Early Bayesian Dose Adjustment of Vancomycin Continuous Infusion in Children in a Randomized Controlled Trial

Methicillin-resistant staphylococcal infections are a global burden. Area under the concentration-time curve to MIC (AUC/MIC) ratio is the pharmacokinetic (PK) parameter that best predicts vancomycin efficacy. Its therapeutic range is narrow, difficult to achieve because of a wide intersubject variability, especially in children, and is not routinely targeted since the AUC is rarely available.

ABSTRACT

Methicillin-resistant staphylococcal infections are a global burden. Area under the concentration-time curve to MIC (AUC/MIC) ratio is the pharmacokinetic (PK) parameter that best predicts vancomycin efficacy. Its therapeutic range is narrow, difficult to achieve because of a wide intersubject variability, especially in children, and is not routinely targeted since the AUC is rarely available. We investigated if an early Bayesian dose adjustment would increase the rate of vancomycin target attainment in the first 24 hours of treatment (H24) in children. We conducted a single-center randomized controlled trial in 4 pediatric departments of Necker-Enfants Malades Hospital (Paris, France). Patients aged 3 months to 17 years for whom intravenous vancomycin was started were eligible and randomized in a 1:1 ratio; routine care was compared with an early vancomycin therapeutic drug monitoring (3 h after treatment initiation) followed by an early Bayesian dose adjustment using a previously published population-based PK model that included age, body weight, and serum creatinine as covariates. The primary outcome was the proportion of patients of each group achieving vancomycin therapeutic range at H24, defined by AUC_0–24/MIC of ≥400 and AUC_0–24 of ≤800 mg-h/liter. Ninety-nine patients were enrolled and 49 were randomized to the Bayesian group and 50 to the control group. Modified intention-to-treat analysis included 82 patients; 85% of Bayesian group patients achieved H24 vancomycin target versus 57% of control group patients (P = 0.007) with no difference regarding iatrogenic events. Early Bayesian dose adjustment increased the proportion of children achieving vancomycin target at H24, which may improve clinical outcomes of methicillin-resistant staphylococcal infections. (This study has been registered at ClinicalTrials.gov under identifier NCT02694458.)

INTRODUCTION

The methicillin resistance rate among Staphylococcus aureus is still high and is a major public health issue (1, 2). Coagulase-negative staphylococci (CNS) are also frequently methicillin resistant (3). The latest data from the European Centre for Disease Prevention and Control showed that 16.9% of invasive isolates of Staphylococcus aureus are methicillin resistant in Europe, reaching more than 40% in some countries (1, 2). Cassini and colleagues showed that the estimated incidence of methicillin-resistant Staphylococcus aureus (MRSA) infections increased by 1.28 times between 2007 and 2015, with infants being particularly affected (4). Bielicki and colleagues found that Staphylococcus aureus was the commonest pathogen in bloodstream isolates in children of all ages in Europe (27% of all pathogens), with a methicillin-resistance rate of 16.4% (5). Larru and colleagues found that Staphylococcus aureus and coagulase-negative Staphylococcus spp. were the two most commonly isolated pathogens in bloodstream infections in children in a large, tertiary care children’s hospital in the United States (51.9% of overall), with a significant increase in the incidence of MRSA during the study period (6). Intravenous vancomycin is the first-line antibiotic therapy for confirmed or suspected MRSA or CNS infections. The pharmacokinetic/pharmacodynamic (PK/PD) parameter that was reported in adults to predict vancomycin efficacy is the ratio of the area under the concentration-time curve (AUC) to the MIC (7, 8). Studies in adults support that a vancomycin target of AUC at 24 h (AUC₂₄)/MIC of ≥400 at steady state improves both clinical and bacteriological outcomes (7–11). Early target attainment and quick blood culture sterilization have also been shown to improve the clinical prognosis (12–14). In recent retrospective studies, less than 50% of children achieve the vancomycin target using the recommended dosing regimens (15–17). This can be at least partially explained by the wide intersubject variability of vancomycin PK parameters, especially in children. Besides, the AUC is rarely available and some authors have shown that it poorly correlates to vancomycin trough levels especially in children (17, 18). Targeting trough concentration to approximate AUC₂₄ in routine care is, therefore, questionable.

Vancomycin-associated nephrotoxicity is still debated, and its predictive PK parameter is unknown. Publications suggest that exposure may be associated with nephrotoxicity in adults (19) and in children with a threshold value of AUC₂₄ of ≥800 mg-h/liter (20). Kloprogge et al. recently showed that cumulative vancomycin exposure was positively correlated with nephrotoxicity in children (21).

By merging a priori information from the population model with the actual observation coming from the patient, the Bayesian approach reduces uncertainty and may improve dose adjustment accuracy. The aim of this study was to assess if an early Bayesian dose adjustment of vancomycin would increase the rate of target attainment in the first 24 hours of treatment.

RESULTS

Study population.

Among 114 patients assessed for eligibility, 15 were ineligible because they did not meet the inclusion criteria. Seven of them were already receiving vancomycin at the time of a possible inclusion (Fig. 1). Nighty-nine patients were randomized and formed the intention-to-treat (ITT) population, namely, 49 were in the Bayesian group and 50 in the control group. Eighty-two patients formed the modified intention-to-treat (mITT) population. Two patients from the Bayesian group were transferred to the control group because they had no therapeutic drug monitoring (TDM) at the third hour of treatment H3 and no dose adjustment at H6. The mITT population was then composed of 40 patients in the Bayesian group and 42 patients in the control group.

FIG 1.

Flow diagram. Trial profile. ITT, intention-to-treat; mITT, modified intention-to-treat.

Baseline characteristics were similar between treatment groups (Table 1). Initial vancomycin doses according to each department are displayed in Table 2. Ninety-eight of the 99 patients received a continuous administration of vancomycin following a loading dose. One patient received one single dose of vancomycin with no maintenance dose because of a decreased glomerular filtration rate.

TABLE 1.

Baseline characteristics

Characteristica	Total (n = 99)	Bayesian group (n = 49)	Control group (n = 50)
Median age, yr [IQR] (min–max)	4.5 [0.9–9.4] (0.2–17.4)	2 [0.8–7.7] (0.2–17.4)	5.7 [1.3–9.6] (0.3–17.3)
Females, n (%)	51/99 (52)	24/49 (49)	27/50 (54)
Median weight, kg [IQR] (min–max)	13.9 [8.7–29] (4–85)	11.3 [7.9–25.1] (4–85)	17 [9.4–30.1] (5–73.4)
Median height, cm [IQR] (min–max)	101.5 [72–129.5] (52–170)	89 [70–130] (52–170)	108 [75.5–128] (61–170)
Serum creatinine, μmol/L [IQR] (min–max)	26 [18–43] (9–160)	24 [16.5–36.2] (9–71)	30 [22–47] (12–160)
Pediatric department of inclusion, n (%)
Immunohematology	52/99 (53)	25/49 (51)	27/50 (54)
PICU	40/99 (40)	21/49 (43)	19/50 (38)
Gastroenterology and Hepatology	7/99 (7)	3/49 (6)	4/50 (8)
Nephrology	0/99 (0)	0/49 (0)	0/50 (0)
Reasons of vancomycin initiationb , n (%)
Suspicion of CVC-related BSI	68/99 (69)	34/49 (69)	34/50 (68)
Proven CVC-related BSI	26/99 (26)	13/49 (27)	13/50 (26)
Febrile aplasia/neutropenia	29/99 (29)	14/49 (29)	15/50 (30)
Sepsis/septic shock	8/99 (8)	6/49 (12)	2/50 (4)
Suspicion of non-CVC-related BSI	3/99 (3)	1/49 (2)	2/50 (4)
Vancomycin method of administration, n (%)
Continuous	98/99 (99)	49/49 (100)	49/50 (98)
Intermittent	1/99 (1)	0/49 (0)	1/50 (2)
Initial dose of vancomycin
Administration of a loading dose, n (%)	99/99 (100)	49/49 (100)	50/50 (100)
Median loading dose, mg/kg [IQR] (min–max)	14.9 [14.7–15] (6–140.8)	14.8 [14.6–15] (6–16)	15 [14.7–15.1] (6.8–140.8)
Median maintenance dose, mg/kg/24 h [IQR] (min–max)	48 [44.6–59.2] (0–64.8)	48 [44.8–58.6] (0–63.8)	55.2 [44.6–59.6] (0–64.8)
No. of other nephrotoxic drugs, n (%)
0	19/99 (19)	9/49 (18)	10/50 (20)
1 or 2	49/99 (49)	23/49 (47)	26/50 (52)
≥3	31/99 (31)	17/49 (35)	14/50 (28)
Nephrotoxic drugsb , n (%)
Cyclosporine	38/99 (38)	17/49 (35)	21/50 (42)
IV aciclovir	33/99 (33)	16/49 (33)	17/50 (34)
IV furosemide	31/99 (31)	21/49 (43)	10/50 (20)
IV aminosides	30/99 (30)	15/49 (31)	15/50 (30)
IV immunoglobulins	23/99 (23)	14/49 (29)	9/50 (18)
NSAIDs/ACE inhibitors/ARBs	8/99 (8)	4/49 (8)	4/50 (8)
Tacrolimus	7/99 (7)	5/49 (10)	2/50 (4)
IV amphotericin B	6/99 (6)	2/49 (4)	4/50 (8)
Foscarnet	4/99 (4)	1/49 (2)	3/50 (6)
Cisplatin/ifosfamide/lenalidomide	1/99 (1)	0/49 (0)	1/50 (2)

^aIQR, interquartile range; min, minimum; max, maximum; PICU, Pediatric Intensive Care Unit; CVC, central venous catheter; BSI, bloodstream infection; IV, intravenous; NSAIDs, nonsteroidal anti-inflammatory drugs; ACE inhibitors, angiotensin-converting enzyme inhibitor; ARBs, angiotensin II receptor blockers.

^bOne patient could have more than one reason of vancomycin initiation and could receive more than one other nephrotoxic drug.

TABLE 2.

Role of the initial dose of vancomycin in pharmacological target attainment^a

Department	Dose (mg/kg/24 h), median (IQR)	Control group exposure target attainment, n (%)
PICU	45 (43.5–45.5)	6 (43)
Pediatric Immunohematology	59.4 (55.6–60.2)	14 (67)
Pediatric Gastroenterology and Hepatology	51.4 (44.3–58.7)	3 (50)

^aIQR, interquartile range; PICU, Pediatric Intensive Care Unit. The P value is 0.36 for data in this table.

Outcomes.

Thirty-four (85%) of the Bayesian group patients versus 24 (57%) of the control group patients reached the H24 vancomycin exposure target AUC from 0 to 24 hours (AUC_0–24)/MIC of ≥400 and AUC_0–24 of ≤800 mg-h/liter in the mITT population (P = 0.007) (Table 3; Fig. 2). The difference remains statistically significant in the ITT analysis; 34 patients (69%) of the Bayesian group reached the target versus 24 (48%) of the control group patients (P = 0.041).

TABLE 3.

Primary and secondary pharmacological outcomes

Pharmacological outcome	Analysis type	No. (%) according to:		P value
		Bayesian group	Control group
Vancomycin exposure target attainment, AUCa 0–24/MIC of ≥400 and AUC0–24 of ≤800 mg-h/liter	mITT (n = 82)	34/40 (85)	24/42 (57)	0.007
	ITT (n = 99)	34/49 (69)	24/50 (48)	0.041
Vancomycin concentration target, 20 to 40 mg/liter	mITT (n = 82)	27/40 (68)	16/42 (38)	0.009

^aAUC, area under the concentration-time curve.

FIG 2.

Evolution of vancomycin plasma concentration over time for each patient of each group. Blue and red points symbolize vancomycin plasma concentration measurements. Blue and red lines represent Bayesian-estimated vancomycin plasma concentration. The two horizontal black lines represent the concentration threshold equivalent to an AUC of 400 mg-h/liter at steady-state (16.7 mg/liter) and the toxicity concentration threshold used for continuous infusion (40 mg/liter).

For 30 patients (79%), the Bayesian dose adjustment was an increase of the vancomycin dose. The median increase was 50%, with a minimum of 12.5% and a maximum of 140%. For three patients, the dose adjustment was a decrease of 15%, 20%, and 50% of the initial maintenance dose. For five patients, the maintenance dose was not modified. Two patients did not receive an initial maintenance dose after the loading dose because of the occurrence of Red man syndrome. The maintenance dose was straightaway calculated at H6 with the Bayesian method. The median (minimum − maximum) maintenance dose after Bayesian dose adjustment was 72 mg/kg/24 h (30.4 to 109.3 mg/kg/24 h). According to simulations, with a covariate-adjusted first dose, 55 patients (67%) would have reached the target (95% confidence interval [CI], 56% to 77%). The initial maintenance doses used in the involved departments were slightly different with no consequence on target attainment (Table 2).

Twenty-seven patients (68%) from the Bayesian group versus 16 (38%) from the control group reached the H24 vancomycin concentration target of 20 to 40 mg/liter in the mITT population (P = 0.009) (Table 3).

Concerning clinical, biological, and bacteriological outcomes, data were analyzed only for patients with a final diagnosis of infection treatable by vancomycin and who had received vancomycin for at least 7 days. Infections were considered treatable by vancomycin if the isolated pathogen was a bacterium commonly known as susceptible to vancomycin. Twenty-eight (34%) of the 82 patients analyzed in the mITT population had an infection caused by vancomycin-susceptible bacteria. The 32 bacteria identified were mainly CNS, namely, Staphylococcus epidermidis (n = 17), Staphylococcus haemolyticus (n = 3), Staphylococcus hominis (n = 3), Staphylococcus capitis (n = 1), nontypeable CNS (n = 1), methicillin-sensitive Staphylococcus aureus (n = 3), Streptococcus mitis (n = 2), group A streptococcus (n = 1), and Enterococcus faecalis (n = 1). For eight of these 28 patients, vancomycin was discontinued before the 7th day of follow-up. Thirteen of the 20 remaining patients were part of the Bayesian group. The delay in obtaining sustainable apyrexia and C-reactive protein (CRP) evolution was not statistically different between groups. The duration of bacteremia was analyzable in only 14 patients and was not different between groups.

Vancomycin-associated nephrotoxicity, defined by the criteria previously described, occurred in 10 patients (12%), namely, 6 (60%) were in the control group and 4 belonged to the Bayesian group (P = 0.74). Patients with vancomycin-attributable nephrotoxicity all had vancomycin concentrations within the therapeutic range. The other four iatrogenic events (two in each group) were Red man syndrome. Finally, three patients died during the follow-up period. None of the deaths was attributed to an infection nor to an iatrogenic event.

DISCUSSION

This is the first randomized trial to prospectively assess the contribution of vancomycin early Bayesian dose adjustment. We showed that an early Bayesian dose adjustment of vancomycin at H6 significantly and safely increased pharmacological target attainment in children at the 24th hour of treatment. The six patients who did not reach the target in the Bayesian group received a lower dose than the Bayesian-calculated dose because of physician input. All of them had an AUC_0–24 of <400 mg-h/liter, which suggests that those patients would probably achieve the target with the Bayesian-calculated dose. Therefore, the proportion of target attainment in the Bayesian group would have been 100%. Most of the current strategies of vancomycin TDM and empirical dose adjustment fail to regularly achieve the vancomycin target (15–17). Target attainment is correlated with clinical and bacteriological outcomes (7–11). A recent meta-analysis showed that achieving a high AUC_0–24/MIC of vancomycin could significantly decrease mortality rates by 53% and rates of infection treatment failure by 61%, with 400 being a reasonable target (10). Early target attainment and quick blood culture sterilization also improved the clinical prognosis (12–14). Thus, an early Bayesian dose adjustment of vancomycin could allow an earlier control of staphylococcal infections in children and then improve clinical outcomes as well as decrease emergence of resistant strains (8, 22–24). Individual parameter estimation of vancomycin with the Bayesian approach reduces uncertainty and improves dose adjustment accuracy, which is particularly useful in a population of children. In the context of TDM, interoccasion variability (IOV) on PK parameters is of great interest. However, published vancomycin population pharmacokinetic models do not include interoccasion variability. The clearance of vancomycin in pediatric patients appears to be related primarily to the degree of renal function. Therefore, IOV for vancomycin should be mainly driven and explained by intrapatient changes in renal function throughout follow-up.

The population-based PK (POPPK) model used to make the Bayesian estimation of individual PK parameters was published by Le et al. in 2013 (9). The proportion of patients with impaired renal function is not known. Serum creatinine is not sufficient to evaluate the glomerular filtration rate in children, as it varies with height that is itself linked to age (25). In this model, both age and serum creatinine (sCr) were found to be independent covariates that influence vancomycin clearance. The effect of sCr is expected to vary with the age of patients, but no interaction between age and sCr effects was included in the modeling. Therefore, this POPPK model may not be appropriate for young children with renal impairment. The use of an age-corrected creatinine as a continuous covariate on clearance could be an option to get around this issue (21).

If covariates are found to affect PK parameters that may be important to intersubject variability, these could be used to individualize the dose a priori. According to simulations, with a covariate-adjusted first dose, the proportion of patients who would have reached the target at H24 remains lower than with an early Bayesian dose adjustment. It is also noteworthy that despite the different vancomycin doses in each department because of different local protocols, the proportion of patients achieving the pharmacological target in the control group was not statistically different between those three departments. Taken together, these data show that variations in the initial dose of vancomycin, whether individualized or not, seem to be less effective than early Bayesian dose adjustment in improving target attainment at H24.

The median maintenance dose after Bayesian dose adjustment was 72 mg/kg/24 h (interquartile range [IQR], 63 to 90). This is not the dose that we would recommend to initiate vancomycin treatment; it is the dose that was necessary to make up the 6 hours of inadequate vancomycin rate. The median (IQR) initial maintenance dose that should have been given was recalculated a posteriori and estimated to be 63 (48 to 88) mg/kg/24 h. Vancomycin initial doses used in our study were similar to those used in other studies and recommended in guidelines (8, 18).

Clinical, biological, and bacteriological outcomes were not significantly different between groups. This study was not designed for this purpose. The analysis of these secondary outcomes was relevant only in patients infected by vancomycin-susceptible bacteria. Only a small number of patients with vancomycin-susceptible infections was identified among patients for whom vancomycin had been started (28 patients, 34%). As a first-line empirical antibiotic therapy for methicillin-resistant staphylococcal infections, vancomycin is often started in a probabilistic way (26, 27). In our study, the proportion of empirical prescription was particularly high (72%), and the proportion of vancomycin-treatable infections secondarily documented among those empirically treated patients was low. This may be partly due to the large number of immunocompromised children in our population.

Vancomycin-related iatrogenia is a major concern. Our definition of vancomycin-related nephrotoxicity had already been used in many studies (20, 22, 28, 29). The incidence of nephrotoxicity in our study (12.3%) was similar to that reported recently (29). None of the patients of the Bayesian group was above the pharmacological target of vancomycin. There was no statistically significant difference of nephrotoxicity between the two groups. Even if our data did not point out that early Bayesian dose adjustment decreases iatrogenia, it helped to avoid three overdosages. Indeed, for three patients of the Bayesian group, the vancomycin dose was decreased by 15%, 20%, and 50% at the 6th hour of treatment, with a final AUC_0–24 of 749, 764, and 752 mg-h/liter, respectively.

The major strength of our study is the prospective use of the AUC/MIC ratio as a pharmacological target for vancomycin, instead of an inaccurate approximation using trough concentrations that poorly correlate to exposure (17, 18). Furthermore, Bayesian dose adjustment was performed using tools transposable into routine care, and the use of a single laboratory to measure vancomycin plasma concentrations limited measurement-related variability. Vancomycin PD and PK are particularly variable in intensive care unit (ICU) patients and in patients with neutropenia (15, 30). Another strength of this study is the diversity of conditions of included patients (e.g., immunocompromised, undernourished, aplasic/neutropenic, and ICU patients) and of local protocols, which may reduce the potential bias of single center inclusions and increase the generalizability of our results. This study was not conducted in a blind manner, but the use of objective study outcomes limited the impact of study design on results.

Our study showed that an early Bayesian dose adjustment of vancomycin increased the proportion of children achieving vancomycin pharmacological target at H24, which could improve clinical and bacteriological outcomes of methicillin-resistant staphylococcal infections in this particular population. This trial is the first randomized trial for any drug that assessed the contribution of Bayesian TDM and dose adjustment. Our findings are important since we showed that this Bayesian approach seems to work. Further studies are needed, in a larger population of patients infected by vancomycin-treatable bacteria, to prove the clinical and bacteriological benefits of this personalized strategy and to assess if it could help to reduce adverse effects of vancomycin.

MATERIALS AND METHODS

Study design.

We conducted an open-label 1:1 randomized controlled trial in two parallel groups. The trial involved four pediatric departments of Necker-Enfants Malades teaching hospital (Paris, France), namely, the Pediatric Intensive Care Unit (PICU), the Department of Pediatric Gastroenterology and Hepatology, the Department of Pediatric Immunohematology, and the Department of Pediatric Nephrology. The study took place during 1 year from February 2016 to February 2017. The Institutional Review Board (Comité de Protection des Personnes Ile-de-France I) approved the protocol. This trial was registered at ClinicalTrials.gov, number NCT02694458.

Patients.

Children aged 3 months to 17 years, male or female, were eligible for inclusion if (i) their medical condition included an indication to start intravenous vancomycin, (ii) their bodyweight was ≥4 kg, (iii) their serum creatinine (sCr) concentration was ≤250 μmol/L, and if (iv) they were not undergoing renal replacement therapy at the time of inclusion. Patients were not eligible if they were already receiving intravenous vancomycin at the time of inclusion. Patients were excluded from the study if the vancomycin treatment duration was less than 24 hours. Patients and legal representatives were informed, and their consent was obtained.

Procedures.

Patients were randomly allocated using a department-stratified computer-generated block randomization in a 1:1 ratio into an intervention group (Bayesian group) or a control group (Fig. 3). No masking was used after randomization.

FIG 3.

Procedures. TDM, therapeutic drug monitoring.

Initial time (H0) was defined as the start of the first vancomycin infusion. According to local protocols, a loading dose of 15 mg/kg was administered over 60 minutes before the continuous infusion. Patients of both groups received initial vancomycin doses according to local protocols in each department. Patients of the control group underwent a measure of vancomycin serum concentration at the end of the first day of treatment (H24), namely, at the 24th hour for patients receiving continuous infusion or before the 5th infusion in case of intermittent infusions every 6 hours. For patients of the Bayesian group, an early therapeutic drug monitoring (TDM) was performed at the 3rd hour of treatment (H3), with a Bayesian dose adjustment at the 6th hour of treatment (H6). The H3 time point was selected as the earliest time allowing vancomycin clearance assessment after a 1- to 2-hour loading dose, followed by a continuous vancomycin infusion. Another TDM was then performed at H24 under the same conditions as in the control group.

Vancomycin and serum creatinine assay.

Vancomycin plasma concentrations were measured using a Cobas 8000 instrument (Roche Diagnostics, Indianapolis, IN, USA) (lower and upper limits of quantification at 1.7 and 80 mg/liter, respectively) with appropriate quality assurance measures in place. The intraday and interday coefficients of variation (CVs) were all <8%. Serum creatinine concentrations were measured using the isotope dilution mass spectrometry (IDMS) traceable enzymatic method (Architect C16000; Abbott diagnostics, IL, USA).

Bayesian dose adjustment.

Individual vancomycin PK parameters were derived from a Bayesian approach using the one-compartment model with linear clearance published by Le and colleagues (9). Both clearance (CL) and volume of distribution (V) parameters were related to body weight according to allometric scaling. CL decreased with increasing sCr and age. This model was built from the analysis of 1,660 vancomycin serum concentrations from 702 patients. Median age was 6.6 years (interquartile range [IQR], 2.2 to 13.4), median weight was 22.7 kg (IQR, 12.6 to 46), and median baseline sCr was 35 μmol/liter (IQR, 27 to 53). The final covariate model on CL and V parameters was:

$$\mathit{CL}={\theta }_{\mathit{CL}}\times {\text{BW}}^{0.75}\times {\left(\frac{0.48}{\text{sCr}}\right)}^{0.362}\times {\left(\frac{\text{ln}(\text{age})}{7.8}\right)}^{0.995};V={\theta }_V\times \text{BW}$$ (1)

where θ_CL is the typical value for clearance estimated to 0.248; θ_V is the typical value for volume estimated to 0.636; BW stands for body weight (in kg), age stands for postnatal age (in days), and sCr stands for serum creatinine (in mg/dl).

In the Bayesian group, PK parameters were derived from the H3 concentration measurement with a Bayesian strategy to meet a posteriori maximum likelihood estimate for an individual patient. A posteriori maximum likelihood estimates of individual patient parameters were found by minimizing the following function (phi) with the “nlm” function implemented in R software:

$$\varphi ={\displaystyle \sum }_{k=1}^p\frac{[\log \left({\theta }_{\mathit{ind},k}\right)-\log \left({\theta }_{\mathit{pop},k}\right){]}^2}{{{\omega }_k}^2}+{\displaystyle \sum }_{j=1}^{\mathit{ni}}\frac{[\log \left(C_{\mathit{obs}i,j}\right)-\log \left(C_{\mathit{pred}i,j}\right){]}^2}{{{\sigma }_{\mathit{prop}}}^2}$$ (2)

This function accounts for the gap between observed concentrations for patient i at times j (C_{obs i,j}) and the model-predicted concentrations (C_{pred i,j}) as well as the gap between the k pharmacokinetic parameters of the patient (θ_{ind, k}) and those from the mean population (θ_pop,k). ω_k² stands for the variance of the interindividual variability on parameter k, and σ_prop² is the proportional residual error estimated from the population PK model. The theoretical dose providing an AUC_0–24 of 400 was then calculated according to the individual pharmacokinetic parameters derived from the Bayesian estimation. In the control group AUC_0–24 was derived from a Bayesian estimation of the individual PK parameters.

Covariate-adjusted first dose simulation.

The dose individualization on beforehand (so called a priori dose adaptation) was also assessed through simulations. Individual covariates were used along with the population-based PK (9) (POPPK model) to derive a priori doses maximizing the likelihood of achieving the target exposure. Concentration time courses were simulated using these a priori doses and the Bayesian estimated PK parameters. Individual AUC_0–24/MIC ratios that would have been obtained were then estimated.

Outcomes.

The primary outcome was the proportion of patients with a vancomycin exposure, for the first 24 h of treatment, in the target range AUC_0–24/MIC of ≥400 and AUC_0–24 of ≤800 mg-h/liter. If the MIC was not known at the time of inclusion, it was set at 1 mg/liter, the most frequent MIC for MRSA and for most of CNS according to the European Committee on Antimicrobial Susceptibility Testing (EUCAST). It is also the highest MIC recorded by the EUCAST, which allows achievement of the vancomycin pharmacological target without exceeding the toxicity threshold. Secondary outcomes included (i) the proportion of patients with a vancomycin serum concentration, at the 24th hour of treatment, in the target range of routine TDM, namely, 20 to 40 mg/liter, if administration was continuous, and trough concentration of 15 to 20 mg/liter before the 5th infusion in case of intermittent dosing regimen; (ii) the delay in obtaining sustainable apyrexia defined by a body temperature of less than 38°C; (iii) the evolution of C-reactive protein (CRP) over time; (iv) the duration of bacteremia assessed by the time until the last positive blood culture; and (v) the vancomycin-associated nephrotoxicity assessed by sCr. Vancomycin-associated nephrotoxicity was defined as (i) an increase of >44 μmol/liter (0.5 mg/dl); or (ii) a 50% increase in sCr over baseline in consecutively obtained daily sCr values; or (iii) a drop in calculated creatinine clearance of ≥50% from baseline calculated using the bedside Schwartz formula (25), over 2 consecutive days without an alternative explanation, from the beginning until 72 h after the end of vancomycin treatment (20, 22, 28, 29).

Statistical analysis.

The sample size required was calculated assuming a proportion of 30% of patients achieving the pharmacological target in the control group (15). We calculated the sample size with 80% power (a two-sided alpha risk of 0.05) and assuming a target attainment rate of 60% in the Bayesian group. This calculation yielded a planned sample size for this study of 84 randomized patients (42 per group).

Quantitative variables were compared in nonparametric Wilcoxon tests, and proportions were compared in Fisher’s exact tests. Evolution of CRP was compared using linear mixed regression. We considered P values of <0.05 to be statistically significant for all analyses. All comparisons were based on two-tailed tests. Statistical analyses were made using R software 3.2.2 version.

Both intention-to-treat (ITT) and modified intention-to-treat (mITT) analyses were performed for the primary outcome. Our ITT population consisted of all randomized participants who received at least one infusion of vancomycin. In the ITT analysis, missing primary outcomes were treated as failures. A mITT population was also defined, including all randomized patients without violation of eligibility criteria and whose primary outcome was evaluable.