Predicting the dose of vancomycin in ICU patients receiving different types of RRT therapy: a model‐based meta‐analytic approach

Abstract

Aim

Previous pharmacokinetic (PK) studies have proposed various dosing regimens for vancomycin in intensive care unit (ICU) patients undergoing renal replacement therapy (RRT), but all are restricted to specific RRT modalities. To be useful in practice, a population PK model would need to predict vancomycin clearance during any RRT modality. Development of such a model is feasible using meta‐analysis of published summarized estimates of vancomycin PK parameters. Our aims were: (i) to develop and validate a population PK model for vancomycin that takes into account any RRT modalities, and (ii) to predict vancomycin dosing for RRT patients in ICU.

Methods

Vancomycin pharmacokinetics were assumed to be two‐compartmental, total body clearance being the sum of non‐RRT clearance and RRT‐induced clearance. Drug disposition and non‐RRT clearance parameters were estimated by systematic review and meta‐analysis of previously published parameter estimates. The relationship between RRT‐induced clearance and RRT flowrate settings was assessed using a model‐based meta‐analysis. Prediction performances of the PK model were assessed using external data.

Results

The meta‐analyses of disposition parameters, non‐RRT clearance and RRT‐induced clearance included 11, 6 and 38 studies (84 RRT clearance measurements) respectively. The model performed well in predicting external individual PK data. Individual vancomycin concentrations during RRT were accurately predicted using Bayesian estimation based solely on pre‐RRT measurements.

Conclusions

The PK model allowed accurate prediction of the vancomycin pharmacokinetics during RRT in ICU patients. Based on the model of RRT‐induced clearance, an appropriate adjustment of the vancomycin dosing regimen could be proposed for any kind of flowrate settings.

1.

What is already known about this subject

• Previous pharmacokinetic studies have proposed vancomycin dosing regimens in intensive care patients under renal replacement therapy, but all are restricted to the specific renal replacement therapy modalities and flowrate settings used in the study.

• A model‐based meta‐analysis approach could be used to characterize the dependence between renal replacement therapy flowrate settings and drug clearance.

What this study adds

• The model of RRT‐induced clearance allows a good prediction of vancomycin pharmacokinetics during renal replacement therapy.

• Estimation, for any RRT flowrate settings, of the optimal dose of vancomycin to infuse for both continuous and intermittent dosing management.

2. INTRODUCTION

In ICU patients, vancomycin is recommended for the treatment of severe to life‐threatening infections caused by Gram‐positive bacteria, in particular methicillin‐resistant Staphylococcus aureus.1

Approximately half of ICU patients develop acute kidney injury. A quarter of these patients subsequently require renal replacement therapy (RRT).2 For continuous dosing, a serum vancomycin concentration between 20 and 30 mg/L3 is generally targeted but, the concentration ranges observed in practice are often suboptimal.4, 5 The pharmacokinetics of vancomycin in these patients are affected by both pathophysiological alterations and RRT treatment. As vancomycin is renally cleared, exposure is increased by renal failure but at the same time reduced as a result of the increase in the volume of distribution related to sepsis and the enhanced clearance induced by RRT.

Various types of RRT are used in the ICU each with a unique combination of blood (Q _B), dialysate (Q _D) and haemofiltrataion (Q _HF) flow rate, collectively referred to as ‘flowrate’ settings. Depending on the removal mechanism used, the various types of RRT may be classified as follows:

• Haemodialysis (HD), based solely on a diffusive mechanism (Q _D ≠ 0 and Q _HF = 0)

• Haemofiltration (HF), based solely on a convective mechanism (Q _D = 0 and Q _HF ≠ 0)

• Haemodiafiltration (HDF), based on both diffusive and convective mechanisms (Q _D ≠ 0 and Q _HF ≠ 0)

RRT modalities may also be classified according to their duration:

• Intermittent RRT: duration 3–4 h with high flow rates (Q _B > 300 mL/min, Q _D > 500 mL/min and Q _HF > 100 mL/min)

• Hybrid RRT or sustained low‐efficiency dialysis (SLED): duration 6–12 h with intermediate flow rates (Q _B = 100–300 mL/min, Q _D = 100–300 mL/min and Q _HF = 50–100 mL/min)

• Continuous RRT (CRRT): duration 48–72 h with low flow rates (Q _B = 100–200 mL/min, Q _D ~ 33 mL/min and Q _HF ~ 33 mL/min)

Together with filter characteristics, in particular filter area, these settings determine drug clearance in the context of RRT.

Previous pharmacokinetic studies have proposed various vancomycin dosing regimens for patients in ICU undergoing RRT.6, 7, 8 However, each of these dosing regimens is restricted to the specific RRT modality and settings used in the study concerned. Consequently, vancomycin dosing recommendations for all RTT modalities used in the ICU are not available. We propose that a vancomycin population PK model could be used to predict RRT clearance for any modality based on the values of flowrate settings used. Ideally, the predictions generated by such a model should be based on the pooled individual data obtained in all previous PK studies conducted in ICU patients undergoing RRT. However, the feasibility of such a strategy is rather unrealistic due to data availability issues. An alternative is to use summarized data of RRT clearance estimates and build a meta‐model that can predict vancomycin RRT clearance for any flowrate settings.

The aims of this study were: (i) to develop and validate a PK model of vancomycin in ICU patients that could predict the RRT‐induced clearance for any flowrate settings, and (ii) to predict the optimal dosing regimen for any flowrate settings in order to maintain target concentrations of vancomycin.

3. METHODS

To propose a PK model of vancomycin in ICU patient undergoing RRT, an estimation of three types of parameters is needed:

• disposition parameters (volumes of distributions, inter‐compartmental clearance)

• non‐RRT clearance

• RRT‐induced clearance

To provide these estimates, a separate systematic review and meta‐analysis was performed for each parameter. For disposition and non‐RRT clearance parameters, a point estimate was obtained by combining all the previously published values in ICU patients using a standard meta‐analysis approach. To capture the dependency between RRT‐induced clearance and flowrate settings, we conducted a model‐based meta‐analysis.9, 10 We characterized the relationship between RRT clearance and flowrate settings using a nonlinear regression model estimated from published RRT‐induced clearance values. These three steps are summarized in Figure 1.

Figure 1.

Schematic representation of the vancomycin PK model and the different steps of the literature‐based estimation. CL, clearance; CL _non‐RRT, non‐RRT clearance; CL _RRT, renal replacement therapy‐induced clearance; C_C, central compartment; C_P, peripheral compartment; ICU, intensive care unit; PK, pharmacokinetic; Q, inter‐compartment clearance; RRT, renal replacement therapy; V _C, volume of distribution of the central compartment; V _P, volume of distribution of the peripheral compartment

3.1. Vancomycin pharmacokinetic model

In this study, the pharmacokinetics of vancomycin were described using a two‐compartment model in which total vancomycin clearance (CL) comprised the sum of non‐RRT clearance and a supplementary clearance term representing RRT‐induced clearance. This model is based on the following equations:

$$\left\{\begin{array}{c}\frac{d{A}_C}{\mathit{dt}}=\left({\sum }_d{\mathit{IR}}_d\left(t\right)\right)+Q\left(\frac{A_P}{V_P}-\frac{A_C}{V_C}\right)-\frac{{\mathit{CL}}_{\mathit{TOT}}}{V_C}{A}_C\\ \frac{d{A}_P}{\mathit{dt}}=Q\left(\frac{A_C}{V_C}-\frac{A_P}{V_P}\right)\\ {\mathit{IR}}_d\left(t\right)=\frac{{\mathit{\text{Dose}}}_d}{T_{{\mathit{INF}}_d}}\mathit{\text{if}}{t}_d\le t\le t_d+T_{{\mathit{INF}}_d}\mathit{\text{else}}{\mathit{IR}}_d\left(t\right)=0\\ A_C\left(0\right)=A_P\left(0\right)=0\end{array}\right.$$ (1)

where $C_C=\frac{A_C}{V_C}$ and $C_P=\frac{A_P}{V_P}$ are the concentrations of vancomycin in the central and peripheral compartments. The drug disposition parameters V _C, V _P and Q correspond to the volume of distribution of the central compartment, the volume of distribution of the peripheral compartment and the inter‐compartmental clearance, respectively. Function IR_d(t), corresponds to the infusion rate of the d ^th administrated infusion given at time t_d with a dose Dose_d and infusion duration $T_{{\mathit{INF}}_d}$.

The parameter CL _TOT corresponds to the total clearance and is defined as follows:

$${\mathit{CL}}_{\mathit{TOT}}=\left\{\begin{array}{c}{\mathit{CL}}_{\mathit{\text{non}}-\mathit{RRT}}+{\mathit{CL}}_{\mathit{RRT}}\left(Q_B,Q_D,Q_{\mathit{HF}}\right)\text{if}\mathrm{RRT}\text{is ongoing}\\ {\mathit{CL}}_{\mathit{\text{non}}-\mathit{RRT}}\text{otherwise}\end{array}\right.$$ (2)

where CL _non‐RRT corresponds to non‐RRT clearance and CL _RRT (Q _B, Q _D, Q _HF) to RRT‐induced clearance, which depends on the flowrate settings, namely blood flow rate (Q _B), dialysate flow rate (Q _D) and haemofiltration flow rate (Q _HF).

3.2. Meta‐analysis of volumes of distribution and intercompartmental clearances parameters

3.2.1. Literature review and data extraction

A systematic review of published articles concerning vancomycin pharmacokinetics in ICU adult patients was performed. An independent review of citations from Medline from its inception to March 2018 was conducted. We used the following Medline search strategy: pharmacokinetic AND vancomycin AND (“intensive care” OR “critically ill”). Additional studies were identified from the reference lists of the selected published articles. We hypothesized that disposition PK parameters did not differ significantly in ICU patients according to whether or not they were undergoing RRT. This enhanced the statistical power of the analysis by allowing the inclusion of a greater number of studies. However, it corresponds to a major assumption and its validity was therefore explored in a sensitivity analysis.

Two of the authors (E.O. and J.C.T.) independently evaluated studies for possible inclusion in the meta‐analyses. To be included in the meta‐analysis of disposition parameters, studies had to have performed a PK analysis taking into account the bi‐compartmental kinetics of vancomycin in ICU patients. Data were independently extracted by the same two authors. In the event of discrepancies between the reviewers, consensus was reached by discussion.

Vancomycin PK parameters were assumed to follow a log‐normal distribution within each study, for example:

$$log\left(Q_{i,k}\right)=log\left({\mu }_{Q,i}\right)+{\eta }_{i,k}$$ (3)

where the random effect of the k ^th subject in the i ^th study is normally distributed with η_{i, k}~ $\mathcal{N}\left(0,{\omega }_{Q,i}^2\right)$. For each study, we extracted: details concerning the study characteristics (names of authors, year of publication, journal name, number of subjects (N), number of samples per subject (n)); typical values (μ) and between‐subject variability (ω²) of disposition PK parameters (Q: inter‐compartmental clearance, V _C: central volume of distribution, V _P: peripheral volume of distribution). Typical values of the volumes of distribution were expressed in L/kg. When reported in L (unscaled), volume parameters were scaled by weight using the body weight summary metric provided in the study. If the summary data concerning PK parameters were reported on a raw scale, they were transformed on to a log‐normal scale.11 If disposition parameters were estimated as distribution rate constants (k _CP = Q/V _C and k _PC = Q/V _P), they were transformed to inter‐compartmental clearance (Q = k_CP × V_C) and peripheral volume of distribution ( $V_P=\frac{k_{\mathit{CP}}}{k_{\mathit{PC}}}\times V_C$).

3.2.2. Meta‐analysis

The summary statistics for typical values and between‐subject variability of each PK parameter were generated using a fixed‐effect model. Estimates of each study were weighted according to the size of the trial (N) multiplied by the number of samples per subject (n). Summary statistics of typical values were calculated using the log‐transformed estimates of each study. Summary statistics of between‐subject variabilities were calculated using variance estimates. For example, the summary statistics of the inter‐compartmental clearance parameter Q correspond to the following equations:

$$\left\{\begin{array}{c}log\left({\widehat{\mu }}_Q\right)=\frac{1}{{\sum }_i{W}_i}{\sum }_i{W}_{i}log\left({\mu }_{Q,i}\right)\\ {\widehat{\omega }}_Q^2=\frac{1}{{\sum }_i{W}_i}{\sum }_i{W}_i{\omega }_{Q,i}^2\\ W_i=N_i{n}_i\end{array}\right.$$ (4)

The analysis was performed with R software.12

3.2.3. Sensitivity analysis

We conducted a sensitivity analysis in order to test the assumption that volumes of distribution and intercompartmental clearance parameters would not differ significantly between ICU patients undergoing extra‐corporeal membrane oxygenation (ECMO) or RRT and other ICU patients.

3.3. Model‐based meta‐analysis of RRT‐induced vancomycin clearance

3.3.1. Literature review and data extraction

We conducted a systematic review of published articles concerning RRT‐induced clearance of vancomycin using the same procedure described above. Only studies reporting the use of haemodialysis (HD), haemofiltration (HF) or haemodiafiltration (HDF) were considered. We used the following Medline search strategy: vancomycin AND (pharmacokinetic OR clearance) AND (dialysis OR filtration OR diafiltration). Additional studies were identified from the reference lists of the published articles selected.

To be included in the meta‐analysis, studies had to meet all the following criteria: (i) concern the use of HD, HF or HDF techniques with high flux filters, (ii) report the RRT‐induced clearance of vancomycin, and (iii) describe the flowrate settings used.

For each study, we extracted: details concerning study characteristics (names of authors, year of publication, journal name, number of subjects); RRT‐induced vancomycin clearance (mean, standard deviation); flowrate settings (blood flow rate [Q _B], dialysate flow rate [Q _D] and haemofiltration flow rate [Q _HF]); membrane characteristics (filter area, K _UF). If a study provided clearance measurements for different flowrate settings or membrane characteristics, these were considered as distinct observations.

3.3.2. Nonlinear mixed effect model‐based meta‐analysis

A mathematical function was developed to model the relationship between flowrate settings and RRT‐induced clearance. This function had to satisfy basic constraints concerning the relationship between flow rates (Q _B, Q _D and Q _HF) and CL _RRT: (i) if Q _B is null, then CL _RRT is equal to zero, (ii) for a non‐null Q _B, CL _RRT differs from zero if at least Q _D or Q _HF is non‐null. Fulfilment of this latter constraint allows the combined study of data concerning the three types of RRT: HD data (Q _D ≠ 0 and Q _HF = 0), HF data (Q _D = 0 and Q _HF ≠ 0) and HDF data (Q _D ≠ 0 and Q _HF ≠ 0).

The relationship between RRT‐induced vancomycin clearance and flowrate settings (Q _B, Q _D and Q _HF) was represented using the following mathematical model:

$${\mathit{CL}}_{\mathit{RRT}}={\mathit{CL}}_{\mathit{MAX}}\times H\left(Q_B,Q_B^{50}\right)\times \left(H\left(Q_D,Q_D^{50}\right)+H\left(Q_{\mathit{HF}},Q_{\mathit{HF}}^{50}\right)-H\left(Q_D,Q_D^{50}\right)\times H\left(Q_{\mathit{HF}},Q_{\mathit{HF}}^{50}\right)\right)$$ (5)

where the functions H (Q, Q ⁵⁰) correspond to standard Hill functions:13

$$H\left(Q,Q^{50}\right)=\frac{Q^{\mathrm{\alpha }}}{Q^{50}+Q^{\mathrm{\alpha }}}$$ (6)

The parameter CL _MAX corresponds to the maximum vancomycin clearance that can be attained with RRT. The parameters $Q_B^{50}$, $Q_D^{50}$ and $Q_{\mathit{HF}}^{50}$ correspond respectively to the values of Q _B, Q _D and Q _HF that are needed to reach half the maximum vancomycin clearance (CL _MAX). The parameter α corresponds to the curvature coefficient. This model allows fulfilment of the basic constraints between flow rates and CL _RRT: (i) if Q _B is null, then CL _RRT is equal to zero, (ii) for a non‐null Q _B, CL _RRT differs from zero if at least Q _D or Q _HF is non‐null.

If the observed RRT‐induced CL measurement does not reach a clear maximum, there may be an identifiability issue. In this case, the model can be re‐parameterized using the parameterization proposed by Schoemaker et al. 14 in order to improve the model's identifiability. If we apply this parameterization to model (5), we obtain the equation:

$${\mathit{CL}}_{\mathit{RRT}}=\frac{{\mathit{CL}}_{\mathit{MAX}}{S}_0^B{Q}_B}{{\mathit{CL}}_{\mathit{MAX}}+S_0^B{Q}_B}\times \left(\frac{S_0^D{Q}_D}{1+S_0^D{Q}_D}+\frac{S_0^{\mathit{HF}}{Q}_{\mathit{HF}}}{1+S_0^{\mathit{HF}}{Q}_{\mathit{HF}}}-\frac{S_0^D{Q}_D}{1+S_0^D{Q}_D}\times \frac{S_0^{\mathit{HF}}{Q}_{\mathit{HF}}}{1+S_0^{\mathit{HF}}{Q}_{\mathit{HF}}}\right)$$ (7)

where the parameters $S_0^B$, $S_0^D$ and $S_0^{\mathit{HF}}$ correspond to the slope of the tangent at Q _B = 0, Q _D = 0 and Q _UF = 0 respectively.

The observed measurements of RRT‐induced vancomycin clearance were then analysed using the following nonlinear mixed effect model:15

$$Y_{\mathit{ij}}={\mathit{CL}}_{\mathit{RRT}}\left(Q_B^{\mathit{ij}},Q_D^{\mathit{ij}},Q_{\mathit{HF}}^{\mathit{ij}},{\mathit{CL}}_{\mathit{MAX}}^i,Q_B^{50},Q_D^{50},Q_{\mathit{HF}}^{50}\right)+{\epsilon }_{\mathit{ij}}$$ (8)

where Y _ij corresponds to the j ^th measurement of RRT‐induced vancomycin clearance in study i using the flowrate settings $Q_B^{\mathit{ij}},Q_D^{\mathit{ij}}$ and $Q_{\mathit{HF}}^{\mathit{ij}}$. The maximum vancomycin clearance parameter of the i ^th study, ${\mathit{CL}}_{\mathit{MAX}}^i$, was assumed to follow a log‐normal distribution:

$$log\left({\mathit{CL}}_{\mathit{MAX}}^{\mathit{ij}}\right)=log\left({\mu }_{{\mathit{CL}}_{\mathit{MAX}}}\right)+{\beta }_X\times X^{\mathit{ij}}+{\eta }_i$$ (9)

where β_X is the effect of the covariate X and η_i is the random effect of the i ^th study, assumed to be normally distributed with η_i~ $\mathcal{N}\left(0,{\omega }^2\right)$. The study characteristics (year of publication, in ICU patients or not) and filter characteristics (area, K _UF) were tested as covariates. Year of publication was used as a surrogate covariate to take into account potential unobserved confounding factors (eg, improvement of filter performance with time). Residual unexplained variability was assumed to be normally distributed and scaled according to the standard error of each vancomycin clearance measurement:

$${\epsilon }_{\mathit{ij}}~\frac{{\widehat{\sigma }}_{\mathit{ij}}}{\sqrt{N_{\mathit{ij}}}}\mathcal{N}\left(0,{\sigma }^2\right)$$ (10)

where ${\widehat{\sigma }}_{\mathit{ij}}$ is the standard error of the observed clearance values and N _ij is the number of subjects.

3.3.3. Sensitivity analysis

In order to investigate the different relationships between Q _D and Q _HF in HDF, a purely additive model with respect to Q _D and Q _HF was also tested:

$${\mathit{CL}}_{\mathit{RRT}}={\mathit{CL}}_{\mathit{MAX}}\times H\left(Q_B,Q_B^{50}\right)\times \left(\raisebox{1ex}{$H\left(Q_D,Q_D^{50}\right)$}\!\left/ \!\raisebox{-1ex}{$2$}\right.+\raisebox{1ex}{$H\left(Q_{\mathit{HF}},Q_{\mathit{HF}}^{50}\right)$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right)$$ (11)

3.3.4. Parameter estimation and model selection

Data were analysed using MONOLIX^® nonlinear mixed‐effects modelling software (Lixoft, version 2018R1) with the SAEM algorithm.16 All graphics were generated using the ggplot2 software package17 with R software.12

Model evaluation and selection were based on visual inspection of the goodness‐of‐fit plots, the precision of parameter estimates, and the decrease in the Bayesian Information Criterion (BIC).18 Covariates were included in the model using a stepwise method with forward inclusion and backward elimination using a decrease in BIC as selection criterion. The goodness of fit was established by plotting the predictions of the model versus observations and the normalized prediction distribution errors (NPDEs) vs. predicted values.19

3.4. Meta‐analysis of non‐RRT vancomycin clearance

3.4.1. Literature review and data extraction

Based on the results of the literature search concerning RRT‐induced clearance of vancomycin, we identified studies conducted in ICU patients in which non‐RRT clearance was estimated or could be calculated. The data extraction procedure was the same as that used for disposition PK parameters. For each of these studies, we additionally extracted: non‐RRT vancomycin clearance (typical values and between‐subject variability).

3.4.2. Meta‐analysis

The summary statistics for typical values and between‐subject variability of non‐RRT clearance was obtained using the same methodology as that employed for disposition parameters.

3.5. Evaluation of the population PK model using published PK data

Based on the result of the literature search concerning the RRT‐induced clearance of vancomycin, studies which provided individual data on vancomycin PK in ICU patients undergoing RRT were included in the external validation step. These studies were not used in the meta‐analysis steps, even if they fulfilled the eligibility criteria, but only for assessment of the predictive properties of the PK model developed.

This assessment was based on visual inspection of observed vs. predicted concentrations of both mean population and individually adjusted models. Individual predictions of RRT‐induced vancomycin pharmacokinetics were obtained by Bayesian estimation of individual disposition parameters (V _C, V _P, Q and CL _non‐RRT) based solely on the vancomycin measurements performed before the beginning of the RRT session. Bayesian estimation was performed using the maximum a posteriori probability method15 with R software.12 Distributions of disposition PK parameters (V _C, V _P, Q and CL _non‐RRT) estimated from the literature were used as Bayesian prior. The residual unexplained variability was assumed to follow a combined error model. Parameters of the error model were estimated from the literature estimates using the same methodology as for the summary statistic of between‐subject variabilities (equation 4). Only PK studies which estimated a combined error model were considered. A simulation‐based diagnosis was also obtained, based on NPDE vs. population predictions.2

3.6. Loading and maintenance doses in ICU patients undergoing RRT

Under a continuous vancomycin dosing regimen and based on PK parameters, we proposed a loading dose (LD) and a maintenance dose (MD) to achieve a target concentration (TC) of 25 mg/L for ICU patients with impaired renal function not undergoing RRT. These two doses were determined using the following classical equations:20

$$\begin{array}{l}\mathit{LD}=\left(V_C+V_P\right)\times \mathit{TC}\\ \mathit{MD}={\mathit{CL}}_{\mathit{\text{non}}-\mathit{RRT}}\times \mathit{TC}\end{array}$$ (12)

where V _c and V _p are the volumes of distribution of the central and peripheral compartment respectively.

The model of RRT‐induced vancomycin clearance developed in this study allowed us to determine the additional MD (∆MD) needed to maintain vancomycin concentrations at the targeted level during RRT for any flowrate settings. Like the MD, this was determined using the following equation:

$$\mathrm{\Delta }\mathit{MD}={\mathit{CL}}_{\mathit{RRT}}\left(Q_B,Q_D,Q_{\mathit{HF}},\mathit{FA}\right)\times \mathit{TC}$$ (13)

where the predicted RRT‐induced vancomycin clearance depends on Q_B, Q_D, Q_HF and FA, the area of the filter used during RRT.

A dosing regimen with additional MD based on intermittent infusion of vancomycin administrated at the beginning of the RRT session was also explored. For a short infusion, the dose proposal must take into account volumes of distributions and vancomycin rebound at the end of the RRT session. Based on the linearity of vancomycin's pharmacokinetics and the superposition principle, we derived a closed form solution to estimate the optimal dose to administer during a short infusion in order to reach the desired target concentration at a time t^* after the end of the RRT session. This optimal dose ΔMD_SI is given by the following equation:

$${\mathrm{\Delta }\mathit{MD}}_{\mathit{SI}}=\frac{\mathit{TC}-C_C^{\mathit{CI}}\left(t^{*}\right)}{G\left(t^{*}\right)}$$ (14)

where $C_C^{\mathit{CI}}\left(t^{*}\right)$ is the concentration obtained at time t^* from the continuous maintenance infusion (infusion rate equal to MD) and the loading dose. The quantity G(t^*) corresponds to the concentration obtained at time t^* from the short infusion for a dose of 1 mg. The derivation of this formula is described in Supplementary Appendix 1.

3.7. Monte Carlo simulations of vancomycin pharmacokinetics

Simulations of vancomycin pharmacokinetics were performed using Monte Carlo simulations of 1000 individual PK parameters. Three different RRT modalities were considered: (i) intermittent HD (Q _B = 300 mL/min, Q _D = 500 mL/min, Q _HF = 0 mL/min, during 4 h every 48 h), (ii) SLED (Q _B = 200 mL/min, Q _D = 200 mL/min, Q _HF = 100 mL/min, during 8 h every 24 h) and (iii) continuous HDF (Q _B = 150 mL/min, Q _D = 33 mL/min, Q _HF = 30 mL/min, during 72 h). Simulations were performed over a 120‐hour period. The first RRT session started 5 hours after the administration of the loading dose. The filter area was set at 1.9 m².

4. RESULTS

4.1. Meta‐analysis of volumes of distribution and intercompartmental clearances parameters

A total of 167 potentially relevant articles were identified through a search of the Medline database and the reference lists of the published articles selected. After examination of the titles and abstracts, 111 articles were excluded. The full texts of the remaining 56 studies were screened and 11 studies were selected for the meta‐analysis of disposition parameters. The flow chart of the study selection process is presented in Supplementary Figure S1. Figure 2A shows the individual study estimates of both typical values and between‐subject variabilities for each disposition parameter. It also presents the weighted mean estimates obtained by meta‐analysis. The numerical values are given in Supplementary Table S1. The subgroup analysis did not reveal any significant difference between standard ICU patients and ICU patients undergoing ECMO and/or RRT. The p‐value for interaction was greater than 0.7 for both typical value and between‐subject variability of each PK parameter. This is illustrated graphically in Figure 2A.

Figure 2.

A, Estimated results from each of the studies included with weighted mean estimates for each disposition parameter. Dark blue squares: estimates for patients not undergoing extracorporeal membrane oxygenation (ECMO) or renal replacement therapy (RRT). Light blue circles: estimates for patients undergoing ECMO. Yellow triangles: estimates for patients undergoing RRT. Orange diamonds: estimates for patients undergoing both ECMO and RRT. B, Estimated results from each study included and weighted mean estimates for non‐RRT clearance. CL, clearance; CV, coefficient of variation; Q, intercompartment clearance; V _C volume of distribution of the central compartment; V _P, volume of distribution of the peripheral compartment

4.2. Model‐based meta‐analysis of RRT‐induced vancomycin clearance

A total of 219 potentially relevant articles were identified through a search of the Medline database and the reference lists of selected articles. After examination of the titles and abstracts, 162 studies were excluded. Among the remaining 57 studies, the data were found to be fully exploitable in 38 studies, yielding a total of 84 clearance measurements. The flow chart of the study selection process is presented in Supplementary Figure S1. Figure 3A displays the RRT‐induced vancomycin clearance measurements reported in the studies included in the meta‐analysis according to the blood flow rate, the dialysate flow rate and the ultrafiltration flow rate. Few studies evaluated RRT‐induced vancomycin clearance at dialysate flow rates between 100 mL/min and 400 mL/min. This range corresponds to the range of dialysate flow rates used in SLED. Supplementary Table S2 provides the list and characteristics of each RRT‐induced vancomycin clearance measurement included in the analysis.

Figure 3.

A, RRT‐induced vancomycin clearance measured in the studies included with respect to blood flow rate (left), dialysate flow rate (centre) and ultrafiltration flow rate (right). Blue circles, red squares and yellow triangles correspond to vancomycin clearance measurements in patients undergoing haemodialysis (HD), haemofiltration (HF) and haemodiafiltration (HDF), respectively. The size of each point is proportional to the standard error of the corresponding vancomycin clearance measurement. B, Goodness of fit plots for the renal replacement therapy (RRT)‐induced clearance model. Left: observed vancomycin clearances vs. population predictions; centre: observed vancomycin clearances vs. individual predictions; right: normalized prediction distribution error (NPDE) vs. population predictions. For population predictions (left) and individual predictions (centre), the dashed grey line corresponds to the identity, the continuous blue line to the spline regression and the grey shaded area to its 95% confidence interval. The blue circles, red squares and yellow triangles correspond to vancomycin clearance measurements under HD, HF and HDF, respectively. The size of each point is proportional to the standard error of the corresponding vancomycin clearance measurement. CL, clearance; Q, flow rate

Model (5) best described the data and was chosen as the final model (Model defined by equation (5): BIC = 519; Model defined by equation (11): BIC = 531). The model defined by equation (11) was used for sensitivity analysis; it overpredicted RRT clearances during HDF. Estimation of the curvature coefficient α did not improve the model's predictions. The parameter α was therefore set at 1.

As illustrated in Figure 3A, the observed RRT clearances did not reach a clear maximum. Consequently, estimation of the parameters CL _MAX and $Q_B^{50}$ was not fully accurate. Only their ratio was accurately identifiable. The parameterization proposed by Schoemaker et al.14 (equation (7)) was therefore used for the final estimation.

Among the covariates evaluated (filter area, K _UF, ICU patients, year of publication), only filter area (∆BIC = −16.06) and K _UF (∆BIC = −12.84) were significantly correlated with CL _MAX. The stepwise procedure selected only filter area as a covariate (area + K _UF vs. area: ∆BIC = +9.27). Unexplained inter‐study variability was then decreased by 17.3%.

The final parameter estimates of the reparametrized model are presented in Table 1. Inter‐study variability of the CL _MAX parameter was moderate (CV = 33.9%). The goodness‐of‐fit plots, shown in Figure 3B, exhibit no apparent bias in terms of model prediction.

Table 1.

Model‐based meta‐analysis parameter estimates

PK parameters	Typical value (% RSE)	Inter‐study variability (% RSE)
CL MAX (mL/min)	48.7 (14.2)	0.339 (16)
βArea	0.723 (15.4)	–
$S_0^B$	1.19 (25.4)	–
$S_0^D$	0.0154 (23)	–
$S_0^{\mathit{HF}}$	0.0177 (21.5)	–
Residual error parameters
σ	2.32 (9.87)	–

Abbreviation: CL, clearance; PK, pharmacokinetic; RSE, random study effect.

Note: The individual parameter ${\mathit{CL}}_{\mathit{MAX}}^{\mathit{ij}}$of the j^th measurement of the i^th study is defined as follows: $\mathit{log}\left({\mathit{CL}}_{\mathit{MAX}}^{\mathit{ij}}\right)=log\left({\mathrm{CL}}_{\mathit{MAX}}\right)+{\beta }_{\mathit{\text{Area}}}\times \frac{{\mathit{FA}}^{\mathit{ij}}}{1.2}+{\eta }_i$, where FA^ij corresponds to the area of the filter used for the j^th measurement of the i^th study.

4.3. Meta‐analysis of non‐RRT vancomycin clearance

Among the 38 studies included for the estimation of RRT‐induced vancomycin clearance, six were performed in ICU patients and provided an estimation of non‐RRT clearance. The PRISMA flow chart of the study selection process is presented in Supplementary Figure S1. Figure 2B shows individual study estimates of both typical values and between‐subject variabilities for non‐RRT clearance. It also presents the weighted mean estimates obtained by meta‐analysis. Supplementary Table S3 lists the non‐RRT clearance measurements included in the analysis, by author, and presents their characteristics.

4.4. Final population PK model and external evaluation based on published PK data

Table 2 summarizes the parameter estimates of the two‐compartment PK model obtained with each meta‐analysis. During the study selection process for the estimations of RRT‐induced clearance and non‐RRT clearance, only four studies were found to provide individual data for vancomycin PK in ICU patient undergoing RRT,21, 22, 23, 24 The study of Ahern et al.21 was excluded from the external evaluation step as it did not sufficiently describe individual patient characteristics (e.g. body weight) and therefore did not allow us to correctly specify the PK model. Finally, we included in the external evaluation step data from three independent studies: Golestaneh et al.,22 Salaroli de Oliveira et al.23 and Santré et al.24 The first two studies investigated the pharmacokinetics of vancomycin during SLED in ICU patients and the last one focused on continuous HDF. The characteristics of each study are summarized in Table 3.

Table 2.

Literature‐based estimates of vancomycin PK parameters

PK parameters	Typical value	Inter‐study variability
Disposition parameters
V C (L/kg)	0.298	0.354
V P (L/kg)	0.571	0.606
Q (L/h)	9.57	0.773
CL non‐RRT (L/h)	0.99	0.457
RRT‐induced clearance
${\mu }_{{\mathit{CL}}_{\mathit{MAX}}}$ (mL/min)	48.7	–
βArea	0.723	–
$S_0^B$	1.19	–
$S_0^D$	0.0154	–
$S_0^{\mathit{HF}}$	0.0177	–
Residual variability
Constant (mg/L)	1.52	–
Proportional	0.046	–

Note: The parameters V _C, V _P, Q and CL _non‐RRT correspond respectively to the central and peripheral volumes of distribution, and to the inter‐compartmental and non‐RRT clearance. RRT‐induced clearance is defined by equation (C) with the CL_MAX parameter defined as $log\left({\mathit{CL}}_{\mathit{MAX}}\right)=log\left({\mu }_{{\mathit{CL}}_{\mathit{MAX}}}\right)+{\beta }_{\mathit{\text{Area}}}\times \frac{\mathit{FA}}{1.2}$, where FA corresponds to the area of the filter used for RRT.

Table 3.

Characteristics of studies used for external evaluation of the PK model

Study	RRT modality	Number of patients	Dosing regimen	Sampling schedule	Time between last vancomycin infusion and RRT
Golestaneh et al.22	SLED	10	17.5 mg/kg/24 h for 48 h	0 h, 2 h, 4 h and 8 h from the start of RRT	4 h
Salaroli de Oliveira et al.23	SLED	24	11.25 mg/kg/24 h for 72 h	0 h, 0.5 h, 1 h, 2 h, 4 h and 6 h from the start of RRT	median = 30 h
Santré et al24	continuous HDF	3	7.5 mg/kg infused over 1 h	1 h, 3 h, 6 h, 12 h, 18 h and 24 h from the start of vancomycin infusion	0 h

The results of the evaluation of the population PK model on these external data sets are shown in Supplementary Figure S2. The plot of individual predictions vs. observed concentrations (Supplementary Figure S2, centre panel), shows only vancomycin concentration measurements that were not used for the Bayesian estimation of individual disposition PK parameters (i.e. all measurements except that corresponding to the sample taken at the start of the RRT session). Vancomycin concentrations reported by Santre et al. were excluded from the individual predictions as all samples were taken during RRT. The mean population model (Supplementary Figure S2, left panel) slightly underpredicted vancomycin concentrations especially with respect to the data reported by Salaroli de Oliveira et al.23 Concerning individual predictions, there was no apparent bias for concentrations lower than 60 mg/L corresponding to concentrations usually observed in routine clinical practice. There was a potential misspecification for large concentration values greater than 60 mg/L. There was no apparent bias in plot of NPDE. Mean of NPDE was equal to −0.108, and the standard deviation was 0.853. For concentrations lower than 60 mg/L, the model of RRT‐induced vancomycin clearance seems to effectively predict vancomycin removal during SLED in these external validation data sets. Figure 4 shows examples of individual vancomycin kinetics during RRT.

Figure 4.

Examples of individual vancomycin kinetics. The black circles correspond to observed vancomycin concentrations and the red circles to the observed vancomycin concentrations used for Bayesian estimation. The grey shaded areas represent the periods when RRT was ongoing. The dashed blue line corresponds to the mean population model and the continuous yellow line to the median of the individual prediction interval. The yellow shaded areas correspond to the 90%, 70% and 50% prediction intervals, respectively. BW, body weight; Q _B, blood flow rate; Q _D, dialysate flow rate; Q _HF, haemofiltration flow rate; VMC, vancomycin

4.5. Loading and maintenance doses of vancomycin in ICU patients undergoing RRT

Using Monte Carlo simulations of individual PK parameters, we obtained a median LD of 22.41 mg/kg (interquartile range [IQR] = [17.15–29.67]) and a median MD of 24.74 mg/h (IQR = [18.26–33.42]) for ICU patients with impaired renal function not undergoing RRT. The additional MD required during RRT was evaluated for both continuous and intermittent infusion dosing. For the continuous dosing strategy, this additional MD was equal to: (i) 141 mg/h for intermittent HD (Q _B = 300 mL/min, Q _D = 500 mL/min, Q _HF = 0 mL/min), (ii) 126 mg/h for SLED (Q _B = 200 mL/min, Q _D = 200 mL/min, Q _HF = 100 mL/min), and (iii) 69 mg/h for continuous HDF (Q _B = 150 mL/min, Q _D = 33 mL/min, Q _HF = 30 mL/min). Concerning the intermittent dosing strategy, in order to reach target concentration 4 hours after the end of the RRT session, we obtained a median additional MD to be infused over 1 hour of: (i) 19.19 mg/kg (interquartile range [IQR] = [17.21–22.45]) for SLED and (ii) MD of 8.06 mg/kg (IQR = [7.50–8.98]) for intermittent HD. Our simulations suggest that repeated intermittent infusion would be necessary for continuous HDF as the additional MD was unrealistic (>400 mg/kg) and preclude the use of an intermittent dosing strategy based on a single pre‐RRT infusion. Repeated intermittent infusions are then necessary for intermittent HD.

Figure 5 shows PK simulations for vancomycin in an 80‐kg ICU patient with and without an additional MD (∆MD) during RRT for intermittent HD, SLED and continuous HDF. The additional MD was administered using either a continuous or an intermittent infusion strategy. The baseline LD was set at 22.41 mg/kg (infusion rate 1 g/h) and the MD at 24.74 mg/h. For the continuous infusion strategy, based on the predefined flowrate settings, the additional MD (∆MD) was equal to 141 mg/h during intermittent HD, 126 mg/h during SLED and 69 mg/h during continuous HDF. For the short infusion strategy, vancomycin was administrated over 1 hour from the beginning of the RRT session with a dose of 19.19 mg/kg for SLED and 8.06 mg/kg for intermittent HD. These simulations show that provision of this additional MD during RRT allowed maintenance of vancomycin concentration at the targeted level during RRT. Supplementary Figure S3 shows the evolution of the proportion of patients with a concentration above 20 mg/L.

Figure 5.

Simulations of vancomycin kinetics for a patient of 80 kg receiving RRT. Left: intermittent HD (Q _B = 300 mL/min, Q _D = 500 mL/min, Q _HF = 0 mL/min, FA = 1.9 m²). Centre: SLED (Q _B = 200 mL/min, Q _D = 200 mL/min, Q _HF = 100 mL/min, FA = 1.9 m²). Right: continuous HD (Q _B = 150 mL/min, Q _D = 33 mL/min, Q _HF = 30 mL/min, FA = 1.9 m²). The upper row corresponds to vancomycin concentrations after vancomycin administration with a loading dose (LD) of 22.41 mg/kg (infusion rate 1 g/h) and a maintenance dose (MD) of 24.74 mg/h without any additional maintenance dose during RRT. The middle row corresponds to vancomycin concentrations after vancomycin administration with an LD of 22.41 mg/kg (infusion rate 1 g/h) and an MD of 24.74 mg/h with a continuous additional maintenance dose during RRT of 141 mg/h for intermittent HDF, 126 mg/h for SLED, and 69 mg/h for continuous HD. The lower row corresponds to vancomycin concentrations after vancomycin administration with an LD of 22.41 mg/kg (infusion rate 1 g/h) and an MD of 24.74 mg/h with an intermittent additional maintenance dose during RRT of 645 mg for intermittent HDF and 1535 mg for SLED. HD, haemodialysis; HDF, haemodiafiltration; LD, loading dose; MD, maintenance dose; SLED, sustained low‐efficiency dialysis. The grey shaded areas represent the periods when RRT was ongoing

5. DISCUSSION

In this study, we developed a population PK model of vancomycin in ICU patients undergoing RRT. Parameters were estimated on the basis of a systematic review and meta‐analysis of previously published parameter estimates. RRT‐induced vancomycin clearance was estimated using a model‐based meta‐analysis methodology allowing the prediction of RRT clearance for any values of flowrate settings. The model developed exhibited satisfactory predictive properties on an external data set of individual PK data during SLED and continuous HDF and may be used to guide the choice of vancomycin dosing regimen.

In view of the nonlinearity of the relationship between RRT clearance and flowrate settings, we conducted a model‐based meta‐analysis taking into account the cross‐dependency of blood, dialysate and haemofiltration flow rates. This methodology has already been used in other fields,25 but has never been used to describe the impact of flowrate settings on RRT‐induced drug clearance. Jamal et al.26 analysed the impact of variation in flowrate settings on piperacillin, meropenem and vancomycin clearance using linear regression. Unfortunately, the analysis was mostly restricted to continuous RRT and therefore explored a narrow range of flowrate settings. Moreover, these authors used an unweighted univariate linear regression analysis, which did not take into account the cross‐dependency of blood, dialysate and haemofiltration flow rates. In our analysis, inter‐study variability was partially taken into account by including a random effect on the parameter CL _MAX. However, even with inclusion of filter area as a covariate, unexplained inter‐study variability remained non‐negligible. Other variables, such as albumin concentration, might explain this inter‐study heterogeneity, but such information was missing in the majority of the articles reviewed.

Concerning vancomycin PK disposition parameters, there was a large inter‐study variability in the point estimates of both typical value and between‐subject variability. This could be explained by two phenomena: (i) the high variability of pharmacokinetics processes in ICU patients, unexplained by clinical and biological covariates (bodyweight, age, RRT/ECMO, etc.) and (ii) the lack of power of included studies (low number of subject and/or sparse sampling design) that is a source of large estimation variability.

Even with the advent of new drugs directed against Gram‐positive cocci, vancomycin is still frequently used in ICU. Like other time‐dependent antibiotics, its efficacy depends on the time during which its concentration remains above a certain threshold concentration. This time can be shortened during any kind of RRT, exposing the patient to underdosage. Based on the RRT‐induced clearance model, it is possible to adjust the vancomycin infusion rate when RRT is ongoing. The necessary dose adjustment may be easily calculated by evaluating the model of RRT‐induced clearance at the desired (Q_B, Q_D, Q_HF and FA) values. The formula including the final parameter estimates may be found in Supplementary Appendix 2. To the best of our knowledge, this approach is not widespread and is of interest, especially in the context of CRRT or SLED. These techniques are currently preferred during initial care, when patients are most unstable and deleterious underdosage is more frequent. Early dose adjustment at this time remains a major issue for intensivists. Another strength of our study is that this dose adjustment calculation can be applied to all RRT modalities and can easily be implemented in a target‐controlled continuous infusion vancomycin regimen.3 The same approach may be used with other time‐dependent antibiotics, such as beta‐lactams.

Based on the proposed model, the Bayesian estimation technique could be used to predict individual vancomycin kinetics in patients undergoing RRT, based solely on vancomycin concentrations measured before the first RRT session. This methodology may enable the use of personalized vancomycin dosing regimens. However, in order to provide a robust and accurate prediction, we need a better understanding of vancomycin disposition in ICU patients undergoing RRT. Previously published population pharmacokinetic studies were conducted on small populations and/or with a small number of samples per subject. Such designs did not allow the identification of covariates that influence volumes of distribution and thereby to reduce the large unexplained interpatient variability. Another crucial issue will be to find a way of taking into account the variations in volumes of distribution secondary to RRT sessions. As large quantities of fluid may be removed during dialysis, vancomycin disposition of vancomycin is certainly modified after repeated RRT sessions.

6. CONCLUSIONS

The PK model developed in this study allowed accurate prediction of the vancomycin pharmacokinetics during SLED and continuous HDF in ICU patients. Based on the model of RRT‐induced clearance, an appropriate adjustment of the vancomycin dosing regimen could be proposed for any kind of flowrate settings used.

COMPETING INTERESTS

There are no competing interests to declare.

CONTRIBUTORS

Data extraction: G.C., P.J.Z., J.C.T., E.O. Data analysis: P.J.Z., X.D., E.O. Writing of manuscript: G.C., N.M., S.L., J.C.T., E.O. Revision of manuscript: G.C., J.C.T., E.O., S.L.

Supporting information

TABLE S1 Numerical values of PK POP parameters extracted for the meta‐analysis of volumes of distributions and inter‐compartemental clearance.

TABLE S2 Characteristics of each RRT‐induced vancomycin clearance measurement included in the analysis.

TABLE S3 Numerical values of Non‐RRT clearance extracted for the meta‐analysis.

Supplementary Appendix 1

Supplementary Appendix 2

FIGURE S1 PRISMA flow chart of study selection for the two meta‐analyses. Left: Meta‐analysis of vancomycin disposition parameters. Right: Meta‐analysis of RRT‐induced vancomycin clearance and non‐RRT clearance. Cl clearance, PK pharmacokinetic, RRT renal replacement therapy, vancomycin vancomycin.

FIGURE S2 External validation plots of the vancomycin PK model. Left, observed vancomycin concentrations versus population predictions; centre, observed vancomycin concentrations versus individual predictions; and right, normalized prediction distribution error (NPDE) versus population predictions. The blue, yellow and red circles correspond to the vancomycin concentration measurements reported by Golestaneh et al. 22, Salaroli de Oliveira et al. 23 and Santré et al. 24 respectively. Black dashed lines correspond to identity lines. The continuous grey lines correspond to spline regression.

FIGURE S3 Proportion of patients with a vancomycin concentration above 20 mg/L, estimation from a set of 1000 simulations of vancomycin kinetics for patients of 80 kg. Left: intermittent HD (Q_B = 300 mL/min, Q_D = 500 mL/min, Q_HF = 0 mL/min, FA = 1.9 m²). Centre: SLED (Q_B = 200 mL/min, Q_D = 200 mL/min, Q_HF = 100 mL/min, FA = 1.9 m²). Right: continuous HD (Q_B = 150 mL/min, Q_D = 33 mL/min, Q_HF = 30 mL/min, FA = 1.9 m²). The upper row corresponds to vancomycin concentrations after vancomycin administration with a loading dose (LD) of 22.41 mg/kg (infusion rate 1 g/h) and a maintenance dose (MD) of 24.74 mg/h without any additional maintenance dose during RRT. The middle row corresponds to vancomycin concentrations after vancomycin administration with a LD of 22.41 mg/kg (infusion rate 1 g/h) and a MD of 24.74 mg/h with a continuous additional maintenance dose during RRT of 141 mg/h for intermittent HDF, 126 mg/h for SLED, and 69 mg/h for continuous HD. The lower row corresponds to vancomycin concentrations after vancomycin administration with a LD of 22.41 mg/kg (infusion rate 1 g/h) and a MD of 24.74 mg/h with an intermittent additional maintenance dose during RRT of 645 mg for intermittent HDF and 1535 mg for SLED. HD haemodialysis, HDF haemodiafiltration, LD loading dose, MD maintenance dose, SLED: sustained low‐efficiency dialysis. The grey shaded areas represent the periods when RRT was ongoing

Claisse G, Zufferey PJ, Trone JC, et al. Predicting the dose of vancomycin in ICU patients receiving different types of RRT therapy: a model‐based meta‐analytic approach. Br J Clin Pharmacol. 2019;85:1215–1226. 10.1111/bcp.13904