Eur J Clin Pharmacol (1990) 39:155-159 EuropeanJournalof ( ~ : ~ ( ~ ( ~ ©

Springer-Verlag 1990

Comparison of non-kinetic and kinetic approaches to individualization of gentamicin dosage Y. M. E1-Sayed 1 and S. I. Islam 2 1Department of Pharmaceutics, Collegeof Pharmacy, King Saud University,Riyadh, and 2Drug Monitoring Unit and Department of Pharmacology, College of Medicine and Allied Sciences,King Abdulaziz University, Jeddah, Saudi Arabia Received: September 19,1988/Acceptedin revised form: December 1, 1989 Summary. A prospective study was carried out in 40 acutely ill patients to compare the non-kinetic and kinetic approaches to individualization of the dosage regimen of gentamicin. The patients were divided into two equal groups. For the non-kinetic group, the doses were derived from the physician's personal experience, on a mg/kg basis, and by use of nomograms. The total daily dose ranged from 1.43 to 4.5 mg/kg. Based on serum concentration measurements, the dosage regimen for individual patient was calculated by Sawchuk-Zaske's method. The calculated doses were compared to the prescribed doses in each patient. Of the patients on empirically prescribed doses 65% received 36% more drug than the calculated dose and 20% received 36% less than the calculated dose. The calculated dosing intervals were greater than the recommended intervals in 60% of the patients. The gentamicin trough concentration was > 2 gg/ml in 70% of the patients. There was a significant tendency to overdosage of the patients. For the kinetic group, following administration of the calculated dose, the steady-state peak and trough concentrations in each patient were measured. The correlation of measured to predicted steady-state serum concentrations was excellent (r = 0.9968, p < 0.05). About 85% of the served trough concentrations and 90% of the peak values fell within the therapeutic range. The mean of the prediction error (ME), mean absolute error (MAE), mean squared error (MSE), and root mean squared error (RMSE) of the trough and peak concentrations were calculated. The 95% confidence interval of the ME for the trough and peak concentrations included zero, which shows that the prediction was not significantly biased. A significant relationship between gentamicin clearance and the ratio of the peak and trough concentrations achieved to the administered dose (r= 0.873, 0.916 for trough and peak, respectively) was found. The findings suggest that the individualized approach to dosage determination using pharmacokinetic principles, in conjunction with daily monitoring of serum gentamicin concentrations, may provide safe and effective therapy

Key words: Gentamicin, Dosage, kinetics, dose individualization, dose prediction

Gentamicin, an aminoglycoside antibiotic, is frequently chosen for the treatment of life-threatening Gram-negative bacterial infections. The wide interpatient variation in the elimination of gentamicin is a continuing clinical problem. Several pharmacokinetic variables may influence the attainment of therapeutic drug concentrations. Although the serum concentration in the individual patient increases as the dose is increased, the same dosage, even when standardized on a body weight or surface area basis, does not produce predictable therapeutic concentrations [1, 10, 24, 2628]. It has been recognized that many factors affect gentamicin elimination, including renal function [10, 13], age [15, 29], haematocrit [1, 17], fever [16, 23], and obesity [25]. These variables are especially important in patients with Gram-negative sepsis, in whom several of them are abnormal and they may change during therapy. Therefore, failure to individualize the dosage regimen may result in ineffective therapy or toxicity. These problems have encouraged the development and use of various nomograms for predicting dosage regimens [3, 12, 18]. The nomograms take into account various individual factors that contribute towards variability, such as age, sex, serum creatinine or creatinine clearance and body weight. Moreover, most of the nomograms fail to achieve the accuracy needed for optimal therapy [4,11]. The individualization of gentamicin therapy using serum concentration data to obtain pharmacokinetic parameters, which are then used to calculate the dosage regimen, has often been attempted [6--8, 19, 20, 22]. Such methods have been very valuable and are widely used to derive aminoglycoside dosage regimes [26]. The aim of the present study was to compare the nonkinetic and kinetic approaches to determination of individual dosage regimens for patients in the King Abdulaziz University Hospital, Jeddah. The non-kinetic approach depended on traditional methods and the kinetic tech-

156

Y. M. E1-Sayed and S. I. Islam: Individualization of gentamicin dosage serum concentrations of 5-8 gg. ml 1 and ~<2 gg. m1-1, respectively. The patients had been on a fixed regimen for at least 48-72 h, and were therefore considered to be at steady-state. Blood samples were collected immediately prior to the seventh dose (steady-state trough concentration), 30 min after the end of the infusion (steady-state peak concentration) i h before the next dose and subsequently before and after each dose during treatment. Based on the serum concentration measurements, the dosage regimen for the individual patient was calculated according to Sawchuk-Zaske's method [19]. For the kinetic group, a test dose of 2.32 to 4.1 mg .kg -1 was administered for 48 h and three blood samples were obtained - immediately before (trough) and 30 min after the end of the infusion (peak), and usually an additional sample i h before the next dose. The dosing intervals varied depending upon the estimated elimination half-life, using the relationship proposed by Hull and Saruubi [9]. The concentrations in the three blood samples were analyzed by the method of Sawchuk-Zaske [19] giving for each patient an estimate of the elimination rate constant (K) by least-squares linear regression analysis, and the apparent volume of distribution (V) from the following equation:

n i q u e was b a s e d o n t h e d e t e r m i n a t i o n of p h a r m a c o k i n e tics i n i n d i v i d u a l s .

Materials and m e t h o d s

Patients Forty acutely ill patients in the King Abdulaziz University Hospital, Jeddah, treated with gentamicin for presumed or documented Gram-negative, life-threatening bacterial infections complicating, either medical or surgical disorders, were studied prospectively. The patients had varying impairment of renal function, as measured by the serum creatinine concentrations and clearance. The mean age of the patients was 52 y (range 21-90 y), and their mean body weight was 66.3 kg (range 49-95 kg). Initial creatinine clearance ranged from 17.0 to 123 ml- rain 1, and the mean creatinine concentration was 1.41 mg. d1-1(range 0.75 to 2.82 rag. alP1). Serum creatinine was determined daily and creatinine clearance was estimated by the Cockcroft and Gault method [5]. Thirty seven % of the patients were less than 50 y old. There were 18 males and 22 females. Patients were randomly divided into two groups, each of 20 patients. For the first group doses were derived from personal experience of the physician, on a mg/kg basis and using nomograms (nonkinetic group). The second group was given doses of gentamicin based on the use of pharmacokinetic principles for individualization of the regimen (kinetic group). Clinical comparison revealed that the groups were similar in respect of age, sex, weight, renal function and severity of the disease.

Dosage regimensand pharmacokinetic calculations Gentamicin was administered by a time-constant rate i.v. infusion over 30 min period. The dose was diluted in 30 ml sterile NaC1 0,9 g. 1-~solution. In the non-kinetic group the total daily dose of gentamicin ranged from 1.43 to 4.5 rag. kg-~ and the dosing interval varied from 8 h (18 patients) to 12 h (2 patients). The empirical dosage schedule was designed to produce steady-state peak and trough

V-

Ko (1-e~t in) K (Gm.--Cpoe Kt in)

where Ko is the infusion rate of the study dose, tin is the duration of infusion, Cp,,,oxis the serum concentration at the end of the infusion period, and Cpo is the serum level prior to the infusion. The product of K and V was used to calculate the total body clearance (CL). The resultant parameters were then used to predict the required dose and dosing interval for each patient. Following administration of the calculated dosage regimen the steady-state peak (Cp~x), and trough (Cp~o) concentrations were predicted as: CpSmS~o_ K0 (1- e Kt in) K. V (1 - e Kr) CpSn~ n = C p ~ × " e - K (T -~in)

where T is the dosing interval. Steady-state peak and trough concentrations in each patient were measured after at least 4 half-lives of maintenance therapy.

Table 1. Calculated and prescribed dosage regimens in the non-kinetic group Patient

01 02 03 04 05 06 07 08 09 10 11 12 .13 14 15 16 17 18 19 20

Creatinine clearance ml/min.

Prescribed regimen

Calculated regimen

Dose (mg)

Dosing interval (h)

Dose (mg)

Dosing interval (h)

90.6 27.4 39.7 51.0 73.6 32.8 69.5 67.8 22.6 98.2 17.0 41.9 30.9 40.3 27.2 18.4 23.2 53.9 91.2 93.0

80 80 60 80 80 60 60 60 60 80 60 60 40 80 40 40 60 60 40 80

08 08 08 08 08 08 08 08 12 08 08 08 08 08 08 08 08 12 08 08

100 070 055 065 100 080 055 060 045 080 080 080 060 100 040 035 065 060 080 115

08 12 12 08 08 12 12 12 12 08 30 12 12 24 12 18 12 12 08 08

a Prescribed (mg/24 h) - Calculated (mg/24 h) × 100 Prescribed (mg/24 h)

% Difference a between prescribed and calculated doses (mg/24 h) 25 42 44 19 25 11 39 33 25 64 11 58 33 61 28 100 44

157

Y. M. E1-Sayed and S. I. Islam: Individualization of gentamicin dosage

f

The measured and predicted steady-state peak and trough serum gentamicin concentrations were compared ones by simple linear regression. The predictive performance for each serum gentamicin concentration was also evaluated by calculating the prediction error, which was used to determine the mean prediction error (ME), mean absolute error (MAE), mean squared prediction error (MSE) and root mean squared error (RMSE) with 95% confidence intervals. Peak and trough concentrations were analyzed separately for predictive performance using the statistical analysis of Sheiner and Beal [21], which allowed evaluation of the relative bias and precision of the predictive method. The correlation was also examined between gentamicin clearance and the ratio of the observed peak and trough serum concentrations according to the dose.

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Fig.1. Correlation between measured (X-axis) and predicted (Yaxis) steady-state peak and trough gentamicin concentrations. Solid line represents least square regression line: intercept 0.1195 gg. ml-~, slope 0.9692

Serum gentamicin concentration was determined by the fluorescence polarization immunoassay (FPIA) method, using an automated fluorescence polarization analyzer (Abbott Diagnostic Division, Irving, TX, USA). Intra-day coefficients of variation at concentration of 4 and 8 gg.ml ~were 2,62 and 1.77% respectively. The inter-day coefficients of variation were 2.57 and 3.09%, respectively. The mean recovery for two spiked controls was 100.4%. Therapeutic trough concentrations were defined as ~<2 pg/ml and peak concentrations as 5-8 gg. ml z [2].

Results o

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Genfarnicin clearance (ml.kgml.min-1) Fig.2. Gentamicin clearance in 20 adult patients in relation to the ratio of the observed peak and trough serum concentrations and the administered dose per dosing interval

The calculated and prescribed dosage regimens for the non-kinetic group are shown in Table 1. Sixty-five % of the patients receiving empirical doses of gentamicin received a dose that was 36% larger than the calculated value. 20% were prescribed a dose that was 36% smaller than the calculated level, only 10% of t h e m were dosed properly, and 5% were given the same dose over the 24 h period but at different intervals. In 60% of the patients the intervals r e c o m m e n d e d empirically were shorter than the calculated times. This indicates a significant t e n d e n c y to o v e r d o s a g e of patients. T h e percentage difference b e t w e e n the calculated and prescribed dose is shown in Table 1; it ranged f r o m 11-100%. In a g r e e m e n t with this observation, 70% of the patients had a t r o u g h serum gentamicin c o n c e n t r a t i o n > 2 gg. m1-1 (range 2.14 to 4.33 gg. mkl), and 40% of p e a k concentrations were outside the therapeutic range of 5-8 g g - m l -~ (range 3.3-11 gg. ml-1). T h e m e a s u r e d and predicted steady-state serum gentamicin concentrations in the kinetic group are plotted in Fig. 1. T h e correlation of m e a s u r e d and predicted steadystate serum c o n c e n t r a t i o n was excellent (r=0.9968), p < 0.05), with a slope near to unity.

Table 2. Evaluation of predictive performance of the trough and peak gentamiein serum concentrations in the kinetic group Concentrations

Bias

Precision

ME

MAE

MSE

RMSE

Trough 0.047 @0.021, 0.115) 0.156 (0.125, 0.187) 0.030 (0.018, 0.042) 0.174 (0.162, 0.186) Peak -0.030 (~).131, 0.071) 0.169 (0.092, 0.246) 0.066 (0.000, 0.132) 0.257 (0.191, 0.323) Units are in gg- ml- except those of the MSE which are in (gg. m1-1)(2). ME, mean prediction error; MAE, mean absolute error; MSE, mean squared prediction error; RMSE, root mean squared error. 95% confidence interval is given in parentheses. 1

158 The measurements of prediction bias and precision for the trough and peak steady-state serum gentamicin concentrations predicted by Sawchuk-Zaske's method are summarized in Table 2. The 95% confidence interval of the ME for the trough and peak concentrations included zero, showing that the prediction was not significantly biased. The precision of the prediction for the trough and peak concentrations was excellent. The MAEs, MSEs; and RMSEs were similar in magnitude and their 95% confidence intervals overlapped. The relationship between gentamicin clearance (ml.kg q-min -1) in the 20 adult patients in the kinetic group and the ratio of peak and trough concentrations achieved to the administered dose (mg. kg -~) is shown in Fig. 2. A significant relationship was observed, accounting for the wide range of doses required to maintain the serum concentration within the therapeutic range. The correlation coefficient for the trough and peak was excellent (r = 0.873, 0.916, P < 0.05, respectively).

Discussion

It is well recognized that gentamicin has a narrow margin of safety. The observed pharmacokinetic variability of gentamicin makes it difficult for the physician to select a safe and effective dosage. Therefore, pharmacokinetic individualization of gentamicin therapy has become a standard practice in many hospitals. The present study was undertaken to evaluate and compare a traditional non-kinetic approach and an idividualized kinetic method for deriving dosage regimens. It has been shown that the majority of patients in the non-kinetic group achieved serum gentamicin concentrations above the therapeutic range. This reinforces the documented view that pharmacokinetic monitoring and calculation of parameters should be used as the basis for recommending adjustment of dosages. The findings, namely that 65% of the patients on prescribed doses received 36% more drug than the calculated amount, and 70% of the patients had a trough serum gentamicin concentration > 2 gg/ml, show the increased risk in those patients of causing oto- and nephrotoxicity. Moreover, 20% of the patients were not prescribed sufficient gentamicin and they had subtherapeutic trough and peak concentrations, which may lead to the development of resistant strains and breakthrough bacteraemia [14]. The difference in dosing intervals was significant. The calculated dosing intervals were greater than those empirically recommended in 60% of the patients. This, too, indicates a notable tendency to overdose the patients. The study also showed that good predictions were achieved in the kinetic group and the dose prediction method in the main yielded clinically acceptable, predictive accuracy and precision (Table 2). The 95% confidence interval of the ME for the trough and peak gentamicin concentrations included zero, which shows that the prediction was not significantly biased. About 85% of the served trough and 90% of the peak concentrations fell within the therapeutic range after administration of the predicted dosage to patients. Moreover, the correlation of

Y. M. E1-Sayedand S. I. Islam: Individualization of gentamicin dosage

measured to predicted steady-state serum concentrations was excellent (r = 0.9968,p < 0.05) (Fig. 1). In order to demonstrate the considerable variability in the disposition of gentamicin, and the difficulty of determining a dosage regimen which would result in serum concentrations within the narrow therapeutic range, in patients with various degrees of renal function, the correlation between gentamicin clearance and the ratio of the peak and trough concentrations achieved to the dose administered (kinetic group) was calculated. A significant relationship was found, confirming the wide range of doses required to maintain serum concentrations within the therapeutic range (Fig. 2). Patients with slower serum clearance of gentamicin require less frequent dosage than those with more rapid elimination (Fig. 2). This appears to be due primarily to variation in the rate of renal elimination of gentamicin, while the rates of elimination remain relatively constant throughout the period under normal circumstances, alteration in kidney function may be a confounding factor if it causes a decrease in gentamicin clearance and thereby requires dosage adjustment. The present results strongly support the need for measurements of serum gentamicin concentration in all patients with a life-threatening infection. The gentamicin dosage regimen should then be individualized using the pharmacokinetic approach to provide optimal trough and peak concentrations. In addition, patients with reduced renal function and prolongation of the half-life of gentamicin may require an increased dosing interval to prevent drug accumulation and minimize the risk of nephrotoxicity.

Acknowledgement.The work was supported by the King Abdulaziz City for Science and Technology (KACST, Project No. AR-4-021; Principal Investigator Prof. Samira I. Islam). The authors gratefully acknowledge the cooperation of the Physicians, Residents, Nurses and Laboratory Technicianswho participated in this study.

References

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20. Sawchuk RJ, Zaske DE, Cipolle RJ, Wargin WA, Strate RG (1977) Kinetic model for gentamicin dosing with the use of individual patient parameters. Clin Pharmacol Ther 21:366-369 21. Sheiner LB, Beal SL (1981) Some suggestions for measuring predictive performance. J Pharmacokinet Biopharm 9:503-512 22. Sheiner LB, Beal SL, Rosenberg B, Marathe VV (1979) Forecasting individual pharmacokinetic. Clin Pharmacol Ther 26: 294-305 23. Siber GR, Echeverrion P, Smith DL, Paisley JW, Smith DH (1975) Pharmacokinetics of gentamicin in children and adults. J Infect Dis 132:637-651 24. Siber GR, Smith AL, Levin MJ (1979) Predictability of peak serum gentamicin concentration with dosage based only on body surface area. J Pediatr 94:135-138 25. Sketris I, Lesar T, Zaske D, Cipolle RJ (1981) Effect of obesity on gentamicin pharmacokinetics. J Clin Pharmaco121:288-293 26. Zaske DE (1986) Aminoglycoside: In: Evans WE, Schentag JJ, Jusko WJ (eds) Applied pharmacokinetics: Principles of Therapeutic Drug Monitoring. Applied Therapeutics, Spokane WA, pp 331-381 27. Zaske DE, Cipolle RJ, Strate RJ (1980) Gentamicin dosage requirements: Wide interpatient variations in 242 surgery patients with normal renal function. Surgery 87:164-169 28. Zaske DE, Irvine P, Strand LM, Strate RG, Cipolle RJ, Rotschafer J (1982) Wide interpatient variations in gentamicin dose requirements for geriatric patients. JAMA 248:3122-3126 29. Zaske DE, Sawchuk RJ, Gerding DN, Strate RG (1976) Increased dosage requirements of gentamicin in burn patients. J Trauma 61:824--828 Dr. Yousry M. E1-Sayed Department of Pharmaceutics College of Pharmacy King Saud Un!versity R O. Box 2457 Riyadh 11451 Saudi Arabia