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Antimicrob Agents Chemother. 2016 November; 60(11): 6806–6812.
Published online 2016 October 21. Prepublished online 2016 September 6. doi:  10.1128/AAC.00970-16
PMCID: PMC5075089

Comparative Evaluation of the Predictive Performances of Three Different Structural Population Pharmacokinetic Models To Predict Future Voriconazole Concentrations

Abstract

Bayesian methods for voriconazole therapeutic drug monitoring (TDM) have been reported previously, but there are only sparse reports comparing the accuracy and precision of predictions of published models. Furthermore, the comparative accuracy of linear, mixed linear and nonlinear, or entirely nonlinear models may be of high clinical relevance. In this study, models were coded into individually designed optimum dosing strategies (ID-ODS) with voriconazole concentration data analyzed using inverse Bayesian modeling. The data used were from two independent data sets, patients with proven or suspected invasive fungal infections (n = 57) and hematopoietic stem cell transplant recipients (n = 10). Observed voriconazole concentrations were predicted whereby for each concentration value, the data available to that point were used to predict that value. The mean prediction error (ME) and mean squared prediction error (MSE) and their 95% confidence intervals (95% CI) were calculated to measure absolute bias and precision, while ΔME and ΔMSE and their 95% CI were used to measure relative bias and precision, respectively. A total of 519 voriconazole concentrations were analyzed using three models. MEs (95% CI) were 0.09 (−0.02, 0.22), 0.23 (0.04, 0.42), and 0.35 (0.16 to 0.54) while the MSEs (95% CI) were 2.1 (1.03, 3.17), 4.98 (0.90, 9.06), and 4.97 (−0.54 to 10.48) for the linear, mixed, and nonlinear models, respectively. In conclusion, while simulations with the linear model were found to be slightly more accurate and similarly precise, the small difference in accuracy is likely negligible from the clinical point of view, making all three approaches appropriate for use in a voriconazole TDM program.

INTRODUCTION

Voriconazole is a triazole antifungal that exhibits broad-spectrum activity and is a first-line agent for the treatment of Candida sp. infections (1), invasive aspergillosis (2), and other serious fungal infections. With increasing numbers of at-risk immunocompromised populations, such as those undergoing solid-organ transplantation or those with HIV infections, the incidence of invasive mycoses is on the rise (3, 4). Despite the advent of newer antifungals, Aspergillus sp. and Candida sp. infections have exhibited high mortality rates of 60% and 30%, respectively (5, 6).

Recent published studies of voriconazole have shed light on the clinical relevance of therapeutic drug monitoring (TDM) for optimization of dosing based on voriconazole's highly variable pharmacokinetics (PK) and the resultant poor predictability of plasma concentrations (7, 8). Subtherapeutic concentrations have been linked to higher failure rates in patients with life-threatening invasive fungal infections, and supratherapeutic concentrations are associated with neurological and hepatic toxicity (9,19). Voriconazole is primarily metabolized by CYP2C19, which commonly exhibits genetic polymorphism, leading to variable PK and leaving certain populations susceptible to decreased metabolism and increased plasma concentrations of voriconazole (20,23). Patients of Asian descent with polymorphisms in CYP2C19 have up to a 20% incidence of being poor metabolizers while this value is up to 5% for Caucasian and African American individuals (24). Poor metabolizers can have a PK exposure up to four times higher than that of homozygous comparators.

Nonlinearity in voriconazole PK relating to saturable clearance mechanisms has been reported (8), which together with its extensive variability makes dosing profoundly challenging, especially when higher doses are used. Conversely, several previous studies have reported adequate results when voriconazole PK is described by one- and two-compartment linear models such that in one study (7) the absence of saturable elimination was noted even with dosing regimens at larger than approved levels (9, 10, 20). Incorporating adaptive feedback in PK models can allow true personalization of therapy by the design of dosing regimens that achieve the desired exposure targets with improved precision based on the observed concentrations. Bayesian feedback is highly useful for the extrapolation of the “information” contained within single or multiple voriconazole concentrations measured at any time during the course of therapy. The Bayesian system uses single or multiple voriconazole concentrations measured at any time during the course of therapy as patient-specific information to identify factors that affect different PK parameters in an individual patient and therefore drug concentrations. Once identified, PK relationships can be used to enable optimized real-time adjustment of voriconazole dosing regimens (25). In order to determine the model(s) best suited for use in a voriconazole TDM program supported by adaptive feedback and Bayesian forecasting, this study compared the predictive performance of three different voriconazole PK models (a linear model, a nonlinear model, and a mixed linear-nonlinear model) (7, 23, 26).

MATERIALS AND METHODS

Patient selection and data collection.

Two separate voriconazole data sets were used in this analysis. First, a TDM data collection and observational study was approved by the local hospital and university ethics committees (Royal Brisbane and Women's Hospital and The University of Queensland), with a waiver for informed consent granted because of the retrospective nature of the study. This first data set included adult patients who had received voriconazole for prophylaxis or treatment for suspected or proven fungal infections and who had at least two plasma voriconazole samples available from routine clinical TDM (samples were taken as peak and trough samples). Data were collected from December 2009 to July 2012. Demographic data collected included sex, age, and total body weight. Drug administration and blood sampling histories, including the route of administration, date, time, and actual dosage given, were also collected.

Second, a previously published set of voriconazole PK data and dosing information from 10 hematopoietic stem cell transplant (HSCT) recipients was also used (27). This patient group all received the FDA-approved standard regimen of 6 mg/kg every 12 h (q12h) intravenously (i.v.) for two doses followed by 4 mg/kg q12h i.v. for 2 weeks. Plasma concentration-time data from this study were extracted from the published paper using WebPlotDigitizer (http://arohatgi.info/WebPlotDigitizer/).

Determination of voriconazole concentrations.

For the first data set, voriconazole plasma samples were precipitated with two-volume equivalents of acetonitrile containing deuterated internal standards. After protein precipitation, the samples were centrifuged, and the supernatant was transferred to an autosampler vial. An aliquot of 2 μl was injected onto an ultraperformance liquid chromatography tandem mass spectrometry (UPLC-MS/MS) system operating in positive electrospray ionization (ESI) mode. Voriconazole samples and the deuterated internal standards were measured using selected reaction monitoring. The accuracy range varied from 100 to 102%; intraday precision varied between 2% and 2.9% while interday precision was between 4% and 4.5%. For the second data set, the methods used to determine voriconazole concentration have been published elsewhere (27).

Evaluation of population pharmacokinetic models.

The dosing application used to predict plasma voriconazole concentrations taking into account patient demographic and laboratory information for these analyses used individually designed optimum dosing strategies (ID-ODS) (http://www.optimum-dosing-strategies.org/). ID-ODS is a TDM and simulation tool powered by the R software (version 2.15.3; Institute for Statistics and Mathematics [http://www.r-project.org/]) (28,30). Based on patient demographic information readily available at the bedside, ID-ODS incorporates Monte Carlo simulation and inverse Bayesian modeling (31) into the design of personalized dosing regimens. Voriconazole concentration-time profiles were simulated using inverse modeling based on linear, mixed linear and nonlinear, and fully nonlinear one- and two-compartment i.v. infusion models written in the R language using the published population pharmacokinetic parameter values and respective interindividual variabilities. Changes in the estimated PK parameters were allowed to ensure that changing physiological variables were incorporated during the course of therapy.

Bland-Altman plots were constructed to evaluate the agreement between observed and predicted concentrations using the calculated percentage mean differences and their 95% limits of agreement. The 95% confidence interval (CI) for the percent mean difference was also determined such that the inclusion of the value of zero in the interval would indicate the lack of a statistically significant degree of systematic bias between the observed concentrations and model predictions. Also, it was expected that approximately 95% of the percent differences between the observed and predicted values would lie between the percent mean difference ±1.96 standard deviations (SD), called the limits of agreement. These limits of agreement were then employed to indicate whether there was any difference in magnitude between the three competing methods in the agreement for the data from the observed and the predicted concentrations (32). Prediction errors were evaluated to outline the absolute and relative biases and precision of the three dose optimization strategies. Absolute bias and precision were established by calculating mean prediction errors (ME) and mean squared prediction errors (MSE) and their 95% confidence intervals, while relative bias and precision were established by calculating the changes in mean prediction errors (ΔME) and in mean squared prediction errors (ΔMSE) and their 95% confidence intervals, respectively (33). These measures of bias and precision were identified by evaluating all predictions at once and at intervals of predictions based on sequences in the time course of therapy and as new measured concentrations became available from the first set of plasma concentrations through the fifth set of concentrations. The aim of this approach was to identify possible differences in system adaptations to measured concentrations and resulting Bayesian model predictions. Furthermore, measures of predictive performance were calculated separately for patients on dosing regimens greater than the recommended 4 mg/kg q12h to compare the models in the range of dosages where saturable elimination could be suspected (34). The clinical significance of the results was also evaluated by calculating the percent agreements between the decisions made for the need to dose adjust based on the observed versus the predicted concentrations. The chosen target trough concentration range was 2 to 5 mg/liter. For interpreting the need for dose adaptation, if the trough concentration was <2 mg/liter, the dose was increased, and if the trough concentration exceeded 5 mg/liter, then the dose was decreased. Dose adjustments were not required when the predicted or observed trough concentration was between 2 mg/liter and 5 mg/liter. Confidence intervals for the means of the error estimates were calculated by a one-sample Student's t test using the R software.

Simulation to demonstrate the clinical utility of using the patient-specific models.

We employed the Bayesian inverse modeling approach to illustrate its potential use for a simulated patient with trough concentrations predicted to be >5 mg/liter and at increased risk of concentration-dependent toxicity. This patient was to receive the standard regimen of 6 mg/kg i.v. q12 h on day 1 and then 4 mg/kg i.v. q12h onward. We used the trough concentration measured before the seventh dose to establish the patient-specific model, and then we predicted future concentrations after 2 weeks of treatment and suggested a revised dosing regimen to potentially avoid supratherapeutic concentrations.

RESULTS

Patient characteristics and dosing data.

TDM data from the two data sets included 67 adult patients with a total of 519 collected samples available for analysis. The mean number of concentrations per subject was 7.7. The patient demographic and clinical characteristics are shown in Table 1. Indications for the use of voriconazole varied among the patients, with treatment of suspected or proven fungal infections being the most common reason for administration. The doses of i.v. and oral voriconazole ranged from 200 to 400 mg and were given at intervals of 8 to 12 h, with seven patients receiving more than 8 mg/kg/day i.v. or orally following the initial i.v. loading doses (Fig. 1).

TABLE 1
Demographics and clinical characteristics of the studied patients
FIG 1
Histogram of daily voriconazole doses administered.

Comparative accuracy of observed concentrations with model-based predictions.

Three population PK models were available to predict voriconazole concentrations for the individual patients (Fig. 2) using Bayesian methods. Overall, the mean (95% CI) percent difference ranged from 3.57% (−2.33%, 9.48%) for the mixed to 7.51% (1.82%, 13.21%) for the fully nonlinear and to 11.74% (6.45%, 17.02%) for the fully linear models, respectively. The linear model was found to be slightly more in agreement with the measured concentrations, as evidenced by the narrowest range of the 95% limits of agreement (95% CI) of −108.33% (−117.47%, −99.19%) to 131.81% (122.68%, 140.95%). Plots of relative percentages for all models are shown in Fig. 3. The predictive performances of these three methods were also compared by calculating ME, MSE, ΔME, and ΔMSE. Table 2 describes the absolute and relative performances of the three approaches in terms of ME and MSE against the observed concentrations and of the ΔME and ΔMSE against the method with the leading absolute performance (the fully linear approach). Compared to the linear predictor, the mixed model showed a ΔME (95% CI) of 0.13 mg/liter (0.01 mg/liter, 0.27 mg/liter), and the nonlinear approach had a ΔME (95% CI) of 0.25 mg/liter (0.11 mg/liter, 0.40 mg/liter). All models were found to be equally precise, as evidenced by the nonsignificantly different ΔMSE (95% CI) values of 2.88 mg/liter2 (−0.82 mg/liter2, 6.59 mg/liter2) for the mixed approach and a ΔMSE (95% CI) of 2.86 mg/liter2 (−2.30 mg/liter2, 8.03 mg/liter2) for the nonlinear method.

FIG 2
(A) One-compartment model with first-order absorption and linear elimination. (B) Two-compartment model with first-order absorption and mixed linear and nonlinear (Michaelis-Menten and time-dependent Vmax) elimination. (C) Two-compartment model with first-order ...
FIG 3
Bland-Altman plots of relative differences between predicted (Pred) and observed (Obs) voriconazole concentrations against the mean of predicted and measured concentrations for the tested models. The biases and 95% limits of agreements are shown as solid ...
TABLE 2
Evaluation of the predictive performance of the studied models

The accuracy and precision of the predictions for the three methods against the observed concentrations after the first, second, third, fourth, or fifth measured set of concentrations became available for dose optimization are shown in Table 3. We found no indications of one model being particularly superior to the others, as evidenced by the constant change in the significance and magnitude of ME and MSE values for predictions based on the first through the fifth sets of concentrations. Similar results showing the lack of significant differences in predictive performance were found during analysis of 46 concentrations measured in patients receiving doses greater than 8 mg/kg/day, as evidenced by the full set of 95% CIs crossing the value of zero for the ΔME and ΔMSE measurements (Table 4). The difference in the predictions from the studied models in terms of whether a dose adjustment is indicated was established using 356 trough concentration measurements. Dose adjustment decisions predicted by the three methods agreed with the decisions determined by the observed concentrations 79.5%, 78.9%, and 78.7% of the time for the linear, mixed, and nonlinear models, respectively.

TABLE 3
Evaluation of the predictive performance of the studied models against the observed concentrations after the first, second, third, fourth, or fifth measured set of concentrations became available for dose optimization
TABLE 4
Evaluation of the predictive performance of the studied models in patients receiving a voriconazole dose of >8 mg/kg daily

Simulation to demonstrate clinical utility of using the patient-specific models.

The usefulness of the patient-specific models for TDM is illustrated in Fig. 4, which represents a patient for whom the standard voriconazole regimen after time results in a trough concentration that is higher than the target of <5 mg/liter. Adjusting the dose to 3 mg/kg q12h i.v. starting with the seventh dose would satisfactorily correct the plasma profile and would achieve trough concentrations in the safe range of 2 to 5 mg/liter.

FIG 4
Simulation to demonstrate clinical utility of using the patient-specific models. A patient receiving the standard regimen of 6 mg/kg i.v. every 12 h, followed by 4 mg/kg twice a day, had a trough sampled before the seventh dose (open triangle) which was ...

DISCUSSION

An aim of the published PK models studied here is to predict voriconazole concentrations from dosing regimens in individual patients. Indeed, aiming for voriconazole exposures associated with maximal clinical effects will increase the likelihood of optimal treatment outcomes, including minimization of the emergence of drug toxicity. The results of this analysis appear to confirm the suitability of all three models for accurately and precisely predicting voriconazole concentrations in a heterogeneous cohort of patients. We found similar frequencies of dose adjustments recommended by the linear, mixed, and nonlinear models at 79.5%, 78.9%, and 78.7%, respectively.

The use of standardized voriconazole dosing regimens has proved to be inadequate at achieving optimal target therapeutic exposures in various clinical settings (7, 8). In a population PK and Monte Carlo simulation study, the proportions of patients (n = 64) receiving i.v. and oral voriconazole with concentrations outside the recommended therapeutic range were 43.3% and 58.5%, respectively (8). Utilizing a priori and a posteriori PK approaches to dosing can increase the likelihood of achieving optimum PK/pharmacodynamic (PD) targets of voriconazole.

The relationship between voriconazole plasma exposure and improved clinical outcomes was initially described in a phase II study of voriconazole for invasive aspergillosis. In this study, a serum concentration of <0.25 mg/liter was associated with a higher probability of clinical failure (35). In another study of 34 patients with hematological disease given chemotherapy, all TDM patients with voriconazole serum concentrations of >2 mg/liter showed positive response. Two out of six TDM patients with concentrations of <2 mg/liter were nonresponders (16). Meanwhile, in a multicenter study of voriconazole PK and TDM involving 201 patients, 26% of patients with concentrations of <1.7 mg/liter failed treatment while only 7% of patients with concentrations of >1.7 mg/liter were nonresponders (14). Comparable serum concentrations for treatment failure were found in a study by Pascual et al., where patients with concentrations of <1.5 mg/liter had <85% probability of response (11). A higher target (e.g., 2 mg/liter) may be warranted if there is disease with a poor prognosis (e.g., central nervous system [CNS] infection, bulky disease, or multifocal infection). This target is also supported by a number of retrospective studies suggesting a relationship between drug exposure and positive results, where the target concentration of ≥2 mg/liter was identified as being associated with improved outcomes (13,16, 36). Studies completed to evaluate effects of voriconazole TDM on patient outcomes have also yielded promising results. Park et al. compared clinical outcomes in patients who had voriconazole dosages adjusted based on plasma concentrations with the outcomes in those who received a fixed regimen. In this study, outcome measures of complete or partial response and a reduction in rate of drug discontinuation resulting from adverse side effects in patients undergoing TDM were significantly better than those in the non-TDM group (18).

The evidence supporting the need for an upper concentration threshold with voriconazole is based on data of neurotoxic adverse events (such as hallucinations, confusion, and encephalopathy), which appear to be associated with a steep exposure-response relationship, as opposed to a weaker exposure-response relationship with hepatotoxicity (37). While voriconazole toxicity thresholds of <5 mg/liter have been identified in some studies, the recently updated 2016 practice guidelines for the diagnosis and management of aspergillosis from the Infectious Diseases Society of America (IDSA) support an upper threshold of <5 to 6 mg/liter to minimize toxicity (2).

The present study is highly valuable and establishes that the currently available published PK models for voriconazole are all suitable for inclusion in Bayesian forecasting (with or without adaptive feedback) software. Such an approach is likely to result in a more rapid achievement of therapeutic voriconazole exposures. Interestingly, the results of our comparison for the predictive performance of the Bayesian models established using TDM data in a diverse group of patients showed a numerical advantage for reduced bias for the linear model over the two other models. No significant difference was found in precision measures. The favorable, although likely clinically insignificant, performance of the linear model compared to that of the often cited nonlinear PK models of voriconazole is perhaps unsurprising for the following reasons. First, published reports in adult and pediatric patients in the past appropriately described voriconazole PK with one- or two-compartment linear models wherein the evaluation of the structural approaches with nonlinear elimination did not result in improved prediction of the observed concentrations compared with that with the linear models (9, 10, 20). Second, we used a sequential approach to Bayesian modeling, which allowed the PK parameter values to change during the course of therapy. Prior analysis using this approach also reported improved predictive performance for aminoglycosides and vancomycin. That study hypothesized that the superior predictions were due to the better adaptation of the models to the patients' changing physiologic parameters (38). Third, the dosing regimens and the patient population evaluated in our study were unlikely to represent the ideal population to show meaningful variability in dose- and metabolism-related differences in saturable metabolism of voriconazole. Our population consisted of mostly patients of Caucasian descent for whom the percentage of the population expected to exhibit nonlinear clearance is equal to or less than 5%. Fourth, the identification of nonlinear PK of voriconazole is commonly realized in subjects with dosing regimens that are altered over time, a strategy that was infrequently applied in our cohort of patients. Moreover, the nonlinearity in PK has been previously described at doses of 10 mg/kg/day or higher, a daily dose intensity that was achieved in only two patients, representing a small portion of the studied population here (34).

Another aspect of the study relevant for the clinical setting is the rather inconsistent change—as opposed to the clear improvement one may expect—in the measures of predictive performance of the models as the number of observed concentrations included in the modeling process increased during the course of therapy. This may be the result of the inherent limitations of our data, which were derived mostly from therapeutic drug monitoring of voriconazole trough concentrations, a rather poorly informative concentration-time point design. The purpose of trough concentration monitoring for voriconazole is mainly to ensure that the trough measurement is within the therapeutic range and not necessarily to describe the exact pharmacokinetic profile of a specific patient. Optimal sampling times, a potentially more onerous approach to the day-to-day care of the patient, that are maximally informative can be used to more accurately describe individual voriconazole pharmacokinetics that, when applied, may have the potential to improve predictions of future concentrations in the clinical setting (8).

The last limitation of these results may be that our cohort of patients were subjects with hematological malignancies, exclusive of the solid-organ transplant population, a group where voriconazole pharmacokinetics are likely to be influenced by specific covariates that are distinctive of that subset of the population. Therefore, extrapolating this study's results to those patients may not be appropriate (20).

Conclusion.

To the best of our knowledge, this is the first paper comparing the predictive performance of the Bayesian models using linear, mixed linear and nonlinear, and fully nonlinear structural approaches in patients where voriconazole was used for treatment or prophylaxis of fungal infections. We found the predictive performance of all models to be sufficient for use in daily practice and for TDM, and we found that these models tend to slightly overestimate the observed concentrations, which in some circumstances could potentially lead to the design of suboptimal dosing regimens resulting in higher risks of treatment failure but a lower risk of toxicity in the clinical setting. The observed values of ΔME (95% CI) of 0.13 mg/liter (0.01 mg/liter, 0.27 mg/liter) for the mixed model and the ΔME (95% CI) of 0.25 mg/liter (0.11 mg/liter, 0.40 mg/liter) for the nonlinear approach compared to the values with the linear method in our opinion represent a clinically insignificant difference in accuracy, making all three ways equally adaptable for use in the clinical setting for a TDM program.

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