Abstract
Model based personalised dosing (MBPD) is a sophisticated form of individualised therapy, where a population pharmacokinetic (PK) or pharmacodynamic model is utilised to estimate the dose required to reach a target exposure or effect. The choice of which model to implement in MBPD is a subjective decision. By choosing one model, information from the remaining models is ignored, as well as the rest of the literature base. This manuscript describes a methodology to develop a ‘hybrid’ model for voriconazole that incorporated information from prior models in a biologically plausible manner. Voriconazole is a triazole antifungal with difficult to predict PK, although it does have a defined exposure–response relationship. Nine population PK models of voriconazole were identified from the literature. The models differed significantly in structural components. The hybrid model contained a two-compartment disposition model with mixed linear and nonlinear time-dependent clearance. The parameters for the hybrid model were determined using simulation techniques. Validation of the hybrid model was assessed via visual predictive checks, which indicated the majority of the variability in the literature models was captured by the hybrid model. The predictive performance was assessed using four different sampling strategies of limited concentrations from ten richly PK sampled subjects to predict future concentrations. Overall, the hybrid model predicted future concentrations with good precision. Further prospective and retrospective validation of the hybrid model is required before it could be used in clinical practice.
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Introduction
Determination of a medicine dose for a specific individual is commonly termed ‘personalised medicine’ in the medical literature. This approach aims to achieve a specific response in an individual, which might be a pharmacokinetic (PK) target e.g. a peak plasma concentration of an antibiotic, or a pharmacodynamic (PD) target e.g. specific blood clotting time. Determination of personalised medicine doses thus requires knowledge as to whether a PK or PD response is clinically relevant, and can be realised using a variety of methods, each of which vary in their degree of sophistication.
The simplest form of personalised dosing is to use demographic data such as total body weight (TBW), to calculate the dose. This method is used when dosing the triazole antifungal agent, voriconazole (4 mg/kg TBW), and is the focus of this paper. Similarly, medicines which are predominantly renally cleared such as vancomycin, can be dosed based on an estimate of the individual’s glomerular filtration rate.
A more sophisticated approach is to use model-based personalised dosing (MBPD) also known as Bayesian dose forecasting. MBPD was first described in 1969 as a method for monitoring anticoagulant therapy [1]. MBPD is achievable using either parametric or non-parametric techniques. This manuscript will exclusively focus on parametric methods. Interested readers may refer to the extensive works of Roger Jelliffe and colleagues for a discussion on non-parametric methods [2–4].
The backbone of parametric MBPD is a population PKPD (PPKPD) model that describes the dose–exposure or dose–response relationship, and the variability between subjects in the population. An overview of PPKPD and pharmacometrics is described in detail elsewhere [5–7]. Sophisticated software is used to predict the most appropriate medicine dose for an individual subject, with an overview of current software provided by Roberts et al. [8]. Briefly, the population model serves as a Bayesian prior to estimate individual PKPD parameters. The subjects’ prior dose(s), PK and/or PD result(s), and covariates (e.g. weight, renal function) are used to determine the individual’s model parameters. These parameters are specific to the way an individual is absorbing, clearing and distributing a medicine, which are then used to determine the next dose to reach the target exposure or response. Experimental models have demonstrated voriconazole target exposure is best described by the area under the curve over the dosing interval:minimum inhibitory concentration (AUC τ :MIC) ratio of 25 for both candidia and aspergillus [9]. Clinically however, trough concentrations (Ctrough) are used as a surrogate exposure metric for AUC τ , as they are highly correlated [10, 11]. A target Ctrough range of 1.5–5 mg/L has demonstrated improved outcomes in multiple studies [12–16]. As the number of PK or PD samples increases for an individual, the predictions become more personalised and less population based, provided the samples are informative [17].
Choosing a population model for MBPD
Often, for the same drug, there are several population PK (PPK) models published in the literature. As of December 2014, we identified nine different PPK models in the literature for voriconazole, which are summarized in Table 1 (an extensive summary is available in online resource 1) [10, 11, 13, 18–23]. These models were developed in different populations i.e. paediatrics versus adults, healthy volunteers vs. patients, all with different dosage regimens and different sampling strategies. Given that the development of a PPK model varies due to their subjective nature [24], and are heavily dependent on study design, the structural and statistical components diverge considerably between these published models. Structurally, the voriconazole models differ with regard to the number of compartments, clearance mechanisms, and covariates, which makes choosing a PPK model for MBPD subjective. Typically, software providers might choose to implement a particular published model based upon the following factors: (a) the population recruited in the model development and the intended use e.g. intensive care unit (ICU) patients; (b) precision of the parameter estimates; (c) magnitude of the residual unexplained variability (RUV); and (d) covariates included in the PPK model.
We believe there are several limitations in the subjective ‘best model’ approach. The major one is the loss of information from the models that are not selected, which seems contrary to the Bayesian ideology of utilizing prior information. We therefore propose an alternate method, which seeks to best use all information from the population models published. This model, herein termed the ‘hybrid model’, incorporates as much information as possible by combining all prior models in a biologically plausible manner.
Methods
Model identification and inclusion
A thorough electronic literature search was undertaken to identify previously published population pharmacokinetic models for voriconazole, using the methods described by McLeay et al. [25].
The following Boolean search terms were used in PUBMED:
{((population AND (model* OR analysis*)) OR (non AND linear AND mixed AND effect*) OR population OR nlme OR ADAPT OR *bugs OR Kinetica OR NONMEM OR NPEM OR NPLM OR WinNonMix) AND (PK OR pharmacokinetic* OR popPK) AND voriconazole}.
For a model to be considered in the hybrid model, all parameter estimates, including fixed and random effects must have been published. Models with oral administration only were excluded as absolute bioavailability (F) could not be estimated, and the parameters were not comparable to other models.
Determination of hybrid model parameter estimates and covariates
For parameters that were published as single point estimates and did not include covariates, the hybrid model parameter was computed as the average of the published estimates, with equal weighting applied to all studies (note: a more detailed discussion on the weighting approach can be found in the discussion). For parameters that could not be averaged due to variability in parameterisation i.e. linear versus nonlinear clearance, or were conditional on a continuous covariate such as body weight, simulation techniques were required to determine the most appropriate parameter values. Details of the techniques used are provided in the results section of this manuscript due to the variability of methods required for differing parameters. The choice of covariates included had to be considered biologically plausible, and be available in the clinical setting as the hybrid model is to be used at the bedside to determine a personalised medicine dose.
Validation of the hybrid model
The hybrid model was validated using simulation techniques, where plasma concentrations from the hybrid model were compared to plasma concentrations from the individual and pooled literature models. Visual predictive checks (VPCs) [26] and numerical predictive checks (NPCs) were then used to determine the hybrid models robustness. For the VPCs and NPCs, 100 subjects, stratified by age, were randomly sampled from the National Health and Nutrition Examination Survey (NHANES) database [27], the demographics of which are displayed in online resource 2. Simulations (ten per subject) were performed for both intravenous (IV) and oral (PO) therapy. In the IV arm, adult subjects received a dose of 6 mg/kg 12 hourly (q12 h) for two doses, then 4 mg/kg q12 h for another 12 doses. Paediatric subjects (<12 and 12–15 years old weighing <50 kg), received 9 mg/kg q12 h for two doses followed by 6 mg/kg q12 h for another 12 doses. In the PO arm, adult subjects received 400 mg q12 h for two doses (200 mg q12 h for adults <40 kg), then 200 mg q12 h for another 12 doses (100 mg q12 h for adults <40 kg). Paediatric subjects received 9 mg/kg q12 h for 14 doses capped at 350 mg. IV doses were rounded to the closest 5 mg, with oral doses rounded to 20 mg.
Predictive performance of the hybrid model
The predictive performance of the hybrid model in a clinical setting was assessed using intensively sampled concentration data published in the literature, that were collected in ten subjects who received IV voriconazole during allogeneic haematopoietic stem cell transplantation [28]. Empirical Bayes estimates of the PK parameters for each subject were determined in NONMEM using the FOCE estimation algorithm with MAXEVAL = 0, with different voriconazole sampling strategies based on clinical feasibility. Four sampling strategies were investigated including: (a) two samples at 12 and 13 h, (b) three samples at 12, 13, and 72 h, (c) four samples at 12, 13, 72, and 168 h, and (d) five samples at 12, 13, 72, 168 and 240 h. The predicted concentration time profiles for the individuals were constructed until day 14. The final Ctrough obtained for each individual was compared to the hybrid models predicted concentrations with bias and precision evaluated by computing the mean error (ME) and root mean square error (RMSE), respectively.
Results
Model identification and inclusion
Nine voriconazole population models were identified in the literature as shown in Table 1. Two were not used to develop the hybrid model as final parameters were not published [10, 23]. An additional model was also excluded as voriconazole was only administered orally [22].
Structural model
Both one and two-compartment models were previously developed, and given parameter estimation for multi-compartments is design dependent, a two-compartmental model was chosen for the hybrid model. This was identified in several of the larger studies as important in describing the PK of voriconazole [11, 18, 20, 21].
Voriconazole clearance was described as a linear process in two of the published models [13, 19], as a nonlinear (Michaelis–Menten) process in three models [11, 18, 21], and mixed (linear and nonlinear) in the remaining model [20]. Voriconazole is known to exhibit nonlinear clearance due to saturable metabolism via CYP2C19 at therapeutic concentrations, and as such a model that included nonlinear clearance was preferred in the hybrid model. A mixed linear and nonlinear model for clearance was chosen as it includes information from all the published materials, allowing for saturable elimination by CYP2C19 as well as linear clearance by CYP3A4, CYP2C9, and flavin-containing monooxygenase 3 (FMO3).
A time dependent clearance, due to auto-inhibition was also included, as it has been identified in two models to be of importance, and was required to describe the observed clinical data during the hybrid models validation [18, 20]. All literature models included first order absorption for oral dosing. A lag time was not included in the hybrid model.
Parameter estimates and covariates
Clearance (CL, V max, K m)
Clearance in the hybrid model was described by both a linear and nonlinear components as shown in Eq. 1
.
The linear component was described using allometric principles [29] applied to measures of body composition described by lean body weight (LBW) as shown in Eq. 2: [25, 30]
where LBW is lean body weight and LBW (70 kg) is the LBW for a typical subject with a TBW of 70 kg (54 kg for a male and 42 kg for a female).
The nonlinear component of clearance was described by a Michaelis–Menton component as shown in Eq. 3, where V max was described by using allometric principles (Eq. 4), and a time dependent function (Eq. 5) as described by Friberg: [20]
where V max,1 is the V max at 1 h, V max,inh is the maximum proportion of inhibition of V max , (T-1) is the time (in hours)-1, T50 is the time to 50 % of inhibition after initiation of dosing. To improve model stability, V max at 1 h (V max,1) was the parameter estimated by the authors as there were no information on V max at time zero.
To determine the hybrid models clearance parameters shown above in Eqs. 2–6, estimates of CL from each of the published population pharmacokinetic models were simulated to generate a distribution of CL values that varied by LBW and age, as well as concentration. In the case of the Friberg model, CL was simulated after 48 h of therapy to allow the time-dependent V max of the Friberg model to come to steady-state. This distribution of CL values was then used to determine the hybrid model parameters using a least squares approach. The simulations were conducted in the following way (Fig. 1).
(a) 15 subjects for each age between 2 and 84 (total of 1245) were randomly sampled from the NHANES dataset (1999–2010) [31] where weight, height, age, and sex was available. This provided virtual subjects with differing ages. LBW was then computed and adjusted for paediatric subjects [30, 32].
(b) For each subject, a plasma concentration of voriconazole was randomly generated from a uniform distribution between 1 and 6 mg/L and assigned to a time of 48 h.
(c) For each of the 1245 subjects in the dataset, a value for total CL was computed using each of the applicable models. For a model to be applicable the weight and age of the subject must be within the range of the population in whom the model was developed. Finally a mean value of total CL for each individual was calculated from the values of total CL computed from the applicable literature models. Paediatric subject was defined as <12 years or 12–14 years and weighing <50 kg.
(d) Finally, nonlinear least-squares regression techniques using the “nls” command in R (which computes nonlinear (weighted) least-squares estimates of the parameters of a nonlinear model [33]) were used to obtain overall estimates of CL (linear), K m , V max , and the exponent on LBW that best described the values of mean total CL for each subject. The parameterisation and estimates for the time-dependency shown in Eq. 5 were adopted from the Friberg model [20]. The V max at 1 h was calculated from the steady-state value, and maximum proportion of inhibition (V max,Inh ).
The final parameter estimates for clearance are displayed in Table 3. Figure 2 represents the average clearance for each subject and the predicted clearance from the hybrid model. It can be seen that there are some high values of clearance calculated from the population models that are not captured by the hybrid model. These values reflect larger paediatric subjects with low random voriconazole concentrations.
Central volume (V c ), peripheral volume (V p ) and inter-compartmental clearance (Q)
Voriconazole is a relatively lipophilic drug with a partition coefficient of 1.8 [34], and as such it is biologically plausible that volume parameters will increase with TBW [35]. For simplicity, Q was also scaled to TBW. Distributions of V c , V p and Q were simulated from the literature models using similar methods defined above for CL. Allometrically scaled TBW with an exponent of 1 was used as displayed in Eq. 7–9 with best-fit parameters shown in Table 3.
Oral bioavailability (F)
Estimates of F from the models were highly variable, with many including between occasion variability (BOV). Paediatric subjects were reported to have a lower F than adults. The exclusive paediatric study estimated F at 45 %, whilst the integrated analysis including adult and adolescents with the same paediatric data estimated F at 64 %. It was concluded that F in adults may be underestimated as the absorption rate constant (k a ) was fixed to 100 with a lag time of 1 h, therefore omitting part of the concentration time curve [20]. Overall the estimates were generally much lower than the 96 % quoted in the product information [36]. A logit transformation was used in the hybrid model to constrain the estimates to a maximum of 100 % as shown in Eq. 10–11. An estimate of 54 % for paediatrics and 85 % for adults was included in the hybrid model.
Absorption rate constant (k a )
Estimates of k a varied across the studies from 0.458 to 3.85 with one study fixing the value to 100 with an absorption lag time of 1 h [20]. For simplicity, the median value of k a of 1.0 was selected for the hybrid model.
The differential equations describing the structural model are displayed in Eqs. 12–14:
where A(1) is the amount in compartment 1 (gut), A(2) is the amount in compartment 2 (central), and A(3) is the amount in compartment 3 (peripheral).
Between subject variability (BSV)
BSV terms varied between the studies described with exponential errors or additive errors on log-transformed concentration data (Table 2). Logit transformations were often included on F to constrain values between 0 and 1. One model included study specific covariates on many parameter values making external applicability of the results difficult [20]. Exponential BSV terms were included in the hybrid model for V max , K m , CL (linear), V c , and V p . An additive BSV on F within a logit transformation was used, with values calculated based on the approximate average of the literature models as shown in Table 2.
Residual unexplained variability (RUV)
The residual unexplained variability (RUV) was generally high in all the published models. The impact of a high RUV on MBPD will result in inability to estimate individual parameters, with variability accounted for by the RUV. As such, a value for RUV was selected with a variance of 0.1, which equates to approximately 30 % coefficient of variation (CV).
Covariates
Covariates on parameters varied between the studies. Where CYP2C19 genotype for individuals was available, it was often included as a covariate on CL. An adjustment for CYP2C19 genotype for V max was included in the hybrid model (adopted from the Dolton model [18]), as shown in Eq. 15, but this is only of importance in initial dosing. If genotype is not available in the clinical setting (as is often the case), subjects should be initially dosed as extensive metabolisers. Once TDM is available, knowledge of an individual genotype adds no benefit to the predictive performance of the hybrid model (see discussion). Concurrent medication is an important covariate on clearance and vital if estimating initial doses. CYP inducers including phenytoin, rifampicin and St Johns Wort, as well as inhibitors such as short-term ritonavir and efavirenz, will have an effect on voriconazole clearance, and are important for initial dosing. Studies have demonstrated an increase in total clearance of between 100 and 300 % with rifampicin and phenytoin [13, 18, 37–41]. A reduction in total clearance of approximately 50 % has been demonstrated for concomitant short term ritonovir [18]. An empiric adjustment for concomitant medications on clearance was therefore included in the hybrid model as shown in Eq. 16:
where EnzInhib is equal to 1 for subjects on and enzyme inhibitor and 0 for subjects not an enzyme inhibitor and EnzInd is equal to 1 for subjects on and enzyme inducer and 0 for subjects not on an enzyme inducer.
Validation of hybrid model
Overall the hybrid model demonstrated similar concentration time profiles with the combination of all the literature models capturing the majority of the variability as displayed in Figs. 3a, b. Following the loading doses in adult subjects, the hybrid model simulated lower median Ctroughs than the median from the combined literature models. This is as a result of the hybrid model containing a time-dependent V max due to auto-inhibition of metabolism resulting in initial higher clearances. Only one of the adult population models used in the combined literature models contained a time-dependent V max .
Predictive performance of hybrid model
Apart from patient three, the hybrid model demonstrated good predictive performance with good precision and minimal bias (Table 4). Figure 4 displays the predicted concentration time profiles for sampling strategy 1. The results for the remaining sampling strategies are given in online resource 3. Sampling strategy 1, with only a 12 and 13 h concentration used to estimate individual PK parameters, performed well with the lowest bias with or without including patient 3. As expected, the RMSE reduced, as more PK samples were available when patient 3 was excluded.
Discussion
Choosing which PPK model to use in MBPD is challenging if many are available in the literature. The ‘best model’ approach seems flawed as it ignores all the information from the models not selected, and may miss extremely important features of a model such as time-dependent or nonlinear CL. Additionally, models for specific populations, such as liver transplant recipients or ICU patients, often have small subject numbers limiting the modelers ability to estimate the BSV parameters as well as important covariates effects [8, 22]. Also, selecting a model developed in a specific population has many practical limitations as multiple models would be required depending up the clinical condition, which increases complexity and decreases applicability to the general patient. Further by relying on the precision of the parameter estimates and the magnitude of the RUV is flawed as they are largely dependent on study design and modeler. We therefore propose that companies that offer MBPD services consider integrating knowledge from the combined literature, which includes PPK models and other known information about the compound, to develop a hybrid model that is analogous to a meta-analysis to summarise clinical trial outcome data.
Performance of the hybrid model
The hybrid model functioned well in both validation and predictive performance. Simulations from the hybrid model overlaid with simulations from the published models demonstrated satisfactory functioning with the majority of the variability captured. The predictive performance of the model, using limited samples to predict future concentrations, was impressive apart from one patient. Patient 3 displayed unusual kinetics with low concentrations early on, followed by increasing concentrations in the second week of therapy. It was behavior that would be expected as a result of an interacting drug being initiated or a dose change. The variable PK in this subject was not captured or estimated well by the hybrid model. Surprisingly using two samples only, at 12 and 13 h, performed well with the lowest bias. As expected, the precision improved as the number of samples increased for each individual when patient three was excluded.
Practical application and development of model
The goal of this paper was to develop a hybrid model that summarises the published population models, as well as other information including biological plausibility, for the exclusive application in MBDF. This process is not trivial, is time intensive and requires skills in modeling and simulation. However, failure to consider this approach could result in poor MBPD predictions, especially where important aspects of a model such as nonlinear CL or important covariates are ignored. Furthermore, covariates included in a hybrid model for MBPD should be biologically plausible, identified in population models, and available at the bedside to clinically aid in dosage decisions. Examples include creatinine clearance for renally cleared drugs, body size descriptors (TBW, LBW etc.).
Although CYP2C19 genotype is statistically important in explaining the variability between subjects dose and exposure it is of little benefit for MBPD after TDM results become available. Simulated concentrations for both extensive and poor metabolisers from the Dolton model are presented in Fig. 5 [18]. There is significant overlap between genotype and phenotype which occurs for many reasons, such as an increase in CYP3A4 metabolism and a reduction in CYP2C19 activity [42]. The only perceived benefit of CYP2C19 genotype in MBPD is in initial dosing, where unfortunately it is seldom available. If CYP2C19 genotype is not available, in our opinion, based on the overlap in the distribution of exposures between genotypes, it is far more beneficial to dose all subjects as extensive metabolisers and use MBPD early to allocate an individual to a phenotype.
To illustrate this point, the hybrid model was used to simulate plasma concentrations of five poor and extensive metabolisers for 7 days of therapy. Plasma concentration simulated at 12, 13 and 72 h were used to estimate the subjects PK parameters and subsequent Ctrough and AUC τ following 7 days of therapy for both the hybrid model, and the hybrid model without the CYP2C19 genotype covariate. Plots of the simulated and estimated concentration time curve for the subjects are presented in online resource 4. The exclusion of CYP2C19 genotype from the model has minimal impact on the bias or precision in the estimates of the exposure metrics as measured by ME and RMSE (online resource 5) adding further weight to the argument that genotype it is of little benefit for MBPD after TDM results become available. Concurrent medications are clinically available for dosing decisions and should be used in first dose recommendations. Similarly, we believe they are of little benefit once TDM results become available, unless the interacting medications are adjusted during voriconazole therapy.
Voriconazole is licensed to be dosed based on body weight and thus the inclusions of body size descriptors such as TBW and LBW as covariates on clearance and volume parameters were investigated. Biological plausibility as well as population model finding must be considered. None of the population models had body weight as a linear covariate on clearance except an exclusive paediatric study (ages 2– <12) [21]. An integrated paediatric–adult model, which included the majority of the subjects from the exclusive paediatric study, allometrically scaled clearance on TBW [20]. This demonstrates that although a linear relationship between clearance and body weight within a limited weight ranged of paediatric subjects was concluded, once the weight ranges analysed were extended to include adults, the effect of body weight on clearance was better explained by an allometrically scaled relationship. This idea has also been presented in a meta-analysis of 458 PPK models [25]. This showed that although many models had no covariate relationships or a linear relationship with body weight, when pooled together, was better described by allometry using body composition. It is also of interest that none of the exclusive adult studies found a significant relationship between CL and TBW. Several observation studies have reported an association between larger body size and higher voriconazole plasma concentrations [43, 44]. This is consistent with the theory that voriconazole’s clearance does not increase linearly with TBW and using licensed dosing recommendations will result, on average, in higher exposures in larger patients. It is not biologically plausible however that body weight will not impact to some extent on clearance. Previous research has demonstrated that LBW is a potentially superior descriptor of body compositions effect on clearance than total body weight, as 99 % of the metabolic processes, including clearance occur in lean tissue [45]. An open label study in obese subjects demonstrated the correlation between LBW and AUC (0.42) greater than any other descriptor of body size including adjusted body weight (ABW) (0.38), ideal body weight (IBW) (0.31) and TBW (0.14) [46]. An allometrically scaled relationship between clearance and LBW was used in the hybrid model.
Body weight as a covariate on V c and V p was included in two of the population models [20, 21]. Voriconazole is a lipophilic drug and V c and V p would be expected to increase with TBW. As such a linear relationship between TBW and V c , V p and Q was included in the hybrid model.
A non-compartmental analysis of a multi-dose oral study in healthy volunteers demonstrated an approximate doubling in both C max and AUC in young females compared to young males [47]. However as sex was not identified as a covariate in any of the PPK models and biological plausibility is unclear it was not included in the hybrid model.
The higher F values in adults compared to paediatrics may be due to multiple factors including healthy volunteers in adult models, which allow for tight control over dosing with relation to food. It is well known that food decreases the AUC of voriconazole [48]. It may also partially be explained by the fact that paediatrics have a larger liver blood flow per mass, which in turn increases the first pass metabolism [21] and in vitro results which demonstrate greater activity of CYP2C19 and FMO in paediatrics [49]. The inclusion of BOV on F is of no benefit in MBPD as it adds extra variability to predictions and was excluded from the hybrid model.
Limitations and discussion of alternative methods
The development of a hybrid model is a potential method for model choice in MBPD. There are several limitations and alternative methods that could have been used. The weighting scheme used can potentially have a large impact on the final model parameters.
Typically in a meta-analysis, weighting is carried out inverse to the variance of the estimate of treatment effect, as this is the maximum likelihood estimator for the fixed-effects parameter and closely correlated with sample size. There are many difficulties encountered when attempting to use the variance of parameter estimates as a weighting scheme in the development of hybrid PPK models. Firstly, models developed in the non-parametric framework cannot be utilised. Secondly, variances can be calculated using many methods such as bootstrapping and NONMEM’s sandwich matrix, and this is often not reported in papers. Thirdly, parameters such as F are often logit transformed and it is difficult to compare variances on difference scales. Finally data driven parameters such as TLag and F will often report low variances and will place undue weighting on a particular study.
Two other proposed methods for weighting include the number of subjects and number of samples included in the analysis. Both options have merit as they are related to the amount of information contained in the PPK model. However the information on the parameters is dependent upon the types of subjects and sampling times included in the data.
For the prior reasons we choose a simpler option, to apply equal weighting to all studies. Using the previous methods detailed, the weightings applied to the studies are based to a large extent on the design of the datasets that were used to construct the models. This can lead to the down weighting a very good model that is based on a poorly designed dataset. Equal weighting allows you to express your prior ignorance and allow the likelihood associated with your data to distinguish between the models.
How well the hybrid model performs with dose recommendations and subsequent dose changes is unclear. Given the nonlinear kinetics the voriconazole displays the ability for the model to estimate the individuals K M value is pivotal for accurate dose recommendations. Future prospective and retrospective assessment, clinical validation, and comparison to current dosing methods is planned. Additionally the development of a dosing nomogram from the hybrid model.
MBPD is currently an underutilised tool in personalising a patient’s medication dosage. There are currently many barriers to the implementation of MBPD in clinical practice including acceptance by clinicians, robust outcome data and access to sophisticated intuitive software. This paper addresses some of the issues and offers a practical solution to many of the problems faced by taking into account all the information currently available, importantly in conjunction with biological plausibility. Furthermore, it presents the first joint model for voriconazole in the literature, which we believe is intuitively superior to existing models because of the inclusion of all the available literature through biological plausibility. However validation and comparison with existing models needs to be undertaken before this model is ready to study in clinical practice.
Supplementary files are available with descriptions of subjects and simulations of the impact of the CYP2C19 on model predictive performance.
References
Sheiner LB (1969) Computer-aided long-term anticoagulation therapy. Comput Biomed Res Int Journal 2(6):507–518
Jelliffe R, Neely M, Schumitzky A, Bayard D, Van Guilder M, Botnen A, Bustad A, Laing D, Yamada W, Bartroff J, Tatarinova T (2011) Nonparametric population modeling and Bayesian analysis. Pharmacol Res Off J Ital Pharmacol Soc 64(4):426
Jelliffe RW, Schumitzky A, Bayard D, Milman M, Van Guilder M, Wang X, Jiang F, Barbaut X, Maire P (1998) Model-based, goal-oriented, individualised drug therapy. Linkage of population modelling, new ‘multiple model’ dosage design, Bayesian feedback and individualised target goals. Clin Pharmacokinet 34(1):57–77
Jelliffe RW, Schumitzky A, Van Guilder M, Liu M, Hu L, Maire P, Gomis P, Barbaut X, Tahani B (1993) Individualizing drug dosage regimens: roles of population pharmacokinetic and dynamic models, Bayesian fitting, and adaptive control. Ther Drug Monit 15(5):380–393
Upton RN, Mould DR (2014) Basic concepts in population modeling, simulation, and model-based drug development: part 3-introduction to pharmacodynamic modeling methods. CPT Pharmacomet Syst Pharmacol 3:e88
Mould DR, Upton RN (2012) Basic concepts in population modeling, simulation, and model-based drug development. CPT Pharmacomet Syst Pharmacol 1:e6
Mould DR, Upton RN (2013) Basic concepts in population modeling, simulation, and model-based drug development-part 2: introduction to pharmacokinetic modeling methods. CPT Pharmacomet Syst Pharmacol 2:e38
Roberts JA, Abdul-Aziz MH, Lipman J, Mouton JW, Vinks AA, Felton TW, Hope WW, Farkas A, Neely MN, Schentag JJ, Drusano G, Frey OR, Theuretzbacher U, Kuti JL, on behalf of The International Society of Anti-Infective Pharmacology and the Pharmacokinetics and Pharmacodynamics Study Group of the European Society of Clinical Microbiology and Infectious Diseases (2014) Individualised antibiotic dosing for patients who are critically ill: challenges and potential solutions. Lancet Infect Dis 14 (6):498–509
Lepak AJ, Andes DR (2011) Antifungal PK/PD considerations in fungal pulmonary infections. Semin Respir Crit Care Med 32(6):783–794
Han K, Capitano B, Bies R, Potoski BA, Husain S, Gilbert S, Paterson DL, McCurry K, Venkataramanan R (2010) Bioavailability and population pharmacokinetics of voriconazole in lung transplant recipients. Antimicrob Agents Chemother 54(10):4424–4431
Hope WW (2012) Population pharmacokinetics of voriconazole in adults. Antimicrob Agents Chemother 56(1):526–531
Dolton MJ, Ray JE, Chen SC, Ng K, Pont LG, McLachlan AJ (2012) Multicenter study of voriconazole pharmacokinetics and therapeutic drug monitoring. Antimicrob Agents Chemother 56(9):4793–4799
Pascual A, Csajka C, Buclin T, Bolay S, Bille J, Calandra T, Marchetti O (2012) Challenging recommended oral and intravenous voriconazole doses for improved efficacy and safety: population pharmacokinetics-based analysis of adult patients with invasive fungal infections. Clin Infect Dis 55(3):381–390
Hamada Y, Seto Y, Yago K, Kuroyama M (2012) Investigation and threshold of optimum blood concentration of voriconazole: a descriptive statistical meta-analysis. J Infect Chemother 18(4):501–507
Miyakis S, van Hal SJ, Ray J, Marriott D (2010) Voriconazole concentrations and outcome of invasive fungal infections. Clin Microbiol Infect 16(7):927–933
Pascual A, Calandra T, Bolay S, Buclin T, Bille J, Marchetti O (2008) Voriconazole therapeutic drug monitoring in patients with invasive mycoses improves efficacy and safety outcomes. Clin Infect Dis 46(2):201–211
Retout S, Mentré F (2003) Further developments of the Fisher information matrix in nonlinear mixed effects models with evaluation in population pharmacokinetics. J Biopharm Stat 13(2):209–227
Dolton MJ, Mikus G, Weiss J, Ray JE, McLachlan AJ (2014) Understanding variability with voriconazole using a population pharmacokinetic approach: implications for optimal dosing. J Antimicrob Chemother 69(6):1633–1641
Wang T, Chen S, Sun J, Cai J, Cheng X, Dong H, Wang X, Xing J, Dong W, Yao H, Dong Y (2013) Identification of factors influencing the pharmacokinetics of voriconazole and the optimization of dosage regimens based on Monte Carlo simulation in patients with invasive fungal infections. J Antimicrob Chemother 69(2):463–470
Friberg LE, Ravva P, Karlsson MO, Liu P (2012) Integrated population pharmacokinetic analysis of voriconazole in children, adolescents, and adults. Antimicrob Agents Chemother 56(6):3032–3042
Karlsson MO, Lutsar I, Milligan PA (2009) Population pharmacokinetic analysis of voriconazole plasma concentration data from pediatric studies. Antimicrob Agents Chemother 53(3):935–944
Han K, Bies R, Johnson H, Capitano B, Venkataramanan R (2011) Population pharmacokinetic evaluation with external validation and Bayesian estimator of voriconazole in liver transplant recipients. Clin Pharmacokinet 50(3):201–214
Nomura K, Fujimoto Y, Kanbayashi Y, Ikawa K, Taniwaki M (2008) Pharmacokinetic–pharmacodynamic analysis of voriconazole in Japanese patients with hematological malignancies. Eur J Clin Microbiol Infect Dis 27(11):1141–1143
Bonate PL (2005) Pharmacokinetic–pharmacodynamic modeling and simulation. Springer, New York
McLeay SC, Morrish GA, Kirkpatrick CMJ, Green B (2012) The relationship between drug clearance and body size: systematic review and meta-analysis of the literature published from 2000 to 2007. Clin Pharmacokinet 51(5):319–330
Holford N (2005) The Visual Predictive Check Superiority to Standard Diagnostic (Rorschach) Plots. Paper presented at the PAGE 14, Pamplona, Spain. http://www.page-meeting.org/?abstract=738. Accessed 1 Dec 2015
Continuous National Health and Nutrition Examination Survey. National Center for Health Statistics Center for Disease Control and Prevention. http://wwwn.cdc.gov/nchs/nhanes/search/nhanes_continuous.aspx. Accessed 29 April 2015
Brüggemann RJM, Blijlevens NMA, Burger DM, Franke B, Troke PF, Donnelly JP (2010) Pharmacokinetics and safety of 14 days intravenous voriconazole in allogeneic haematopoietic stem cell transplant recipients. J Antimicrob Chemother 65(1):107–113
Anderson BJ, Holford NHG (2008) Mechanism-based concepts of size and maturity in pharmacokinetics. Annu Rev Pharmacol Toxicol 48:303–332
Janmahasatian S, Duffull SB, Ash S, Ward LC, Byrne NM, Green B (2005) Quantification of lean bodyweight. Clin Pharmacokinet 44(10):1051–1065
(CDC). CfDCaP (2014) National Health and Nutrition Examination Survey Data. National Center for Health Statistics (NCHS), Hyattsville, MD
Al-Sallami H, Goulding A, Taylor R, Grant A, Williams S, Duffull S (2011) A semi-mechanistic model for estimating fat free mass in children. Paper presented at the Population Analysis Group Europe, Athens. http://www.page-meeting.org/page/page2011/PAGEPosters.pdf. Accessed 1 Dec 2015
Development Core Team R (2014) R: a language and environment for statistical computing. R Found Stat Comput, Vienna
Damle B, Varma MV, Wood N (2011) Pharmacokinetics of voriconazole administered concomitantly with fluconazole and population-based simulation for sequential use. Antimicrob Agents Chemother 55(11):5172–5177
Green B, Duffull SB (2004) What is the best size descriptor to use for pharmacokinetic studies in the obese. Br J Clin Pharmacol 58(2):119–133
Gilbert DN The Sanford guide to antimicrobial therapy 2011. Antimicrobial Therapy, Inc., Sperryville
Rengelshausen J, Banfield M, Riedel K-D, Burhenne J, Weiss J, Thomsen T, Walter-Sack I, Haefeli WE, Mikus G (2005) Opposite effects of short-term and long-term St John’s wort intake on voriconazole pharmacokinetics. Clin Pharmacol Ther 78(1):25–33
Alffenaar J-WC, van der Elst KCM, Uges DRA, Kosterink JGW, Daenen SMGJ (2009) Phenytoin-induced reduction of voriconazole serum concentration is not compensated by doubling the dosage. Br J Clin Pharmacol 68(3):462–463
Purkins L, Wood N, Ghahramani P, Love ER, Eve MD, Fielding A (2003) Coadministration of voriconazole and phenytoin: pharmacokinetic interaction, safety, and toleration. Br J Clin Pharmacol 56(Suppl 1):37–44
Spriet I, Meersseman P, Meersseman W, de Hoon J, Willems L (2010) Increasing the dose of voriconazole compensates for enzyme induction by phenytoin. Br J Clin Pharmacol 69(6):701–702
Verweij PE, de Pauw BE, Meis JF (1999) Voriconazole (Pfizer ltd). IDrugs 2(9):925–937
Hyland R, Jones BC, Smith DA (2003) Identification of the cytochrome P450 enzymes involved in the N-oxidation of voriconazole. Drug Metab Dispos 31(5):540–547
Koselke E, Kraft S, Smith J, Nagel J (2012) Evaluation of the effect of obesity on voriconazole serum concentrations. J Antimicrob Chemother 67(12):2957–2962
Hoenigl M, Duettmann W, Raggam RB, Seeber K, Troppan K, Fruhwald S, Prueller F, Wagner J, Valentin T, Zollner-Schwetz I, Wölfler A, Krause R (2013) Potential factors for inadequate voriconazole plasma concentrations in intensive care unit patients and patients with hematological malignancies. Antimicrob Agents Chemother 57(7):3262–3267
Han PY, Duffull SB, Kirkpatrick CM, Green B (2007) Dosing in obesity: a simple solution to a big problem. Clin Pharmacol Ther 82(5):505–508
Pai MP, Lodise TP (2011) Steady-state plasma pharmacokinetics of oral voriconazole in obese adults. Antimicrob Agents Chemother 55(6):2601–2605
Theuretzbacher U, Ihle F, Derendorf H (2006) Pharmacokinetic/pharmacodynamic profile of voriconazole. Clin Pharmacokinet 45(7):649–663
Purkins L, Wood N, Kleinermans D, Greenhalgh K, Nichols D (2003) Effect of food on the pharmacokinetics of multiple-dose oral voriconazole. Br J Clin Pharmacol 56(Suppl 1):17–23
Yanni SB, Annaert PP, Augustijns P, Ibrahim JG, Benjamin DK Jr, Thakker DR (2010) In vitro hepatic metabolism explains higher clearance of voriconazole in children versus adults: role of CYP2C19 and flavin-containing monooxygenase 3. Drug Metab Dispos 38(1):25–31
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D.A.J.M. is supported by an Australian Postgraduate Award.
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B.G. and J.M. declare no conflicts of interest. E.G.P. is a member of the Antifungal Advisory Boards of Pfizer and Merck.
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McDougall, D.A.J., Martin, J., Playford, E. et al. Determination of a suitable voriconazole pharmacokinetic model for personalised dosing. J Pharmacokinet Pharmacodyn 43, 165–177 (2016). https://doi.org/10.1007/s10928-015-9462-9
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DOI: https://doi.org/10.1007/s10928-015-9462-9