General versus subpopulation values in Bayesian prediction of ...

Aminoglycoside pharmacokinetics Reports

General versus subpopulation values in Bayesian prediction of aminoglycoside pharmacokinetics in hematology–oncology patients KRISTINE M. RADOMSKI, GEORGE A. DAVIS, AND MARY H. H. CHANDLER Abstract: The predictive performance of Bayesian estimates incorporating pharmacokinetic values for hematology–oncology patients was compared with that of Bayesian estimates incorporating general population values. In study phase 1, medical records were reviewed for 50 adult patients with a hematologic or oncologic diagnosis who had received i.v. gentamicin or tobramycin. Aminoglycoside pharmacokinetic values were calculated for the patients by using a modified two-point Sawchuk-Zaske

method, and the subpopulation mean for each variable was determined. In phase 2, data for 10 other hematology–oncology patients receiving aminoglycosides were entered into the Abbottbase Bayesian pharmacokinetics program. Aminoglycoside pharmacokinetic values and serum concentrations for each of these 10 patients were estimated, first using the program’s general population values and then repeating the analysis using the subpopulation means for volume of distribution and renal clearance slope obtained in phase 1.

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The serum aminoglycoside concentrations predicted by each Bayesian method were compared with the actual peaks and troughs. Both the peak and trough predictions of the Abbottbase program using the subpopulation values for volume of distribution and renal clearance slope were significantly less biased than those predicted by the Abbottbase program incorporating the general population values. The methods did not differ significantly in precision. Use of subpopulation pharmacokinetic values in Baye-

sian predictions of serum aminoglycoside concentrations in hematology– oncology patients reduced bias significantly but had no significant effect on precision. Index terms: Aminoglycosides; Blood levels; Calculations; Computers; Drugs, body distribution; Excretion; Gentamicin; Hematologic diseases; Methodology; Neoplasms; Pharmacokinetics; Tobramycin Am J Health-Syst Pharm. 1997; 54:541-4

minoglycosides remain a valuable group of antimicrobials in the management of gram-negative infections. Therapeutic drug monitoring of these agents can improve the patient’s course by decreasing the likelihood of toxicity and enhancing efficacy.1,2 Variability in aminoglycoside pharmacokinetics has been reported for specific patient subpopulations, such as spinal cord-injury patients,3 postpartum patients,4 critically ill patients,5 and hematology–oncology patients.6-10 Bayesian pharmacokinetic forecasting blends population estimates and observed serum drug concentrations to estimate a patient’s pharmacokinetic values.11 Bayesian forecasting begins with population values and integrates patient-specific data to determine dosage requirements. This method of data analysis is especially useful in patients for whom serum drug concentration data are incomplete (when, for example, there is an

accurately collected peak concentration with no trough concentration).12 Because Bayesian forecasting is influenced by initial population values, Bayesian estimates for a patient whose pharmacokinetic values are very different from those of the general population may be inaccurate. When a small number of serum concentration results are available, a calculated pharmacokinetic value different from what is expected may be given less weight in predictions than the population values.13 Bayesian predictions for a patient in a unique subgroup may be improved by using subpopulation-based variables for the initial estimates.14 The objective of our study was to compare the predictive performance of Bayesian estimates incorporating pharmacokinetic values for hematology–oncology patients with that of Bayesian estimates incorporating general population values.

KRISTINE M. RADOMSKI, PHARM.D., is Fellow in Clinical Pharmacokinetics/Dynamics and Drug Development, School of Pharmacy, University of North Carolina at Chapel Hill, and Glaxo Wellcome, Research Triangle Park, NC; at the time of this study she was Specialty Resident in Clinical Pharmacokinetics, College of Pharmacy, University of Kentucky, Lexington. GEORGE A. DAVIS, PHARM.D., is ASHP Foundation Fellow in Geriatric Drug Therapy, College of Pharmacy. MARY H. H. CHANDLER, PHARM.D., FASHP, FCCP, is Associate Professor, Pharmacy Practice and Science, College of Pharmacy, UK, and Director, Clinical Pharmacokinetics

Service, University of Kentucky Medical Center, Lexington. Address reprint requests to Dr. Chandler at the University of Kentucky Medical Center, 800 Rose Street, Room C-117, Lexington, KY 40536-0084. Presented in part at the Annual Meeting of the American College of Clinical Pharmacy, Washington, DC, August 9, 1995. Copyright © 1997, American Society of Health-System Pharmacists, Inc. All rights reserved.1079-2082/97/0301-0541$06.00.

Vol 54 Mar 1 1997 Am J Health-Syst Pharm 541

Reports Aminoglycoside pharmacokinetics

Methods Our institutional review board ruled that informed consent was not required of patients whose medical records were used in this study. In phase 1, we examined the medical records of 50 adult patients on hematology– oncology services who had received intravenous gentamicin or tobramycin for documented infection or as empirical therapy. Patients were recruited from the inpatient population at the cancer center of our institution. Patients were excluded if they were less than 18 years of age, had a nonhematologic or nononcologic diagnosis, did not have a complete set of peak and trough aminoglycoside concentrations with recorded sampling times, had received a β-lactam antimicrobial within two hours of sample collection for peak or trough measurement, or required hemodialysis. Aminoglycosides were infused over 30 minutes, with the peak sample drawn 30 minutes after the infusion and the trough sample drawn within 30 minutes before the dose. In each case, the samples were drawn at steady state, defined as around or after the third maintenance dose. Serum aminoglycoside concentrations were analyzed by fluorescence polarization immunoassay with a TDx analyzer (Abbott Laboratories, Irvine, TX). The lower limits of sensitivity for the gentamicin and tobramycin assays are 0.27 and 0.18 µg/mL, respectively.15,16 The interrun coefficient of variation for the gentamicin assay ranges from 3.7% to 6.1% at a concentration of 3.2 µg/mL and from 2.5% to 4.4% at a concentration of 9.1 µg/mL. The interrun coefficient of variation for the tobramycin assay ranges from 2.7% to 5.9% at a concentration of 1.1 µg/mL and from 2.9% to 5.2% at a concentration of 8.9 µg/mL. We collected the following demographic and laboratory data: age, sex, total body weight (TBW), height, diagnosis, serum creatinine concentration (SCr), and aminoglycoside peak and trough concentrations, dosages, and administration times. We calculated body surface area (BSA) and ideal body weight (IBW) by using the methods of Mosteller17 and Devine,18 respectively. Dosing body weight (DBW) was calculated as IBW + 0.4(TBW – IBW) for all patients whose TBW was greater than IBW.19 For patients weighing less than IBW, TBW was used as DBW. Creatinine clearance (CLcr) was calculated and standardized to a BSA of 1.73 m2.20 We used a modified two-point Sawchuk-Zaske method assuming a one-compartment model to calculate the following pharmacokinetic variables for the aminoglycoside: elimination rate constant (k), half-life (t½), volume of distribution (V) expressed in liters per kilogram of DBW, and total drug clearance (CL) as determined by Vk.21 Renal clearance slope was calculated as the slope of the line obtained when CL was plotted against CLcr.22 The 50 patients in phase 1 were used to establish the mean values for V and renal clearance slope, and thus the subpopulation values for the hematology–oncology population. The Abbottbase pharmacokinetics program (Abbott) 542 Am J Health-Syst Pharm Vol 54 Mar 1 1997

provides Bayesian forecasting but does so with pharmacokinetic estimates based on data for the “general” adult patient population; this population does not represent subgroups like hematology–oncology patients. However, the Abbottbase program can add mean subpopulation pharmacokinetic values to optimize estimates for specific subgroups. Therefore, in phase 2 the mean values for V and renal clearance slope obtained in phase 1 were entered into the Abbottbase program to create the baseline subpopulation pharmacokinetic values. We collected the same demographic and laboratory data for 10 additional hematology–oncology patients with the same inclusion and exclusion criteria. These 10 patients’ demographics, aminoglycoside dosage histories, and serum concentrations were entered into the Abbottbase program. We performed Bayesian forecasting of aminoglycoside pharmacokinetic values and serum concentrations for each of these patients, first using the program’s general population values and then repeating the analysis using the subpopulation means for V and renal clearance slope obtained in phase 1. We compared the serum aminoglycoside concentrations predicted by each Bayesian method with the actual measured peaks and troughs. The method of Sheiner and Beal23 was used to compare the performance of each Bayesian method in predicting the actual serum concentrations in the 10 patients in phase 2. As in a previous study, we assessed bias by calculating the mean prediction error (ME), calculated as ME = ΣPE/n, where PE, or prediction error, is the difference between the predicted value and the actual value.24 The difference in bias between the two methods was determined by calculating the 95% confidence interval (CI) for the mean difference in prediction errors (MDPE). A CI that did not contain zero indicated that the two predictions differed from each other in bias at a significance level of 0.05. Precision was compared by calculating the mean absolute error (MAE), calculated as MAE = Σ|PE|/n. The difference in precision between the methods was determined by calculating the 95% CI for the mean difference between absolute errors (MDAE). A CI that did not contain zero indicated that the two methods differed from each other in precision at a significance level of 0.05.

Results The characteristics of the study patients are listed in Table 1. Mean ± S.D. values for V and renal clearance slope calculated for the phase 1 subpopulation were 0.28 ± 0.10 L/kg and 0.822 ± 1.018, respectively. The general population values for V and renal clearance slope used as initial estimates in the Abbottbase program are 0.25 ± 0.075 L/kg and 0.815 ± 0.326, respectively. Actual and predicted serum aminoglycoside concentrations for the 10 patients in phase 2 are shown in Table 2. The predictive performance of the two Bayesian methods is depicted in Table 3.

Aminoglycoside pharmacokinetics Reports

Table 1. Patient Characteristics Variable Sex (no. men/no. women) Age (yr)a Dosing body weight (kg)a Total body weight (kg) a Height (cm)a Body surface area (m2)a Serum creatinine conc. (mg/dL) Standardized creatinine clearance (mL/min/1.73 m2)a No. pts. (%) with diagnosis Acute myelogenous leukemia Breast cancer Non-Hodgkin’s lymphoma Lung cancer Myelodysplasia Thyroid cancer Acute lymphocytic leukemia Osteogenic sarcoma Ovarian cancer Otherb

Phase 1 (n = 50)

Phase 2 (n = 50)

21/29 53 ± 16 65.5 ± 13.6 75.2 ± 20.5 168.1 ± 10.6 1.86 ± 0.28

5/5 52 ± 9 64.6 ± 6.9 69.4 ± 11.2 171.5 ± 5.9 1.81 ± 0.14

1.0 ± 0.3

1.1 ± 0.5

78.6 ± 33.1

69.3 ± 24.4

11 (22) 11 (22) 7 (14) 6 (12) 2 (4) 0

4 (40) 2 (20) 1 (10) 1 (10) 1 (10) 1 (10)

3 (6) 2 (4) 2 (4) 6 (12)

0 0 0 0

± S.D. cell leukemia, cervical cancer, adenocarcinoma (primary unknown), pancreatic cancer, colon cancer, and Hodgkin’s disease. aMean

Table 3. Effect of Population Values on Prediction of Aminoglycoside Peak and Trough Concentrations in Hematology–Oncology Patients Population Value Used in Prediction

Mean Error (95% CIa)(µg/mL) Prediction

Gentamicin or Tobramycin Peak General 0.09 (–0.15 to 0.33) Hematology– oncology –0.03 (–0.25 to 0.19)b Gentamicin or Tobramycin Trough General –0.03 (–0.10 to 0.04) Hematology– oncology –0.01 (–0.08 to 0.06)d

Absolute 0.42 (0.28 to 0.56) 0.37 (0.23 to 0.51)c 0.12 (0.08 to 0.16) 0.12 (0.08 to 0.16)e

aCI

= confidence interval. 95% CI for the mean difference in prediction error between methods (0.12 µg/mL) was 0.10 to 0.14 µg/mL; thus, the difference in bias was significant (p < 0.05). cThe 95% CI for the mean difference in absolute error between methods (0.05 µg/mL) was 0.00 to 0.10 µg/mL; thus, the difference in precision was not significant. dThe 95% CI for the mean difference in prediction error between methods (–0.02 µg/mL) was –0.02 to –0.02 µg/mL; thus, the difference in bias was significant. eThe 95% CI for the mean difference in absolute error between methods (0 µg/mL) was –0.01 to 0.01 µg/mL; thus, the difference in precision was not significant. bThe

bHairy

Table 2. Comparison of Actual versus Bayesian Predicted Serum Aminoglycoside Concentrations in Phase 2 Concentration (µg/mL)

Patient

Peak 1 2 3 4 5 6 7 8 9 10 Trough 1 2 3 4 5 6 7 8 9 10

Actual

Bayesian with General Population Values

Bayesian with Subpopulation Values

3.9 6.6 6.2 7.0 2.9 4.5 4.7 4.7 3.0 7.2

4.25 6.74 5.92 6.50 3.25 4.58 5.80 3.83 3.19 7.54

4.13 6.57 5.79 6.43 3.16 4.46 5.59 3.76 3.12 7.41

0.6 2.1 1.1 1.1 0.7 0.4 1.8 0.5 0.8 2.1

0.58 1.91 1.06 1.22 0.57 0.48 1.78 0.78 0.58 1.97

0.60 1.93 1.08 1.23 0.59 0.50 1.78 0.82 0.59 1.98

Both the peak and trough predictions of the Abbottbase program using the subpopulation values for V and renal clearance slope were significantly less biased than those predicted by the Abbottbase program incorporat-

ing the general population values. The methods did not differ significantly in precision.

Discussion The pharmacokinetic variability of aminoglycosides makes it difficult to optimize the dosage regimens of these agents. Therapeutic drug monitoring has become an integral tool in designing an appropriate aminoglycoside regimen for specific patients. While general population values have been described for aminoglycosides, several subpopulations have been identified in which the pharmacokinetic values are altered. Hematology– oncology patients have been shown to have a larger aminoglycoside V, increased CL, and altered t½ compared with non-cancer patients.6-10 These alterations have been found to be independent of the type of malignancy. Davis et al.9 found a correlation between the larger V seen in these patients and hypoalbuminemia, while other investigators have found no correlation of the altered variables with any physiological characteristics, including CLcr, hemoglobin concentration, body temperature, and albumin concentration.7,8,10 In general, Bayesian forecasting is an accurate method of estimating serum drug concentrations when the data for a patient are incomplete. The Abbottbase program uses initial values obtained for patients in the general population who are between the ages of 18 and 65 years. When a patient handles a drug differently than the represented population, Bayesian estimates may give more weight to population values than to the patient’s data if only a few serum drug concentrations are available. There may be a delay in achieving an optimal drug regimen in such a patient. Bayesian estimates for a paVol 54 Mar 1 1997 Am J Health-Syst Pharm 543

Reports Aminoglycoside pharmacokinetics tient differing from the general population may be improved by using subpopulation values as the initial estimates. Bayesian subpopulation values for aminoglycoside dosing have been characterized in the literature for obese,14 pediatric,25 and renally impaired patients26 and for patients with endocarditis.27 However, subpopulation values have not been characterized specifically for hematology–oncology patients. Kosirog et al.28 found that a Bayesian program predicted serum gentamicin and tobramycin concentrations with minimal bias and good precision in neutropenic patients with cancer when values for a critically ill patient subpopulation were used. However, to our knowledge ours is the first study in which hematology–oncology subpopulation values were specifically developed and validated for use in Bayesian forecasting. Our data are consistent with previous reports of increased V and enhanced CL of aminoglycosides in hematology–oncology patients. We did not attempt to correlate V with physiological factors such as changes in the body fluid compartment caused by diuretics or the serum albumin level. The majority (94%) of the patients in phase 1 had normal renal function. Moderately impaired renal function (CLcr,