Title: Aminoglycoside Dosages and Nephrotoxicity: Quantitative Relationships

 

Florent Rougier¹, Michel Ducher¹, Michel Maurin², Stéphane Corvaisier¹, Daniel Claude³, Roger Jelliffe⁴ and Pascal Maire^1,4

 

1 ADCAPT, Service Pharmaceutique, Hôpital Antoine Charial, Francheville, France

2 INRETS, Bron, France

3 Université d’Orsay, Paris-Sud, France

4 Laboratory of Applied Pharmacokinetics, University of Southern California, School of Medicine, Los Angeles CA 90033, USA

 

Running title: Aminoglycoside Nephrotoxicity and Dosage Regimen

 

Corresponding author: Florent Rougier

Phone: +33 472 32 34 87 Fax: +33 472 32 39 08

E-mail address: < florent.rougier@libertysurf.fr >

 

Correspondent Footnote: Corresponding author. Mailing address: ADCAPT, Service Pharmaceutique, Hôpital Antoine Charial, 40 avenue de la Table de Pierre, 69340 Francheville, France. Phone: +33 472 32 34 87 Fax: +33 472 32 39 08

E-mail address: < florent.rougier@libertysurf.fr >

 

ABSTRACT

Objective: To develop a model which relates the probability of nephrotoxicity occurrence to the cumulative area under the curve of amikacin serum concentrations (AUC).

Design and Patients: Two groups of patients for which nephrotoxicity was observed. The first group consisted of patients treated with once-daily AG administration (ODA) (n=13). The second group consisted of patients treated with twice-daily administration (TDA) (n=22).

Main outcomes measures: The probability of nephrotoxicity occurrence.

Results: The model is a powerful tool to represent and describe the influence of the dosage regimens on AG nephrotoxicity. The onset of nephrotoxicity is delayed in the ODA group (p=0.01) for the same total daily-dose among the two groups. The serum AUC values at onset of nephrotoxicity were greater for the ODA group (p=0.029). In addition, for the same probability of nephrotoxicity occurrence (50%), the AUC value for the ODA dosage regimen is 2.613 mg.l^-1.h versus only 1.521 mg.l^-1.h for the TDA dosage regimen. The difference of nephrotoxicity between ODA and TDA is greatest when the AUC=2.495 mg.l^-1.h which corresponds to the standard therapy with 900 mg of amikacin per day during a-7-day-period i.e. 15 mg/kg/j for a 60-kg patient with a normal renal function (CL_CR0>80 ml.min^-1). For an AUC above 2.495 mg.l^-1.h, difference of nephrotoxicity decreases slowly to zero. This result means that ODA is especially justified when the treatment is administered over a short duration i.e. less than 7 days.

Conclusions: The ability to select ODA, in order to obtain less nephrotoxicity in comparison with TDA, is therefore not established when the treatment is prolonged. In clinical use, the choice of the dosage regimen is not so evident and one must take into account both the expected efficacy and the same time the expected toxicity, in order to obtain an overall optimization of each patient’s therapy.

Keywords: aminoglycosides, nephrotoxicity, dosage regimen, model

 

INTRODUCTION

The main constraints to the administration of aminoglycosides (AG) are risks of nephrotoxicity and ototoxicity, which can lead to renal and vestibular failure^[1]. In this article we will focus on nephrotoxicity. Recently, studies have demonstrated that the probability of nephrotoxicity is linked to the dosage schedule^[2,3]. Evidence from studies with animals and humans has demonstrated a correlation between nephrotoxicity of AG and the accumulation of these drugs in the cortex of the kidney^[4,5]. AG accumulation in the kidney may be related to the dosing schedule. Megalin explains that uptake of AG by tubule cells is saturable^[6]. As a consequence, administration of larger doses less frequently may reduce the drug accumulation in the renal cortex, and thereby may reduce the nephrotoxicity of AG^[4,5]. To date, no probabilistic model permits quantification of risk of AG nephrotoxicity. Past studies have shown that the cumulative area under curve of AG serum levels (AUC) seems to be a good predictor of this toxicity^[2,3]. The objective of the present article is: (1) to quantify and clarify the link between AG nephrotoxicity and, the dosage regimen, the dose interval and the duration of treatment, with a probabilistic model and, (2) to discuss the advantage in toxicity terms of a once-daily dosage regimen (ODA).

 

PATIENTS AND METHODS

Patients

634 patients who had clinical evidence of significant infections and who had received intravenous amikacin therapy by 30-minute infusions, were available from seven different pharmacological departments. Amikacin doses were administered after dilution in 100 ml of 5% dextrose in water. Doses were calculated in function of initial creatinine clearance value (CL_CR0) i.e. 15 mg.kg^-1.j^-1 when CL_CR0 was above 80 ml.min^-1 and 7.5 mg.kg^-1.j^-1 when CL_CR0 was between 30 and 80 ml.min^-1.

Selected patients were those for whom at least 3 criteria were observed:

§         None other nephrotoxic drug administered during the amikacin treatment.

§         Constant and not adapted administered doses during the treatment.

§         Nephrotoxicity observed during or after the amikacin treatment.

Nephrotoxicity was defined as an increase in the baseline serum creatinine concentration of 0.5 mg.dl^-1 or a 50% increase, whichever was greater, on two consecutive occasions any time during therapy or up to one week after the cessation of therapy^[7]. The serum creatinine concentration was measured for each patient at baseline (the lowest serum creatinine concentration within the period from 24 h before to 48 h after the initiation of therapy), on days 2, 4, 6 and 9, and twice weekly thereafter or more frequently if it was deemed clinically necessary. To accurately estimate PK parameter values, at least 6 amikacin serum levels should be available for each patient.

Patients were excluded if they had an initial creatinine clearance value under 50 ml.min^-1, weighted 30% above their ideal body weight or in shock.

Thirty five patients satisfied the above criteria. They were treated for infections due to gram-negative pathogens i.e. respiratory infections, endocarditis and pyelonephritis, in association with beta-lactam, and were divided in two groups: 13 patients treated with a once-daily dosage regimen (ODA) and 22 patients treated with a twice-daily dosage regimen (TDA).

The 35 patients were allocated to the ODA or the TDA group in function of clinical practice of the physicians. Data on the 35 patients were stored in files using the PASTRX program (USC*PACK clinical program)^[8]. Each file contained subject covariates such as sex, age, weight, height, serum creatinine concentrations, and corresponding creatinine clearance calculated according to the Jelliffe and Jelliffe formula^[9] ; and treatment data such as doses, times of administration, duration of infusion, timing of blood sampling, and corresponding amikacin serum level measurements. Blood sampling times were usually 30 minutes, 3 hours and 12 hours after the start of the 30-minute infusion.

 

Analytical Method

Amikacin plasma levels were performed using fluorescence polarization immunoassay (FPIA) (TDX, Abbott Laboratories, Rungis, France). The lower detection limit was 0.5 mg.l^-1 and the error assay pattern could be described using the following equation:

 

 

where SD is the assay standard deviation and C the measured amikacin serum level (mg.l^-1).

 

Estimation of amikacin pharmacokinetic parameter values

Each patient PK parameter value was estimated using the non-parametric EM algorithm and computer program (NPEM2)^[10] with a two-compartment model. Parameterisation was: K_s the renal elimination rate constant per unit of creatinine clearance (min.ml^-1.h^-1), K_i the non-renal elimination rate constant (h^-1) (fixed at 0.00693 h^-1),V_s the volume of distribution (l.kg^-1), K_cp the transfer rate constant from the central compartment to the peripheral compartment (h^-1) and K_pc the transfer rate constant from the peripheral to the central compartment (h^-1). The AG elimination rate constant (K_el) (h^-1) depends linearly upon creatinine clearance CL_CR (ml.min^-1) and varies according to:

 

^[11]

 

An iterative two-stage Bayesian population modeling program was used to initiate the NPEM2 analysis^[12]. The model optimization convergence criteria for the estimated log-likelihood values was based on the two following criteria:

§         The difference between two successive populations likelihood values was less than 0.01.

§         The significant linear correlation between predicted and observed amikacin serum levels was 0.99 without bias assessed by the difference from the line of identity.

 

Estimation of the cumulative Area Under Curve of amikacin serum levels (AUC)

AUC is a time-dependent variable, which takes into account both the individual dosage regimen and the individual estimated PK parameter values. It assesses the patient’s individual drug exposure. The individual AUCs were estimated from the beginning of the treatment to the onset of nephrotoxicity, by using individual patient’s PK parameter values in the USC*PACK clinical program^[8].

 

Mathematical representation of the data

We used a probabilistic model inspired by the very classic and historical Hill equation.

 

 

Here this expression may be considered as a cumulative distribution function, and it led us to investigate this original point of view^[13]. This enlarges the former deterministic one^[14,15,16], and when one wants to add a bit of probability, the Hill model seems more appropriate than the use of logit or probit coming from general linear model (GLM) framework^[17] because for instance, as a model it renders possible the violation^[2,3] of “no drug no effect” principle^[18].

There are two parameters in the F(AUC) cumulative function expression, a size parameter c and a shape one a. The c parameter is merely the median of the distribution (same unit than AUC) and it influences the location of the distribution; whereas a (no unit) is linked to the sigmoidicity of the F function. The higher the a, the greater the sigmoidicity. Consequently, Hill family distributions has a wide range curves. Furthermore, moments and entropy calculations are known and a strong connection between deterministic and probabilistic approaches of Hill equation is allowed^[13].

Given from cumulative function F, we deduce the density probability function f and the statistic likelihood L of a sample of independent observations:

 

 

and its logarithm:

 

Then we can estimate the a and c parameters following the classical Fisher maximum likelihood estimation principle. We applied it to two patient samples, the ODA and TDA of respective numbers n_ODA=13 and n_TDA=22. This type of maximization was done using the Matlab program^Ò (the Math Works Inc.).

 

Statistical comparisons

In a first time, the accuracy of the two-compartment model was assessed by a linear regression between observed and predicted amikacin serum values. Second, the theoretical distribution of AUC values calculated with the estimated parameters c and a, was compared to the observed distribution of AUC values for each group of patients with a Pearson c² test. All other statistical comparisons between the two groups (ODA versus TDA) were performed using a non-parametric Mann-Whitney test.

 

RESULTS

Validation of the pharmacokinetic model

For the two-compartment model, a significant linear correlation between predicted and measured amikacin serum level values was observed (r=0.990, p<0.001) with an intercept of 0.04 mg.l^-1 and a slope of 0.9321. The scattergram is shown in Figure 1.

 

The fit of the data with Hill distributions

Table 1 shows the parameter values (c and a) estimated by the maximum likelihood method for the two Hill distributions corresponding to ODA and TDA groups. The c² tests show that there is a significant statistical fit for every group to a Hill distribution with regard to the p values (p_ODA=0.63, p_TDA=0.52). Figure 2A describes the observed and the estimated probabilities of nephrotoxicity for the two groups (ODA and TDA) as a function of AUC values. Figure 2B represents the differences of probabilities in nephrotoxicity occurrence between the two groups as a function of AUC values. This difference is not constant and maximum at 2.495 mg.l^-1.h.

 

Comparisons between the TDA group and the ODA group

The study was retrospective. Hence, patients were not randomized for their treatment arm. However, clinical, biological and pharmacokinetic covariates were comparable in the two groups. As shown in Table 2, the comparisons between the two groups on: patient data, treatment data, population PK parameter values and PK index, show significant differences for the time to onset of nephrotoxicity (p=0.01) and for AUC values (p=0.029).

DISCUSSION

The present study was designed to explore the difference in occurrence of nephrotoxicity seen on two dosage regimens (ODA and TDA). To date, only static analysis have been performed^[4,5]. In the present study, in contrast, we have chosen a dynamic approach which takes into account the effect of the duration of the treatment on the occurrence of AG nephrotoxicity. This approach also quantifies the contribution of the dosage regimen. The results as a whole show less nephrotoxicity for ODA dosage, despite identical total daily doses of amikacin in both groups, corresponding to identical daily-AUC values i.e. an identical daily-exposure. However, results show that ODA is more useful with regard to nephrotoxicity when the treatment is administered over a short period i.e. less than 7 days. The advantage of the ODA regimen is not established when the treatment is prolonged.

AUC is a well-known index which assesses the total individual drug exposure. In our study, AUC can be interpreted at once as a pharmacodynamic index of toxicity and at the same time as a pharmacodynamic index of efficacy. For example, with the same AUC value of 2.495 mg.l^-1.h, the probabilities of nephrotoxicity occurrence are respectively 0.74 and 0.38 for TDA and for ODA. As a consequence, the ratio of relative risk of nephrotoxicity is (0.38/0.74)=0.51 for ODA regimens versus TDA ones, for this AUC value, which is to relate to better or equivalent efficacy of ODA regimen because of theoretical adaptive resistance. This methodology is an interesting and powerful tool to separate the toxicity model as a function of the dosage regimen. Two different Hill models for the two different dosage regimens, with different parameter values, have been described, as shown in Table 1. The two patient groups present no significant difference for the administered daily-dose and for the PK parameter values as shown in Table 2, but the onset of nephrotoxicity is later with the ODA dosage regimen (p=0.01) which induces higher resulting AUC values in regard with TDA dosage regimen (p=0.029). Our methodology is in accordance with pharmacodynamic non-linear and saturable mechanisms such as:

§         AG renal cortex accumulation as it was demonstrated in human^[2,3] or in animal studies^[19] which can be represented by a Michaelis Menten kinetic^[15].

§         The resulting effect of this AG renal cortex accumulation leading to the leakage of intracellular ions (K⁺, Mg²⁺, Ca²⁺), of proteins (beta-2-microglobulin, alpha-2-macroglobulin, lyzozyme) and of enzymes (alanylaminopeptidase, N-acetyl-glucosaminidase) in the renal tubule^[20,21,22].

§         The resulting decline of glomerular filtration, which has a multi-factorial origin and involves a combination of tubular and non-tubular mechanisms. The most important factor seems to be the tubuloglomerular feedback^[23]: detection of ions such as K⁺, Mg²⁺ or Ca²⁺ by macula densa induces stimulation of tubuloglomerular feedback which leads to vasoconstriction on glomerule and finally the decrease of renal function.

For a same amikacin total dose but with two different dosage regimens, the amounts which accumulate in the renal cortex are different and may induce different effects on the decrease of the glomerular filtration rate. For the first 3 days of the treatment (AUC<1.050 mg.l^-1.h), the AG amounts in the renal cortex are small and do not cause a significant decrease of renal function either for the ODA dosage regimen or for the TDA dosage regimen. When the treatment is prolonged between 3 and 7 days (1.050 mg.l^-1.h <AUC<2.495 mg.l^-1.h), the AG amounts in the renal cortex increase more rapidly for TDA than for ODA and cause a greater decrease of renal function. The difference in nephrotoxicity is maximum for 2.495 mg.l^-1.h, which corresponds to the AUC value for which the TDA dosage regimen induces a maximum decrease of the renal function. With the pharmacokinetic parameters described in Table 2, 2.495 mg.l^-1.h corresponds to the standard therapy with 900 mg of amikacin per day during a-7-day-period i.e. 15 mg/kg/j for a 60-kg patient with a normal renal function (CL_CR0>80 ml.min^-1). Above 7 days (AUC>2.495 mg.l^-1.h) the AG renal amounts are still increasing for both dosage regimens, though for TDA, the maximum decrease of the renal function is already attained while for ODA, renal function is still decreasing and approaching to its minimum. As a consequence, for a long-term treatment, nephrotoxicity is maximum and practically the same for both TDA and ODA. However, the difference in nephrotoxicity always favors the least frequent dosage regimen. These results must be compared to those published on efficacy which recommend high doses at the least frequency possible without forget bactericidal constraints^[24,25,26].

 

CONCLUSIONS

The representation of the AG nephrotoxicity by a dynamic approach such as a Hill model, makes it possible to quantify the link between toxicity and dosage regimen. However, the advantage of the ODA dosage regimen in toxicity terms must be considered in terms of the duration of treatment. The pharmacodynamic processes, especially AG renal cortex accumulation, which is saturable, explain these differences in nephrotoxicity. An other model could be derived from the direct correlation between efficacy and concentration. For the different dosage forms, the same pharmacodynamic parameters would result, but a different cumulative area under the effect time curve. The consideration of AUC in the clinical routine will allow us to achieve an overall optimum therapy by taking into account both efficacy and toxicity constraints.

 

REFERENCES

 

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5. Verpooten GA, Guiliano RA, Verbist L, De Broe ME. Once daily dosing decreases renal accumulation of gentamicin and netilmicin. Clin Pharmacol Ther 1989; 45: 22-27

 

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8. USC*PACK [computer program]. Version 10.7. Los Angeles, CA: Laboratory of Applied Pharmacokinetics, University of Southern California. School of Medicine; 1995. USC*PACK PC Collection Clinical Research Programs

 

9. Jelliffe RW, Jelliffe S. A computer program for estimation of creatinine clearance from unstable serum creatinine levels. Math Biosc 1972; 14: 17-24

 

10. Schumitzky A. Non-Parametric EM algorithms for estimating prior distributions. Laboratory of Applied Pharmacokinetics, University of Southern California. School of Medicine, Los Angeles; 1990. Technical Report: 90-2

 

11. Schentag JJ. Renal clearance and tissue accumulation of gentamicin. Clin Pharmacol Ther 1977; 22: 364-370

 

12. Jelliffe RW. The USC*PACK PC programs for population pharmacokinetic modeling of large kinetic/dynamic systems, and adaptive control of drug dosage regimens. Proc An Symp Comput Appl Med Care 1991; 922-944

 

13. Maurin M, Rougier F, Maire P. Note de calcul sur les lois de Hill : aspects probabiliste déterministe et épistémologique 2000. Edition INRETS-LTE 2026. ISRN: INRETS/NST/00-548-FR

 

14. Hill AV. The possible effects of the aggregation of hemoglobin on its dissociation curve. J Physiol 1910. 40: iv-vii

 

15. Michaelis L, Menten ML. Die kinetik der Invertinwirkung. Biochemische Zeitschrift 1913; 49: 333-369

 

16. Clark AJ. The reaction between acetylcholine and muscle cells. J Physiol 1926; 61: 530-546

 

17. McCullagh P, Nelder JA. 1983. Generalized linear models, Chapman and Hall

 

18. Holford HG, Sheiner LB. Understanding the dose-effect relationship: clinical application of pharmacokinetic-pharmacodynamic models. Clin Pharm 1981; 6: 429-453

 

19. Guiliano RA, Verpooten GA, Verbist L, Wedeen RP, De Broe ME. In vivo uptake kinetics of aminoglycosides in the kidney cortex of rats. J Pharmacol Exp Ther 1986; 236: 470-475

 

20. Kosek JC, Mazze RI, Cousins J. Nephrotoxixity of gentamicin. Lab Invest 1974; 30: 48-57

 

21. Tulkens PM. Nephrotoxicity of aminoglycosides. Toxicol Lett 1989; 46: 107-123

 

22. De Broe ME, Paulus GJ, Verpooten G, Roels F, Buyssens N, Wedeen R, Tulkens PM. Early effects of gentamicin, tobramycin and amikacin on the human kidney. Kidney Int 1984; 25: 643-652

 

23. Schnermann J, Häberle DA, Davis JM, Thurau K. Renal Physiology. Oxford University Press, 1992. Chap. 34 Tubuloglomerular feedback control of renal vascular resistance, p. 1675-1705

 

24. Van der Auwera P. Pharmacokinetic evaluation of single daily dose amikacin. J Antimicrob Chemother 1991; 27 (Suppl C): 63-71

 

25. Freeman CD, Nicolau DP, Belliveau PP, Nightingale CH. Once-daily dosing of aminoglycosides: review and recommendations for clinical practice. J Antimicrob Chemother 1997; 39: 677-86

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LEGENDS FOR FIGURES

 

Figure 1. Plot of predicted versus observed amikacin serum level values for a two-compartment model.

 

Figure 2. Representations of the probability of nephrotoxicity for the ODA group (13 patients) and for the TDA group (22 patients) in function of AUC (Figure 2A) and resulting differences of probability between the two groups (Figure 2B).

 

 

TABLE 1. Estimated c and a parameters for the two different dosage regimens

Dosage regimen	c (mg.l-1.h)a	sd (mg.l-1.h)	a (no unit)b	sd (no unit)	c2 testc
ODAd	2613	282	1.86	0.11	p=0.63
TDAe	1521	185	3.21	0.24	p=0.52

a. corresponds to AUC value for which probability of toxicity is equal to 0.5

b. corresponds to Hill sigmoidicity coefficient

c. tests the adjustment of data to a Hill's model

d. once-daily administration group

e. twice-daily administration group

 

TABLE 2. General characteristics for the two groups of patients and statistical comparisons