both pharmacokinetics (PK) and pharmacodynamics (PD) contribute to the more than ten-fold difference in therapeutic dose in adults. Part of this variability is ascribed to clinical and demographic factors, such as treatment indication, concomitant medications, age, weight, interacting drugs and dietary vitamin K intake [14]. There is now extensive evidence that a significant part

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(>40%) of the overall variability in warfarin dose requirement in adults is explained by polymorphisms in the two genes CYP2C9 and VKORC1. How- ever, genotype based dosing is still considered experimental in most countries.

There is no universal consensus on how to dose warfarin. It depends on treatment indication, local traditions, and patient factors such as age, weight and general health status, and treatment goal. There are also practical constraints imposed by available formulations. For instance, in Sweden, warfarin is only available as 2.5 mg tablets [15], and the approved label has been adapted accordingly. In the US, warfarin tablets are available in 9 different strengths, ranging from 1 mg to 10 mg, and in UK warfarin tablets are available as 1, 3 and 5 mg tablets, and since 2010 also as a 1 mg/ml oral suspen- sion. This increased range of dose sizes allows for more flexible dosing rec- ommendations.

The warfarin label in Sweden includes the following dose recommendations for initiation of warfarin therapy in adults [15]:

• Day 1: 5-10 mg (2-4 tablets) depending on weight, age and general health status

• Day 2: 5-7.5 mg (2-3 tablets)

• Day 3: A preliminary maintenance dose, derived from monitoring of clotting time on day 3

For patients not requiring a fast response, a starting dose of 5-7.5 mg per day is recommended, with control of clotting time on day 3 or 4.

The warfarin label also includes a dose recommendation for children. A starting dose of 0.1-0.2 mg/kg is suggested, with further dosing derived from monitoring of clotting time [15]. The lack of a flexible warfarin formulation, however, limits the ability to dose children accurately.

Irrespective of treatment indication and starting dose, all warfarin regimens require that a patient’s response to treatment be followed through frequent monitoring of the clotting time, or prothrombin time (PT). However, due to poor agreement between PT results both within and between laborato- ries, the World Health Organisation introduced a system to standardise results from these tests in 1983. It is based upon the determination of an Inter- national Normalized Ratio (INR), which provides a common basis for com- munication of treatment results and interpretation of therapeutic ranges [16].

The normal INR for a healthy, untreated person is 1 (range 0.8-1.3). For warfarin patients the most common target INR is 2.0-3.0, which means that the PT is prolonged 2-3 times compared to reference samples from healthy untreated volunteers. The target INR can be higher in conditions with an increased risk of clotting or lower in conditions with an elevated bleeding risk [9].

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The methods for monitoring warfarin therapy are either based on Quick’s one-stage method or Owren’s method [17]. Both methods measure the activity of the vitamin K-dependent coagulation factors II, VII, and X, but the Quick method is also sensitive to variability in fibrinogen (factor I) and factor V activity. There is a continuous debate on how well INR results from the two methods agree. Some claim that the Owren method is more reliable than the Quick method [17-19], with lower coefficients of variation and absolute errors [18]. Lack of sample pre-dilution with the Quick-method has been suggested to explain poor precision [20]. The Owren method is mostly used in the Nordic and Benelux countries and in Japan, whereas the Quick method is used elsewhere, accounting for the vast majority (95%) of all INR tests performed worldwide [19]. The “point of care” monitors available for home monitoring of anticoagulation are all based on the Quick method.

Pharmacogenetic research in adults and children

Pharmacogenetics is generally regarded as the study of genetic variation that gives rise to differing responses to drugs [21]. Polymorphisms in genes can result in a reduced production of enzymes, or production of enzymes that are inactive or with reduced enzyme activity.

In 1999, Aithal and co-workers showed that polymorphisms in the CYP2C9 gene were associated with reduced warfarin dose requirements [22]. In 2004, the gene coding for warfarin´s target enzyme VKORC1 was identified [23,24], and soon it was shown that polymorphisms in the VKORC1 gene also explained variability in warfarin dose. For the last decade warfarin has been one of the most thoroughly investigated drugs in the field of pharmacogenetics.

Analyses of large, pooled, cohorts of patients have shown that there are considerable inter-racial differences in the distribution of the CYP2C9 and VKORC1 genotypes [25]. This could explain some of the differences seen in warfarin dose requirement between populations of different ethnicity, with dose requirement on a population level declining in the order African Amer- ican (40 mg/week) > Caucasian (31.5 mg/week) > Asian (21 mg/week) [25].

Reported genotype frequencies in Caucasians, Asians and African Ameri- cans [26] are summarised in Table 1 for CYP2C9, and in Table 2 for VKORC1.

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Table 1. Genotype frequencies (%) of the most common CYP2C9 variants

(*2:rs1799853, *3:rs1057910) in a Caucasian, Asian and Black/African American population (n >6,000) [26].

CYP2C9¹ Caucasian (n=3448)

Asian (n=1881)

Black/African American

(n=828)

*1/*1 64 93 93

*1/*2 21 0 5

*1/*3 11 7 2

*2/*2 2 0 0

*2/*3 2 0 0

*3/*3 1 0 0

1CYP2C9*1 is in this case exclusion of *2 and *3. Other rare CYP2C9 alleles not investigated or reported include *4-*35 (www.cypalleles.ki.se).

Table 2. Genotype frequencies (%) of VKORC1 -1639G>A (rs9923231) in Cauca- sian, Asian and Black/African American populations (n>5,000) [26].

VKORC1 Caucasian (n=2777)

Asian (n=1648)

Black/African American

(n=798)

G/G 36 2 82

A/G 49 18 17

A/A 15 81 2

Warfarin treated adult patients who are carriers of CYP2C9 and/or VKORC1 variant alleles have been shown to have an increased risk of over- anticoagulation and bleeding [27-29], especially during warfarin initiation [30]. A recent study [31] suggest that genotype also plays an important role in the early response to warfarin therapy in children. Children with at least one CYP2C9 variant allele or with the VKORC1 -1639 A/A genotype, had higher mean peak INR values during the first week of therapy, and a higher proportion of INR values above target range during the first month of thera- py, than children with other genotypes.

The increased interest in pharmacogenetics has resulted in the development of several genotype-based dosing algorithms for warfarin, with CYP2C9 and VKORC1 genotype included as important predictors of dose [e.g. 1-3,32-34]. Some of these are currently being tested in controlled clini- cal trials [35-37]. There are also reports that polymorphisms in a third gene, the CYP4F2 gene that codes for an enzyme involved in the metabolism of vitamin K, may influence warfarin dose, with an increased dose requirements in carriers of the variant allele [38-40]. However, the clinical relevance of this polymorphism for warfarin dosing is still under debate [41].

Small studies investigating the relative importance of clinical and genetic factors on warfarin dose requirements in children have started to emerge [42- 45]. Results are inconclusive with regard to the relative importance of indi-

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vidual predictors. For instance, polymorphisms in CYP2C9 have been re- ported to explain 0.5% [42] to 12.8% [44] and polymorphisms in VKORC1 2.8% [42] to 47% [45] of the variability in warfarin dose in children. In one of the studies, including only 34 children and with a median age of 15 years, the authors conclude that there is no significant impact of the CYP2C9 or VKORC1 genotype on warfarin dosing in children [42].

The most common way to present the importance of individual factors is by reporting the percentage of the variability in maintenance dose explained by a given factor, often reported as the R²-value [1-3,25,42,44,46]. This is a measure of what factor is most important for the variability in the population as a whole, and which is due to the effect size of a given factor but also how common this factor is in the population [25]. However, when evaluating predictors important for individualised dosing regimens, the clinical validity of this measure may be questioned. On an individual basis, a more relevant measure would be to quantify how much a given factor can influence the dose in an individual patient, i.e. to look at the expected benefit in outliers.

Studies performed in both adults and children has mainly focused on identifying how much a given factor affects the size of the warfarin maintenance dose, without taking the temporal aspects into account. In other words, there is a certain degree of understanding of the effect of clinical, demographic and genetic predictors on the variability in warfarin maintenance dose, but not of how they influence the treatment effect over time.

One of the main aims of warfarin research should be to learn how to reach target INR levels in all patients, including outliers, in a safe and timely manner. In this respect, a population model, based on pharmacokinetic and pharmacodynamic principles, is expected to provide a better tool than the commonly used linear regression model for deriving individualised dosing recommendations for warfarin. Examples of temporal outcomes of interest include the time delay between administered warfarin dose and INR response, extent and rate of drug accumulation, and time to pharmacokinetic and pharmacodynamic steady state. The population approach, using modern modelling techniques, also has the advantage of being able to include all clinically available observations in the development of the population model [47,48]. This is in contrast to the traditional analysis of warfarin data, in which only one observation per patient that has reached stable maintenance therapy within a predefined target INR is used [1-3,32,42-44]. Furthermore, the definition of stable maintenance therapy is not standardised and often varies between studies [14], which complicates the interpretation and com- parability of study results further. Traditional (linear regression) analysis that only allows data from stable warfarin therapy to be included probably intro- duces a selection bias by excluding the patients that are the most difficult to treat.

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Dose-response relationships

Pharmacokinetics (PK), briefly, is what the body does to the drug after it has been administered to a subject. The drug-levels achieved after dosing can be described by a number of physiological processes, which can be divided into absorption, distribution, metabolism and excretion (ADME). The rate and extent of these processes are dependent on the physicochemical properties of the drug itself, its formulation, and the biology of the subject receiving the drug. Pharmacodynamics (PD) on the other hand, is the study of what the drug does to the body, where the effect size is governed by the amount of drug at the target site, and the sensitivity of the target.

When studying systemically acting drugs, it is not the dose but the concentration that drives the biological effect, and in contrast to the dose the concentration varies with time. Dose-effect relationships can be described with a mathematical model that captures both the dose-concentration relationship (PK) and the concentration-effect relationship (PD), commonly referred to as a PKPD-model (Figure 3).

Figure 3. The dose-response relationship, here described as the dose-concentration relationship (PK), and the concentration-effect relationship (PD).

The drug effect can be exerted through many different mechanisms, but often requires binding to the target, which then translates into a biological response. This effect could either be an immediate reaction or consist of a whole chain of events. Thus, depending on the mechanism of action, the relationship between the drug concentration and the observed effect may be either direct or delayed. In the case of warfarin there is a considerable time delay from inhibition of the target enzyme VKORC1 until the levels of coagulation factors are reduced, leading to a prolonged PT and a measured increase in INR. Hence, when modelling the relationship between warfarin concentration and anticoagulant effect, and translating this into individualised dosing recommendations, it is imperative that this time delay is ac- counted for. In a review article of the dose-effect relationship of warfarin from 1986 [49], it was suggested that a combination of up to four independent models are required to describe the time-course of changes in PT induced by warfarin.

In the vast majority of clinical warfarin studies, and in clinical practice, warfarin concentrations are not measured. Several authors have suggested methods for how to model response-time profiles in the absence of drug

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concentrations, for example Levy [50] and Gabrielsson [51]. These methods have been further developed and evaluated by Jacqmin and co-workers [52], who proposed a way to account for the time course of drug disposition by including prior knowledge on PK as explanatory factors (covariates) in the model. In order to highlight the fact that no PK observations are required to describe the fluctuation in drug levels within a dosing interval, these models are referred to as KPD-models, where K stands for kinetics, the Greek word for movement.

Warfarin dose history and INR observations are routinely collected as part of standard care. This makes a KPD-model an attractive alternative to the standard PKPD-model when modelling clinical warfarin data. KPD-models have also been suggested as a way to facilitate assessment of drug therapies in children since they alleviate the constraints related to invasive PK studies [53]. This type of models are expected to be most useful when the PK of the drug is simple, and/or when response kinetics are delayed compared with the PK of the drug [53].

Pharmacometrics and population modelling

Traditional model based analysis is performed in two steps, the so-called two-stage method. In the first step, individual parameters are estimated followed by a second step where the mean and standard deviations of the parameters in the studied population are calculated. Major drawbacks with this approach are that for step one, many observations are required from each individual in order to identify a model, and for step two, summary parameters can only be calculated if the same structural model has been used in all subjects. Furthermore, estimates of variability between individuals will be upwardly biased using the two-stage method [47].

Pharmacometrics can be defined as the science of quantifying drug behav- iour and drug actions, but it can also include element of disease development and clinical trial design. The quantification usually involves the development of statistical models, which often are mixed effect models. Non-linear mixed effects’ modelling, or population modelling, is a now widely accepted method that involves simultaneous estimation of the mean and variance parameters based on all data from all individuals [48]. With this approach it is possible to analyse rich as well as sparse or unbalanced data, or a mixture of these. The term “mixed” is used because both fixed and random effects are estimated in the model. Fixed effects are the typical parameter estimates.

The random effects are estimated on at least two levels; variability between individuals (interindividual variability, IIV) and the residual variability. In addition, there is a third level of random effects that can be estimated, the inter occasion variability (IOV), which describes the difference between parameter values within the same individual from one occasion to another.

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The individual parameter value is a function of the typical value for the population and an individual random effect, and is commonly described using a lognormal distribution as shown in Equation 1:

Pi =θ * e^ηi

(1) where Pi is the individual parameter value, θ is the typical parameter value for the population (e.g. CL, V or EC50) and ηi is the individual random effect value, which describes the difference between the population and individual parameter value. The η-values are often assumed to be normally or log- normally distributed with a mean of zero and a variance of ω². Individual patient characteristics or covariates (e.g. age, weight, gender, genotype) may explain part of the variability between individuals. In this case the typical parameter value will be a function of the individual covariate value. An example is the effect of body weight on volume of distribution (V), which could be described according to Equation 2:

Vi =TVV * (WTi/WTmedian) * e^ηi (2)

where Vi is the volume of distribution in individual i, WTi is the weight of individual i, WTmedian represents the median weight in the population under study, and TVV is the typical volume of distribution in a subject with the median weight.

The residual variability describes the difference between the individual prediction and the observed value, e.g. the difference between the model predicted drug concentration and the measured drug concentration, or the model predicted INR and the measured INR. The difference may include data errors due to assay or measurement errors, model misspecification or incorrect dosing or sampling history recordings. The j^thobservation of the individual i can thus be described using the general residual variability for- mula in Equation 3:

yij = f (xij,Pi) +εij (3)

where yij is the j^thindividual´s i^th observation (e.g. the measured plasma con- centration in a PK model or the measured response in a PD model), f(…) is the individual prediction, which is described by the independent variables xij

(e.g. dose, time) and the individual´s parameter values Pi, and εij is the residual variability random effect term that describes the difference between the observation and the individual prediction. The ε-values are assumed to be normally or log-normally distributed around zero with a variance of σ². Fig- ure 4 provides a graphic representation of interindividual variability in pa- rameter values (η) and residual variability in observations (ε).

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Figure 4. The principles of population modelling, illustrating the fixed effects (typi- cal parameter values) and the random effects (between subject variability in parameters and residual variability in observations). Used with courtesy to Dr Mallika Lala [54].

Bridging from adults to children

Conducting clinical studies in children is challenging. Common problems are the limited number of patients, the heterogeneity in the patient population ranging in age from preterm neonates to 18 years of age, restrictions in the number and volume of blood samples allowed to be taken per subject as well as ethical constraints. Using a population modelling approach when designing and analysing studies can alleviate many of the difficulties en- countered during drug development and drug use in children. This approach enables use of sparse and unstructured real-life data, rather than relying on data derived from stringent clinical trial settings [55]. It is also possible to include data from different sources, and to bridge from an existing adult population model to paediatrics through the use of physiological principles that acknowledge that adults and children are in some aspects similar and not discrete subgroups [56-58]. A population modelling and simulation approach is also advocated by regulatory bodies to support selection of safe and effi- cacious dosing regimens for new drugs intended for children [59,60].

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For many medicinal products in use today, dosing recommendations for children are based on extrapolation of results obtained in adults. When scaling adult doses to children, linear predictions of dose based on body weight are commonly used, as is also the case for warfarin [11,15,42]. However, it is becoming more widely recognized that the relationship between adult and paediatric doses is often non-linear. Due to a larger liver and/or kidneys in relation to body size, small children often require higher doses per kilo body weight than older children and adults to achieve the same target concentration [61]. This has also been observed with warfarin where higher weight- normalized dose requirements have been reported in the youngest age- groups in order to obtain the same target INR [44,62,63].

A growing amount of data supports that the pharmacokinetics of drugs in children ≥ 2 years can be reasonably well extrapolated from adults by using an allometric adjustment for body size [61,64]. In the youngest age group (<

2 years), adjusting for differences in body size may not be sufficient; it may also be necessary to take into account the impact of maturation of the organs and/or enzymes involved in the elimination of the drug [61,64,65]. Hence, when predicting the pharmacokinetics of drugs in children 0-18 years old, it is important to acknowledge the influence of both body size and age. Wheth- er this will be sufficient for accurate dose predictions in children for a specific drug will also depend on if the disease and/or pharmacodynamic effect of the drug in question can be assumed to be the same in children as in adults [58].

Individualisation of drug dosing

A priori dose individualisation

A suitable starting dose can be estimated based on patient factors that have been previously identified as predictors, or covariates, for individual dose requirements. This is called a priori dose individualisation. An example is the US drug label for warfarin from 2010, which recommends that dosing should be guided according to a patient’s CYP2C9 and VKORC1 genotype when starting warfarin therapy, according to Table 3 [8].

Table 3. Dose table from FDA approved Coumadin label, suggesting genotype based dosing of warfarin [8].

VKORC1 *1/*1 *1/*2

CYP2C9

*1/*3 *2/*2 *2/*3 *3/*3

G/G 5-7 mg 5-7 mg 3-4 mg 3-4 mg 3-4 mg 0.5-2 mg

A/G 5-7 mg 3-4 mg 3-4 mg 3-4 mg 0.5-2 mg 0.5-2 mg

A/A 3-4 mg 3-4 mg 0.5-2 mg 0.5-2 mg 0.5-2 mg 0.5-2 mg

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Other examples of a priori dose individualisation of warfarin therapy for adults include the algorithm published by Gage et al in 2008 [1] and availa- ble online at www.warfarindosing.org, and the IWPC algorithm published in 2009 [2]. Both include CYP2C9 and VKORC1 genotype as predictors for dose, and additionally, another five or seven demographic/clinical predictors, e.g. age, body size, ethnicity and concomitant use of interacting drugs.

General dosing recommendations for warfarin in children include a priori dose individualisation based on bodyweight (0.1-0.2 mg/kg) [11]. The recent algorithms by Nowak-Göttl [42], Moreau [43] and Biss [44] are examples of genotype based a priori dose individualisation of warfarin for children.

A posteriori dose individualisation

If the dose is individualised based on feedback observations from the patient being treated, i.e. a drug concentration or measurement of a biomarker, this is called a posteriori dose individualisation. One example is the routine management of warfarin therapy where the dose is regularly adjusted according to INR response. Doses are commonly adjusted empirically on the basis of the clinician’s own experience, but there are also commercially available computerised tools to guide warfarin dose adjustments, such as AuriculA in Sweden [66] or Dawn in the UK [67], or the pharmacogenetical- ly-based dose revision algorithm after 3 or 4 days of dosing by Lenzini [68].

None of these dose revision tools are, however, based on PKPD principles.

In a review article from 2001 about the history of oral anticoagulants [6], the authors conclude that some changes are necessary to improve the overall quality of anticoagulant management. They suggest an increased use of home monitoring of INR, coupled with use of reliable computerised pro- grams for anticoagulant dosing. Several randomized trials have compared the benefits of computer-assisted a posteriori warfarin dosing with manual a posteriori dosing. These have all shown that the commercial computer pro- grams consistently gave better INR control, even when comparing with ex- perienced medical staff [69,70].

Population models for dose individualisation

Population PKPD-models can serve as valuable tools for generating individual dose predictions, especially for drugs with a narrow therapeutic range and/or complex dose-response relationships. A population analysis provides the information required to individualise initial dosing regimens based on expected (mean or typical) model parameter values for a specific set of patient characteristics, e.g. age, treatment goal and genotype, and the estimates of interindividual and residual variability that are part of the population model will facilitate Bayesian feedback adjustment of a dosage regimen

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[71,72]. Typical for a Bayesian approach is that it balances the uncertainty in the individual´s parameters against the uncertainty in the measured response.

Earlier work by Sandström [73], Wallin [74,75], Dombrowsky [76] and Wright [77,78] provide examples of where population models have been used for development of computer-based tools for a priori and/or a posterio- ri dose individualisation. The first two examples represent PK-based tools for the prediction of individualised initial and maintenance doses for i) busulphan therapy in children and adults [73], and ii) tacrolimus dosing in children after hematopoietic stem cell transplantation [75]. The third example is a PD-based tool for neutrophil-guided dose adaptation of chemothera- py [74], and the fourth example is a Bayesian forecasting algorithm for prediction of methotrexate concentrations and assessment of leucovorin dosing in paediatric cancer patients [76]. The last example is a Bayesian dose- individualisation tool for warfarin [77,78], based on one of the warfarin models presented within this theses. One of the published warfarin models [79], but without inclusion of CYP2C9 and VKORC1 genotypes as predictors for dose, has been implemented in a model-based decision support tool [80], and validated using prospectively collected treatment data from 55 patients.

The tool was evaluated with respect to accuracy and precision in INR predictions using a Bayesian approach. The external evaluation showed that predictions of steady state INR from the tool were both accurate and precise with knowledge of at least one prior INR, and with predictions improving with up to six available INR observations [78].

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Aims

The overall aim of this thesis was to develop PKPD-based population models that can describe the dose-response relationship of warfarin over time, and to identify predictors influencing individual dose requirements in adults and children. Special emphasis was placed on investigating the importance of genetic factors on variability in response to warfarin. The specific aims of the individual studies were:

Paper I

• To develop a population model in NONMEM that describes the PKPD-relationship of warfarin, and to identify and quantify im- portant predictors for a priori dose individualization of warfarin in adults

Paper II

• To reformulate the NONMEM model to remove its dependence on PK observations, and to reduce uncertainty in population parameter estimates for individuals with rare genotypes, and to better account for the early response to therapy

Paper III

• To theoretically bridge the adult warfarin model for use in children, and to evaluate its predictive performance in children Paper IV

• To transfer the bridged warfarin model to a user-friendly decision support tool for a priori and a posteriori predictions of warfarin dose and INR response for adults and children

Paper V

• To optimise performance of the bridged warfarin model in children using data from a large cohort of warfarin treated children

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Material and Methods

Description of data

The clinical data used in this thesis are of two types, data from warfarin treated adults (papers I-III) and data from warfarin treated children (papers III and V). Treatment data from adult patients were collected during pro- spective clinical trials, whereas data from children were collected retrospectively from routine patient care through review of patients’ medical records.

A limitation with available treatment data is that exact clock times for dosing and INR sampling were missing in most cases, and time between dose and PD-observation had to be assumed to follow general treatment recommendations. The single dose data from paper I was an exception, and where exact sample times were available.

Treatment data from adults

Paper I used data from two Italian studies in adult patients eligible for long- term warfarin therapy [81,82]. In study I, data on plasma concentrations of S- and R-warfarin (PK) and INR (PD) after administration of a single 10 mg dose of racemic warfarin was available from 57 patients. PK samples were taken at 12, 36, and 60 h after dose and INR was measured before and at 12, 36, and 60 h post dose. Data from single PK and PD samples during stable maintenance therapy were also available. In study II, a single PK and PD sample from stable maintenance therapy was available from another 93 patients.

The following demographic/clinical information was available and included in the dataset; sex, age, bodyweight, stable maintenance dose, CYP2C9 genotype (all patients) and VKORC1 (-1639G>A) genotype (only from study I).

Paper II re-used the single-dose data from paper I (n=57), but the main part of the dataset came from the Swedish Warfarin Genetics (WARG) study [3]. Longitudinal treatment data from a total of 1,426 patients initiating warfarin treatment at 40 outpatient clinics was available, with data on warfarin doses and INR observations, sex, age, bodyweight (in ~50%), CYP2C9 and VKORC1 (-1639G>A) genotypes.

All WARG patients with data on bodyweight were included in the model revision in paper III. The model was updated with addition of allometric

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weight scaling and a published maturation function for enzyme activity, to enable bridging to children. The WARG with bodyweight information subset included treatment data from a total of 752 patients. The dataset was limited to the first 6 months of therapy so as to focus more on early treatment response, and reduce potential bias from possible deterioration in treatment compliance over time.

Treatment data from children

Warfarin therapy in children is uncommon with around 200 children being treated every year in Sweden. An observational pharmacogenetic study in warfarin treated children was initiated in collaboration with four tertiary care centres in Sweden to ensure access to treatment data from children. Children with underlying heart disease were recruited from the Queen Silvia Chil- dren´s Hospital in Gothenburg, Children´s Heart Centre in Lund, Uppsala University Children´s Hospital in Uppsala and Astrid Lindgren Children´s Hospital in Stockholm. Patients who were receiving or previously had re- ceived warfarin while below the age of 18 years were recruited between October 2010 and December 2011. Data were collected retrospectively from medical records and followed historically for as long as data were traceable, and up until end of therapy or study closure (31 December 2011).

Longitudinal data were collected from 64 children, and included dose and INR, treatment indication, target INR, ethnicity, age and bodyweight. All children were also genotyped for polymorphisms in CYP2C9, VKORC1 and CYP4F2. The data from this study was used in papers III and IV for external evaluation of the bridged warfarin model in children.

The main objective in paper V was to optimise performance of the bridged warfarin model from paper III, and was based on a larger cohort of children. The validation dataset from paper III was combined with a second dataset of warfarin treated children [44], recruited between April 2009 and December 2010 at four hospitals in the UK and one hospital in Canada. The combined dataset for model optimisation included a total of 163 children with information on warfarin dose, INR, treatment indication, target INR, ethnicity, age, bodyweight, CYP2C9 and VKORC1 genotypes, but also CYP4F2 genotype.

Model development

PK- and PD-models

Separate PK-models for S- and R- warfarin were built in paper I. Models tested included linear one-, two, and three-compartment models with elimination from the central compartment. Since no PK samples were taken dur-

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ing the absorption phase (first sample 12 h after dose), the absorption rate constant ka could not be estimated, and was fixed to 2 h^-1 as reported in the literature [83]. This assumption was later challenged in the final PK-models by testing other fixed values (0.5-5 h^-1).

PD-models tested for warfarin´s inhibition of the vitamin K cycle included linear models, power models and EMAX models. Different models were considered for capturing the time delay between drug concentrations and the increase in INR; these included effect compartment models, indirect effect models, and transit compartment models. A transit compartment model is a special case of an indirect effect model with a chain of compartments that represent transduction of the effect and thereby result in a more delayed effect response. The profile of the time delay is flexible and can be adjusted by changing the number of parallel chains, the number of compartments in each chain and the mean transit time through the chains. Concentrations of S- warfarin alone and in combination with R-warfarin, both with additive and competitive effects, were tested as potential predictors for the response.

In order to obtain acceptable run times, a sequential approach was used in which the PK-model was developed first. Individual S- and R-warfarin concentrations were then predicted from the final PK-models and used in the development of the PD-model.

Covariates were screened using scatter plots of individual parameter estimates against individual covariates, and by generalized additive modelling (GAM) in Xpose [84](xpose.sourceforge.net). Additional selection was made based upon possible mechanisms of effect and potential relevance in the clinic. Nested models were compared statistically using a likelihood ratio test on the difference in objective function values. A forward inclusion criteria of P<0.05 was applied for addition of parameter-covariate relations to the model. In the subsequent backwards step, the relations identified were ex- cluded if they failed to achieve statistical significance at the P<0.001 level.

The stricter P-value in the elimination step was applied to compensate for multiple testing.

In paper II, the warfarin model from paper I was updated using a much larger and more diverse dataset. The dataset that was used for this purpose lacked PK observations, and the model was adopted using the KPD frame- work [52] which operates without PK observations. In paper I, clearance of S- warfarin was expressed as a function of CYP2C9 genotype. Not only did this parameterisation require many parameters, it also led to large uncertainties in parameter estimates for rare genotypes. Given that the uncertainty is inversely proportional to the number of individuals within each genotype group, very large studies are required to obtain reasonable sized standard errors for rare genotypes. To address this an alternative approach was tested in paper II, which focused on alleles rather than genotypes. This parameterisation as- sumes an additive contribution from each allele. For purpose of consistence, the same type of allele parameterisation was used for the influence of

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VKORC1 on the sensitivity to warfarin. The overall PD structure from paper I, with three separate PD-models, was unchanged. However, the structure of the transit-compartment model was re-assessed since the data in this paper differed to the dataset used in paper I, with more observations from the induc- tion phase. The family of candidate models explored in a stepwise manner included one to three transit-compartment chains, each with up to eight compartments. Up to three parallel transit-compartment chains were tested, based on the assumption that each chain may represent separate warfarin effects with different onset times, corresponding to inhibition of the coagulation factors II, VII, and X, respectively.

In paper III, the adult KPD-model from paper II was revised to allow pharmacometric bridging to children. This included i) allometric size scaling of clearance (CL) and volume of distribution (V), using total bodyweight as size measure and with allometric exponents of 0.75 for CL and 1 for V [61], and ii) addition of a published maturation function representing ontogeny of CYP2C9 enzyme activity as a function of postnatal age [85].

Model-building criteria and parameter estimation

All analyses were performed using NONMEM, version VIβ (paper I) or version 7 (papers II-V), using the first-order conditional estimation method (FOCE) with interaction [86]. All analyses were carried out using an additive residual error model on log-transformed data, i.e. an approximately constant coefficient of variation (CV) residual error. Interindividual variability was implemented using exponential models.

Model selection was guided by (i) the decrease in the objective function value (OFV) which is the minimization criterion in NONMEM, (ii) the condition number obtained from NONMEM (papers II, III, V), (iii) graphical goodness-of-fit analyses in Xpose [84](xpose.sourceforge.net) and R (www.r-project.org), (iv) the estimated uncertainty in parameter estimates as determined by the standard errors obtained from NONMEM, (v) simulation based diagnostics (papers I, III and V) and (vi) the plausibility of the parameter estimates.

The difference in the OFV between two nested models is approximately χ²-distributed, meaning that a difference of 3.84 corresponds to P< 0.05 for one degree of freedom. Criteria for final model selection included that the model should:

(i) provide a statistically significant improvement over the com- peting simpler model

(ii) have a reasonably low condition number (<1000)

(iii) show good agreement between observations and model predictions with simulation based diagnostics

(iv) provide reasonably sized standard errors

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(v) result in biologically plausible parameter estimates

Model evaluation

Model evaluation techniques can be classified as internal and external. Inter- nal evaluation means that the data used in the evaluation of the model is the same as that used for model development, and external evaluation is when the evaluation is performed on data from a new study. A common problem with external evaluation is that it can be difficult to find a second dataset that is similar in design (e.g. target population, definition of treatment target) and performance (e.g. data quality, analytical methods) as the first dataset. An alternative is to randomly split the original dataset into two parts; one for model building and one for model evaluation. However, there are some drawbacks with this approach. Since only part of the data will be used for model development, the parameter estimates will be less informed and thereby less precise than if using all data available. In a comparison of internal and external model evaluation using data splitting [87], it was shown that internal model evaluation was preferred when evaluating a model´s predictive performance, with the exception of very small studies (n < 25). In this thesis, models have been mainly evaluated using internal model evaluation techniques. External model evaluation was used in paper III, for the evaluation of the predictive properties of the bridged adult warfarin model in warfarin treated children.

Simulation based diagnostics

In paper I, models were evaluated by use of simplified visual predictive checks (VPCs). Ten new data sets were simulated from each model and used to construct 95% prediction intervals. The model was judged to be adequate if approximately 2.5% of the observed data points fell below and above the prediction interval, respectively, and that the median of the simulated data should be similar to the median of the observed data.

In paper II, the model was qualified by comparing parameter estimates obtained using the model-building dataset (A, n=196) with those obtained from the full dataset (B, n=1483), but also by comparing goodness-of-fit plots for the full dataset with the internal validation dataset (B-A, n=1287).

The model was judged to be adequate if no major differences were found.

In papers III and V, models were again evaluated using VPCs. A VPC di- agnoses both the fixed and random effects in a mixed effects model. The VPC examines the ability of a model to simulate results similar to those from the original data set. A prediction corrected VPC (pc-VPC) is a modification of the standard VPC that is appropriate for application to data collected in studies with an adaptive design [88], such as warfarin studies. The pc-VPC

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differs from a standard VPC in that both the observations and the model predictions are normalized for the typical model predictions in each bin of independent variables.

Dose prediction accuracy

The performance of the bridged KPD-model in children was further evaluated in paper III by comparing accuracy in the prediction of maintenance dose relative to published warfarin algorithms for children. This was done by comparing model predicted doses with observed doses in a data set of 49 children (median age 7.2 years) on stable warfarin therapy. Regimens included in the comparison were:

• a fixed 0.2 mg/kg dose, included as a genotype-independent reference regimen

• a priori dose predictions with the genotype-based algorithm de- veloped by Nowak-Göttl [42]

• a priori dose predictions with the genotype-based algorithm de- veloped by Moreau [43]

• a priori dose predictions with the genotype-based algorithm de- veloped by Biss [44]

• a priori and a posteriori dose predictions with the theoretically bridged KPD-model [89]

Table 4 provides a summary of individual predictors included in the four pharmacogenetics-based algorithms for children. The regression models for the three pharmacogenetic reference algorithms are shown below the table.

Prediction of maintenance doses using the published algorithms was performed in Microsoft Excel, Version 12.3.2, whereas dose predictions with the bridged KPD-model were performed in NONMEM, adopting the approach described by Jönsson and Karlsson [90]. How this was done is described in the next section under Model applications, Maintenance dose predictions.

Accuracy of the different models was assessed by calculating the difference between predicted and observed daily maintenance doses, with results expressed as percentage prediction error for individual patients ((predicted dose-actual dose/actual dose)*100), and mean prediction error (MPE) to assess bias, and root mean square error (RMSE) for imprecision. Clinical accuracy was assessed as the proportion of children for which dose predictions were ideal (between 80-120% of actual dose), too low (< 80% of actual dose) or too high (> 120% of actual dose).

Pharmacometric Models for Individualisation of Warfarin in Adults and Children