Poor Correlation between Meropenem and Piperacillin Plasma Concentrations and Delivered Dose of Continuous Renal Replacement Therapy

There is insufficient data on the relationship between antibiotic dosing and plasma concentrations in patients treated with continuous renal replacement therapy (CRRT). In this prospective observational study, we explored the variability in plasma concentrations of meropenem and piperacillin in critically ill patients treated with CRRT and the correlation between concentrations and CRRT intensity.

ABSTRACT

There is insufficient data on the relationship between antibiotic dosing and plasma concentrations in patients treated with continuous renal replacement therapy (CRRT). In this prospective observational study, we explored the variability in plasma concentrations of meropenem and piperacillin in critically ill patients treated with CRRT and the correlation between concentrations and CRRT intensity. Antibiotic concentrations were measured at the middle and end of the dosing interval and repeated after 2 to 3 days when feasible. Measured concentrations were compared to the clinical susceptible breakpoints for Pseudomonas aeruginosa, 16 and 2 mg/liter for piperacillin and meropenem, respectively. CRRT intensity was estimated by delivered, time-averaged, total effluent flow (Q_eff), corrected for predilution. Concentrations were also compared between patients with different residual diuresis. We included 140 meropenem concentrations from 98 patients and 47 piperacillin concentrations from 37 patients. Concentrations at the middle of the dosing interval were above target at all occasions for both antibiotics. For meropenem, 6.5% of trough concentrations were below target, and for piperacillin, 22%. Correlations between Q_eff and antibiotic concentrations or the concentration half-life (t_1/2) were either statistically not significant or weak. Meropenem concentrations and t_1/2 values differed between patients with different residual diuresis. Thus, when treating intensive care patients with CRRT and recommended doses of meropenem or piperacillin, both low, suboptimal plasma concentrations and unnecessarily high, potentially toxic, plasma concentrations are common. Plasma concentrations cannot be predicted from CRRT intensity. Residual diuresis is associated with lower meropenem concentrations, but the correlation is weak. Concentration measurement is probably the most useful approach to avoid suboptimal treatment.

INTRODUCTION

Sepsis remains one of the most common reasons for admitting patients to intensive care units (ICUs). Mortality is high, reaching 60% for patients with acute kidney injury requiring continuous renal replacement therapy (CRRT) (1). Survival depends on optimal multimodal treatment, including early, adequate, antibiotic therapy (2). Beta-lactam antibiotics such as meropenem and piperacillin are primarily eliminated by the renal route (3, 4). Consequently, reduced dosing is recommended for patients with renal failure. However, current recommendations for beta-lactam dosing in patients treated with renal replacement therapy are widely divergent (5), which is also apparent in recent reports on the doses used in clinical practice (6, 7). This reflects insufficient knowledge of the relationship between dosing and plasma concentrations in these patients. In addition, it is often difficult to apply the available literature to current practice because the reported data on CRRT settings are often incomplete, characteristics of the used dialysis filters, and the application of CRRT has changed over the years, often in ways that increase drug clearance. Suboptimal dosing, resulting in lower than intended plasma concentrations, has been suggested to contribute to the high mortality in sepsis patients treated with CRRT (8). Also, unexpectedly high plasma concentrations are associated with neuro- and nephrotoxicity, both of which are difficult to identify in critically ill patients due to the high prevalence of neurologic symptoms and renal failure from other causes (9–11). There is therefore a great need for further knowledge in this field.

In this prospective observational study, our aims were to report the antibiotic plasma concentrations in critical care patients treated with CRRT and standard doses of either meropenem or piperacillin-tazobactam in order to investigate the relationship between these concentrations and the CRRT settings (dosage) and residual renal function. We also evaluated the need for routine therapeutic drug monitoring in this patient population. Compared to prior studies, this report includes data from a larger patient population, including detailed data on the applied CRRT dose and the effect of residual renal function.

RESULTS

Patient demographics and clinical data are reported in Table 1. In total, we included meropenem concentrations from 140 occasions in 98 patients treated with meropenem and from 47 occasions in 37 patients treated with piperacillin. Paired samples (at the middle and end of the dosing interval) were obtained 113 and 32 times, respectively (Table 1). Nine patients were included in both cohorts. For meropenem, the most common dosing regime was 1 g three times daily (1 g q8h) (114 occasions), the regime was 2 g q8h at 8, 1 g q12h at 8, 1 g q6h at 5, 1 g q24h at 1, and 0.5 g q8h at 1 occasion(s). The most common piperacillin regime was 4 g three times daily (4 g q8h) (36 occasions), the dosing was 4 g q6h at 7, 4 g q12h at 3, and 2 g q6h at 1 occasion(s). All measured concentrations are shown in Fig. 1, illustrating the wide variations in concentrations both at the middle and at the end of the dosing interval. For meropenem, the minimal-maximal concentrations at the middle and end of the dosing interval were 2.2 to 48 and 0.2 to 28 mg/liter, respectively; for piperacillin, these concentrations were 18.2 to 139 and 1.5 to 105 mg/liter, respectively. Summary statistics for concentrations and half-lives (t_1/2) are reported in Table 1 and in Table S1 in the supplemental material. The concentrations at the middle of the dosing interval were above the target at all occasions for both antibiotics. In contrast, at the end of the dosing interval, the meropenem concentration was below target in 6.5% of the measurements (nine occasions in six individual patients). The dosing regime was 1 g q8h at all except for one of these occasions. For piperacillin, the concentration was below target in 22% of the measurements (eight measurements in eight individual patients). The dosing regime was 4 g q8h for six of these patients and 4 g q12h for two patients. The correlation between Q_eff and antibiotic concentrations or concentration t_1/2 were either statistically not significant or weak (Fig. 2 and 3). Note the large variation in t_1/2 between occasions with similar CRRT settings. For meropenem, the concentrations and t_1/2 values differed between patients with different residual diuresis, the trend was similar for piperacillin but statistically not significant (Fig. 4). Multiple linear regression showed very little collinearity between the Q_eff value and the diuresis group (tolerance range for all analyses, 0.871 to 0.999). Thus, correlation—or lack of correlation—between antibiotic concentrations and Q_eff was not explained by covariation of Q_eff and diuresis. For both antibiotic, concentrations at the middle interval decreased with greater body weight (Fig. 5). Although the trends were similar, this relationship was not statistically significant for trough concentrations (Fig. 5). We found no significant correlations between antibiotic concentrations and the number of administered doses before measurements (see Fig. S1). The causative pathogen was identified in 59 patients treated with meropenem and 14 patients treated with piperacillin-tazobactam (see Table S1 in the supplemental material).

TABLE 1.

Patient demographics, clinical data, antibiotic concentrations, and CRRT parameters^a

Parameter	Meropenem	Piperacillin
No. of patients	98	37
No. of patients included in both cohorts	9	9
No. of sampling occasions	140	47
No. of sampling occasions with paired samples	113	32
% male	68	73
Mean (range)
Age (yrs)	62 (48–71)	60 (54–71)
Body wt (kg)	83.7 (72.0–94.4)	84.5 (69.5–103.0)
Ht (cm)	177 (170–182) (n = 91)	172 (167–182) (n = 33)
Body mass index (kg/m2)	27.0 (23.7–32.2) (n = 91)	27.2 (24.0–31.9) (n = 33)
Cause of ICU admission, no. (%) of patients
Medical admission	59 (60)	17 (46)
Elective surgery	9 (9)	3 (8)
Acute surgery	18 (18)	9 (24)
Trauma	12 (12)	8 (22)
Community-acquired infection, no. (%)	42 (43)	19 (51)
Hospital-acquired infection	56 (57)	18 (49)
Verified or suspected focus of infection
Lower respiratory tract	34 (35)	10 (27)
Abdominal	31 (32)	15 (40)
Verified microbiological etiology	59 (60)	14 (38)
No. (%)
Severe sepsis	88 (90)	30 (81)
Septic shock	70 (71)	24 (65)
Invasive mechanical ventilation	84 (86)	28 (76)
Chronic renal failure and hemodialysis treatment	7 (7)	3 (8)
ICU mortality	23 (25) (n = 93)	10 (27) (n = 37)
Hospital mortality	38 (41) (n = 93)	13 (35) (n = 37)
Antibiotic concn, mg/liter (range)
Middle of dosing interval	17.0 (12.0–20.0) (n = 86)	48.3 (39.2–60.2) (n = 27)
End of dosing interval	8.0 (4.2–11.5) (n = 97)	26.6 (20.3–46.2) (n = 37)
<MIC at middle of dosing interval, no. (%)	0 (0)	0 (0)
<MIC at end of dosing interval, no. (%)	6 (6)	6 (16)
Terminal half-life (h)	3.8 (2.8–4.6) (n = 85)	4.5 (3.6–6.4) (n = 27)
Measurements after antibiotic dose (no.)	5 (2–9)	4 (2–8)
CRRT parameters
Qb (ml/min)	150 (135–180)	150 (120–193)
Qd (ml/h)	1,000 (652–1,350)	1,000 (673–1,200)
Qpre (ml/h)	1,500 (1,340–1,870)	1,500 (1,200–200)
Qpost (ml/h)	500 (500–500)	500 (500–667)
Qeff adjusted (ml/h)	2,342 (2,168–2,953)	2,678 (2,199–3,159)
Qeff adjusted (ml/kg/h)	30.3 (25.6–35.2)	31.7 (27.8–36.1)

^aValues are expressed as medians (interquartile ranges) unless stated otherwise. Antibiotic concentrations and CRRT parameters correspond to the first observation for each patient and each parameter. CRRT parameters are time averaged for the corresponding dosing interval. The notation “n = x” in the results columns refers to numbers of measurements or patients for parameters with missing data. Q_d, dialysate; Q_pre, replacement fluid administered before the dialysis filter; Q_post, replacement fluid administered after the dialysis filter; Q_eff, total effluent flow (see the text). “Adjusted” indicates values adjusted for predilution.

FIG 1.

The plots show all measured meropenem (upper panel) and piperacillin (lower panel) concentrations at the middle (round, blue markers) and end (diamond, red markers) of the interval. Filled markers denote concentrations with doses of 1 g meropenem and 4 g piperacillin, respectively, three times daily. Unfilled markers are concentrations at other regimens. The x axis represents the consecutive occasions of plasma concentration measurements. For meropenem at the middle and end of the interval, sampling was performed after 114 and 139 different antibiotic administrations in 86 and 97 individual patients, respectively. For piperacillin, sampling was performed after 32 and 47 different antibiotic administrations in 27 and 37 individual patients, respectively. The dashed, horizontal line marks the concentration that corresponds to the susceptibility breakpoint (MIC) for Pseudomonas aeruginosa (see the text).

FIG 2.

Correlations between plasma meropenem concentrations or concentration half-life (t_1/2) and total renal replacement therapy effluent flow (Q_eff). In the left-hand plots, these are denoted as the total flow (ml/h), and in the right-hand plots these are denoted as flow normalized to patient weight (ml/kg/h). Data for plasma concentrations are from the first concentration measurement for each patient and only include patients with a dosing regimen of 1 g three times daily. Data for t_1/2 values are from the first paired concentration measurement for each patient. Solid line, P values, and R² refer to linear regression of the transformed values (see the text), plotted here versus original values to ease interpretation. The dashed horizontal line marks the concentration that corresponds to the susceptibility breakpoint (MIC) for P. aeruginosa (see the text). N, number of patients.

FIG 3.

Correlations between plasma piperacillin concentrations or concentration half-life (t_1/2) and total renal replacement therapy effluent flow (Q_eff). In the left-hand plots these are denoted as total flow (ml/h), and in the right-hand plots these are denoted as flow normalized to patient weight (ml/kg/h). Data for plasma concentrations are from the first concentration measurement for each patient and only include patients with a dosing regimen of 4 g three times daily. Data for t_1/2 values are from the first paired concentration measurement for each patient. Solid line, P values, and R² refer to linear regression of the transformed values (see the text), plotted here versus original values to ease interpretation. The dashed horizontal line marks the concentration that corresponds to the susceptibility breakpoint (MIC) for P. aeruginosa (see the text). n, number of patients.

FIG 4.

Box plots showing concentrations at the middle (upper panels) and end of the dosing interval (middle panels) and the elimination halftime (lower panels) for meropenem (left) and piperacillin (right), respectively. Diuresis refers to the urinary output during the dosing interval but converted to ml/24 h. The P values in the panels refer to Kruskal-Wallis tests for differences between groups; lines between groups refer to P < 0.05 for post hoc Mann-Whitney tests (see the text). The data are from the first paired measurements of antibiotic concentrations at the middle and end of the dosing interval in 78 and 26 patients for meropenem and piperacillin, respectively.

FIG 5.

Correlation between antibiotic concentrations and body weight. The data are from the first concentration measurement for each patient and only include patients with a dosing regimen of meropenem at 1 g or piperacillin at 4 g three times daily. Solid line, P values, and R² refer to linear regression. The dashed horizontal line marks the concentration that corresponds to the susceptibility breakpoint (MIC) for P. aeruginosa (see the text). n, number of subjects.

DISCUSSION

In this study of a large group of CRRT patients treated with two of the most used broad-spectrum antibiotics, we demonstrate that the plasma concentrations vary widely despite similar dosing regimens and that, despite the use of relatively high doses of meropenem and piperacillin, plasma concentrations below the chosen targets occur in a significant number of patients. Our results also demonstrate that the variation in plasma concentrations is not explained by differences in the delivered CRRT dose but, for meropenem, the concentrations are influenced by residual diuresis.

We applied two different endpoints, %fT>MIC values of 50 and 100%; the first corresponds to the traditional target for β-lactam treatment, while the second is supported by experimental data demonstrating that a higher fT>MIC is required for maximal bactericidal activity (12). Although there is a lack of consensus, several authors have suggested that the latter target should be applied when treating critically ill patients (13–17). There is, however, only limited evidence that this is associated with better clinical outcomes (14, 18–21). One possible reason for this might be that a more aggressive treatment is expected to improve outcome only when the causative pathogen has an MIC close to the breakpoint. Infections might be caused by pathogens with a lower MIC which means that a greater fT>MIC is reached even with other dosing regimens. However, recent meta-analyses suggest that continuous infusion or extended infusion time, which results in an increased %fT>MIC, improves the clinical outcome (20, 22–24). At the present time, we believe that it is reasonable based on the available body of evidence to aim for an fT>MIC of 100% when treating septic ICU patients.

Both meropenem and piperacillin are small, hydrophilic molecules with a low volume of distribution and a small fraction bound to plasma proteins. With reference to the unbound plasma concentration, drug clearance via CRRT can therefore be expected to be similar to the total Q_eff. This is supported by prior work finding sieving and saturation coefficients close to 1.0 (25–28), although some studies have reported lower values (29). The terminal t_1/2 values reported in this study, a mean 4.0 h for meropenem and a mean 6.0 h for piperacillin, resemble those reported in previous studies that included fewer patients (25–28, 30–33). For example, Valtonen et al., who used a Q_eff similar to that in the present study, reported median t_1/2 4.7 and 6.0 h values and total plasma clearances of 72 and 82 ml/min for meropenem and piperacillin, respectively (30, 31). Importantly, these and other studies (34) of CRRT patients have shown plasma clearances for both meropenem and piperacillin that are considerably larger than Q_eff even in anuric patients. This suggests substantial clearance by nonrenal routes, which has been shown also in patients not treated with CRRT (4, 35). In fact, several studies of CRRT patients have reported average clearance by other routes than CRRT to be greater than 50% of total clearance, with a great variation between individual patients (26, 28, 34, 36). These observations offer a potential explanation for the lack of correlation between t_1/2 and Q_eff in the present study and other studies showing no effect on CRRT intensity on meropenem and piperacillin pharmacokinetics (6, 7, 34). Further, potential explanations suggest that clearance by CRRT might vary with filter age, residual renal function, protein binding, sieving, and saturation coefficients varying between patients (34). When changing the CRRT intensity while treating the same patient, some but not all studies have demonstrated the expected correlation between Q_eff and drug clearance (30, 31, 34). In contrast, despite comparing clearances at Q_eff 25 and 40 ml/kg/h, Roberts et al. found no significant effect on meropenem and piperacillin systemic or CRRT clearances (34). When combining the results from the available literature for meropenem and piperacillin pharmacokinetics during CRRT, Jamal et al. found good correlations between the average Q_eff and CRRT clearance, but the correlations between Q_eff and total clearance were much less and statistically significant only for piperacillin (36). In a large study of patients treated with CRRT, Roberts et al. recently demonstrated an association between a combined estimate of CRRT and residual renal clearance and trough meropenem and piperacillin concentrations but also concluded that the correlation was too weak for clinical practice guidance (21). Taken together, the results in the present and earlier studies show that CRRT settings have little use for predicting the meropenem or piperacillin dose needed to reach a plasma concentration target in an individual patient. We found that meropenem plasma concentrations were higher in anuric patients than in patients with residual diuresis (Fig. 4). Two prior studies found that total clearance of meropenem, but not piperacillin, during CRRT was influenced by residual diuresis (6, 7).

We demonstrated a negative correlation between body weight and piperacillin and meropenem concentrations at the middle of the dosing interval (Fig. 5). Although not statistically significant, a similar pattern was also observed for concentrations at the end of the interval (Fig. 5). This suggests that the use of a standard dosing regimen is associated with a risk of under- and overdosing patients with a high or low body weight, respectively. However, for these patients the concentrations also varied greatly between patients with similar weights, emphasizing the need for therapeutic drug monitoring in clinical practice.

Although most patients in both cohorts received the same dose, the interpretation of the variation in measured concentrations is hampered by some patients being treated with different regimes. However, when appropriate, the reported correlations include only patients with the same dosing regimen. One limitation is that we examined the correlation between antibiotic concentration t_1/2 and CRRT dose instead of the correlation with plasma antibiotic clearance. Plasma t_1/2 is a result of both clearance and the volume of distribution. Of note, only a few of our measurements were made after the first administration of the antibiotic. It is likely that the percentage of patients not reaching the concentrations targets after the first administration is greater than what we found in this study. For piperacillin-tazobactam, optimal effect depends on adequate concentrations of both drugs. A few studies have analyzed both piperacillin and tazobactam pharmacokinetics in CRRT patients. The results suggest that both drugs are effectively eliminated by CRRT; the clearance of tazobactam has been reported as both lower and higher than for piperacillin (28, 30). We compared measured concentrations with MIC for the least susceptible pathogens that should be treated with meropenem or piperacillin. This “worst case” approach likely exaggerates the percentage of patients with suboptimal concentrations. However, the MIC of the pathogen is rarely known, especially at the start of treatment. We therefore believe that it is appropriate to aim at the concentration targets applied in the present study.

Importantly, our results represent a real-life situation when treating a mixed ICU population with comparatively aggressive doses of meropenem and piperacillin. Despite this, several patients had trough concentrations below the target. Obviously, this would have been even more common with lower doses. The poor correlation between concentrations and CRRT dosing is in good agreement with the statement of Roberts et al. (34) that therapeutic drug monitoring is the most practical method to ensure that intended concentrations are achieved. Although β-lactams are comparatively atoxic, both meropenem and piperacillin are associated with dose-dependent neurotoxicity and nephrotoxicity (9–11). There are no established threshold concentrations for toxicity, but several of the patients in the present study had trough levels considerably greater than the highest target that has considered to be beneficial (4× the MIC). This suggest that for some patients treated with CRRT, the applied dosing regimens were unnecessary aggressive and increased the risk of adverse reactions. No case of neurotoxicity was identified in our study but, in general, neurotoxicity is probably underrecognized in ICU patients because the symptoms, e.g., depressed consciousness and delirium, have other potential explanations.

In summary, our results show that with the applied dosing regimens, both unnecessarily high and potentially toxic plasma concentrations and suboptimal concentrations occur in ICU patients treated with CRRT. The wide variation in plasma concentrations despite similar antibiotic dosing and CRRT intensity, as well as the poor correlation between concentrations and CRRT intensity, suggests that plasma concentration measurements are needed to avoid both potentially dangerous high and low concentrations.

MATERIALS AND METHODS

Patients.

The study was performed at the general intensive care unit at the Karolinska University Hospital Solna, Stockholm, Sweden. At the time of the study, November 2012 to December 2016, measurement of antibiotic concentrations was routine for patients treated with CRRT and either meropenem or piperacillin-tazobactam. The present work uses prospectively collected data from these patients. Here, we mostly refer only to piperacillin because tazobactam concentrations were not measured. Sepsis and septic shock were defined according to the consensus criteria at the time of the study (Sepsis 2) (37) and applied to the time frame of the treated infection. Infections were considered hospital acquired if identified >48 h after hospital admission. The study was approved by the regional ethic review board in Stockholm, which waived the need for individual patient consents (reference 2013/717-31/1).

Antibiotic concentration measurements.

Antibiotic dosing regimens were determined, independent of the study, by the infectious disease consultant visiting the unit daily or by the treating intensivist. Antibiotic administrations were performed as 30-min bolus infusions. According to the clinical routine at the unit it, was recommended that concentration measurements were performed at the middle and end of the dosing interval after the first administration of either antibiotic but in practice it was often performed after a later administration (Table 1; see also Table S1 in the supplemental material). Similarly, repeated measurements were suggested after 2 to 3 days of treatment but not always performed. Blood samples were obtained from an arterial catheter and sent to the hospital pharmacology laboratory according to clinical routines. Meropenem and piperacillin total plasma concentrations were quantified using liquid chromatography-mass spectrometry. Ceforanide was used as an internal standard, and calibration curves were constructed by linear regression of analyte-internal standard area ratios. The validated quantification range for both analytes was 0.1 to 100 mg/liter, method precision was estimated to be ≤ 5% at low (4 mg/liter) and high range (40 mg/liter). The method has been described in detail in a previous publication (38). Total concentrations of piperacillin were adjusted to free concentration assuming a protein binding of 30% (15). No adjustment was applied to the measured meropenem concentrations because protein binding has been reported as 1 to 2% (3).

Continuous renal replacement therapy.

CRRT was performed as continuous venous-venous hemodiafiltration, via a bilumen central venous catheter in the internal jugular or femoral vein, using the Prismaflex system (Baxter Medical Sweden). The dialysis filter used was either ST150 or Oxiris (Baxter Medical Sweden); both AN69 filters had a filter area of 1.5 m². The drug clearance characteristics for these two filters are considered equivalent. The used dialysis and replacement fluids included Prismocitrat, Prism0CAL, Hemosol, or Phoxillium (all from Baxter Medical Sweden). We calculated the time-averaged flow rates for blood (Q_b), dialysis fluid (Q_d), and replacement fluid (Q_pre and Q_post for fluid administered pre- and postfilter, respectively) for each dosing interval. The flow rates were thus corrected for any part of the dosing interval without CRRT (downtime). To obtain a single measure of the theoretical CRRT clearance of unbound antibiotic, we calculated the time-averaged total effluent flow (Q_eff) (8). This calculation included the net fluid withdrawal and adjustment for predilution, i.e., Q_pre reducing the concentration of antibiotic in blood passing through the filter.

Endpoints, definitions, and data analysis.

The adequacy of beta-lactam dosing was determined from the fraction of the dosing interval that the free (unbound) plasma concentrations remain above the MIC for the causative pathogen, denoted as the % fT>MIC (39). Measured plasma concentrations were therefore compared to the European Committee on Antimicrobial Susceptibility Testing (EUCAST) susceptible (S) breakpoints for P. aeruginosa: 16 mg/liter for piperacillin and 2 mg/liter for meropenem (40). These breakpoints are the highest MICs for pathogens considered susceptible for these antibiotics. Our reasoning was that clinically, applied dosing regimens are expected to be adequate for treatment of all pathogens reported as susceptible to the antibiotic used. During treatment with meropenem and piperacillin, the fT>MIC values should be at least 40 and 50%, respectively. It has, however, been suggested that concentrations above MIC (100% fT>MIC) or even higher at the end of the dosing interval might improve the clinical outcome for severely ill patients (12, 41). We therefore analyzed the percentages of patients with antibiotic concentrations (i) above the breakpoints for P aeruginosa at the middle of the dosing interval (50% fT>MIC) and (ii) above the breakpoints at the end of the interval (100% fT>MIC). The 50% fT>MIC endpoint was chosen for both meropenem and piperacillin for practical reasons. We calculated the elimination rate constant (k) and terminal half-life (t_1/2) for the plasma antibiotic concentrations according to the equations 1 and 2:

$$k=\left(\text{ln}{C}_{\text{mid}}-\text{ln}{C}_{\text{end}}\right)/t$$ (1)

$$t_{1/2}=\text{ln2/}k$$ (2)

C_mid and C_end denotes the concentrations at the mid and end of the interval, and “t” is the time interval between the samplings. In addition, we analyzed the correlation between antibiotic concentrations and t_1/2 versus the CRRT dose using linear regression and values transformed according to the theoretical relationships between these parameters, that is, the correlation between the logarithmic concentrations and Q_eff and between t_1/2 and the inverted values for Q_eff. Patients were classified as either anuric (diuresis, <100 ml/24 h), oliguric (diuresis, 100 to 500 ml/24 h), or neither, with reference to the diuresis during the dosing interval.

Because measurements were performed as a clinical routine, blood sampling was not always performed exactly at the intended time. We omitted measurements from samples not obtained within ±20% of the intended time. We therefore report less paired values (concentrations at the middle and end of dosing interval) and t_1/2 estimates than values for each time point. The data are reported as medians and interquartile ranges. Concentrations and t_1/2 values for patients with different diureses were compared using Kruskal-Wallis and post hoc one-sided Mann-Whitney tests with the Bonferroni correction. One-sided tests were used because the hypothesis was that increasing urinary output is associated with lower concentrations and shorter t_1/2 values. For these analyses, we used the first set of two measured concentrations for each patient. We performed multiple linear regressions with logarithmic antibiotic concentrations as the dependent variable and Q_eff and diuresis group as independent variables to assess whether the effect of Q_eff on antibiotic concentration was influenced by a correlation between Q_eff and diuresis, i.e., collinearity between the independent variables. Statistical analyses were performed using IBM-SPSS statistics 23.0 (IBM Corp., New York, NY). A P value of <0.05 was considered significant.