IV Busulfan Dose Individualization in Children undergoing Hematopoietic Stem Cell Transplant: Limited Sampling Strategies

Article Outline

• Abstract
• Introduction
• Patients and Methods
  • Development Phase
    • Busulfan AUC calculation
    • Limited sampling strategy development
    • Busulfan dose adjustment
    • Extent of agreement
  • Validation Phase
    • Busulfan AUC calculation
    • LSS validation
• Results
  • Development Phase
    • LSS development
    • Busulfan dose adjustment
    • Extent of agreement
  • Validation Phase
    • LSS validation
• Discussion
• Acknowledgments
• References
• Copyright

Abstract 

We currently calculate area under the busulfan concentration time curve (AUC) using 7 plasma busulfan concentrations (AUC7) drawn after the first of 16 i.v. busulfan doses given as a 2-hour infusion every 6 hours. The aim of this study was to develop and validate limited sampling strategies (LSSs) using 3 or fewer busulfan concentration values with which to reliably calculate AUC in children undergoing hematopoietic stem cell transplant (HSCT). Children in the development group (44) received i.v. busulfan at Sick Kids; the validation group consisted of 35 children who received care at CHU Ste-Justine. Busulfan doses given and subsequent plasma busulfan concentrations were recorded. LSSs using 1 to 3 concentration-time points were developed using multiple linear regression. LSS were considered to be acceptable when adjusted r² > 0.9, mean bias <15% and precision <15%. Extent of agreement between the AUC7 values and the LSS AUC was assessed by the intraclass correlation coefficient (ICC) and Bland-Altman (BA) analysis. Agreement was considered to be excellent when the lower limit of the 95% confidence limit of the ICC exceeded 0.9 and when the limits of agreement in the BA analysis were ±15% for both AUC and dose. Administration of the theoretic adjusted busulfan doses based on each LSS was simulated and cases where the resulting AUC was >1500 or <900 μM·min were noted. LSSs using 1, 2, or 3 plasma busulfan concentrations were developed that showed excellent agreement with AUC7 and adjusted busulfan doses. In the validation sample, only the 2- and 3-point LSSs demonstrated acceptable precision and lack of bias. LSSs using 2 or 3 plasma busulfan concentrations can be used to reliably estimate busulfan AUC after IV administration in children undergoing HSCT.

Key Words: Busulfan, Area under the curve, Pediatrics, Pharmacokinetics, Limited sampling strategy

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Introduction 

A relationship between busulfan dose intensity, expressed either as the area under the plasma busulfan concentration versus time curve (AUC) or the average plasma concentration, and certain hematopoietic stem cell transplant (HSCT) outcomes has been described 1, 2, 3. This relationship is best substantiated in adults with chronic myelogenous leukemia receiving oral busulfan [4]. The strength of this relationship in other populations and circumstances such as children undergoing HSCT is less clear. Nevertheless, in many HSCT centers the standard of care in patients receiving busulfan-containing preparative regimens includes the determination of plasma busulfan concentrations and calculation of pharmacokinetic parameters after the first of 16 i.v. busulfan doses given every 6 hours. Subsequent i.v. busulfan doses are adjusted to achieve target parameters with a view to minimizing adverse HSCT outcomes such as hepatic venous occlusive disease and engraftment failure.

Traditionally, we have calculated busulfan AUC using 7 plasma concentrations (AUC7) in the 4 hours following the 2-hour busulfan dose infusion and prior to the second busulfan dose. We hypothesized that a sampling schedule using fewer samples could result in an AUC value similar to that calculated using 7 samples, and would lead to a dose adjustment clinically similar to that made based on the AUC7 value. Use of fewer samples to calculate busulfan AUC would result in cost savings (nursing workload, assay costs), reduce patient inconvenience related to obtaining blood samples, and reduce the volume of blood required from each patient.

The objective of this study was to develop and validate limited sampling strategies (LSSs) using 3 or fewer busulfan concentration values with which to reliably calculate busulfan AUC in children undergoing HSCT. The extent of agreement between the AUC7 and the AUC calculated using each LSS was evaluated.

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Patients and Methods 

This study was approved by each of our institutions' research ethics boards.

Development Phase 

Patients who received i.v. busulfan (Busulfex®, PDL BioPharma, Redwood City, CA) for conditioning prior to HSCT from April 1, 2003 through January, 2006 at The Hospital for Sick Children, Toronto, Canada, were identified from pharmacy records. The health records of these patients were reviewed to obtain information including: demographic information, busulfan doses received, busulfan dose administration times, and plasma busulfan concentrations.

Busulfan was given as an i.v. infusion over 2 hours via 1 lumen of a double-lumen central venous catheter. Blood samples were drawn for plasma busulfan determination 2 (at the end of the infusion), 2.25, 2.5, 3, 4, 5, and 6 hours from the start of the infusion. Samples were taken from the catheter lumen that was not used for dose administration. Plasma busulfan concentrations were assayed by gas chromatography with electron capture detection by a laboratory that participates in the proficiency testing program organized by PDL BioPharma 5, 6. The coefficient of variation of the assay is 3.8% to 6.0%. Busulfan AUC was calculated using 1-compartmental analysis using all 7 of the available data points (AUC7; WinNonLin version 5.0.1). A plasma busulfan concentration of 0 immediately before dose administration was assumed.

The relationship between AUC7 plasma busulfan concentrations at individual time points after i.v. administration was assessed by the Spearman rho correlation coefficient. LSSs using 1 to 3 concentration-time points were developed via multiple linear regression analysis. The association between the AUC7 and the AUC values predicted by each LSS was described using the adjusted coefficient of determination (r²); values >0.9 were considered acceptable. Bias and precision of the LSSs were measured using the mean prediction error (bias) and the root-mean-squared prediction error (precision), respectively. Bias and precision values of <15% were considered to be acceptable.

Based on a target AUC of 1300 μM·min, a theoretic adjusted busulfan dose was calculated for each patient using all LSSs that met the criteria for acceptability. The AUC that would have been achieved after simulated administration of the theoretic adjusted busulfan dose was then calculated using the AUC7 value. Patients who achieved an AUC <900 μM·min or >1500 μM·min under simulation were noted.

Intraclass correlation coefficient (ICC; parallel, 1-way random effect model; SPSS version 13.0.1 for Windows) and Bland-Altman (BA) analysis were used to assess the extent of agreement between AUC7 and the AUC values generated by each LSS. The presence of equal variance within the AUC7 and predicted AUC values was evaluated by determining the Spearman rho correlation coefficient between the residuals (AUC7 − AUC predicted) and the predicted values and by plotting the residuals against the predicted AUC values. Variance was deemed to be equal if no significant linear relationship existed between the residuals and the predicted AUC values and if plots of the residuals against the predicted values demonstrated random scatter about the zero reference line. If variance was deemed to be unequal, the data were log transformed and the variance was reevaluated. Agreement was considered to be excellent when the lower limit of the 95% confidence limit of the ICC exceeded 0.9.

In the BAanalysis, the difference (bias) between the AUC calculated using a LSS and the AUC7 (% difference = 100 ([AUC7 – AUC-LSS]/mean of AUC7 and AUC-LSS) was plotted against the mean of the 2 values. The limits of agreement (mean % difference ±2 SD) were calculated. Clinically acceptable limits of agreement for AUC were set as ±200 μM·min (15%) and were based on a target AUC of 1300 μM·min and a target AUC range of 900 to 1500 μM·min.

Validation Phase 

Patients who received i.v. busulfan (Busulfex®, PDL BioPharma) for conditioning prior to HSCT from 2001 through 2006 at CHU Sainte-Justine, Montréal, Canada, were identified from HSCT records. The health records of these patients were reviewed to obtain information as described in the development phase.

Busulfan was given as an i.v. infusion over 2 hours. Seven to 8 blood samples were drawn for plasma busulfan determination at approximately 2 (at the end of the infusion), 2.25, 2.5, 3, 4, 5, and 6 hours from the start of the infusion. Plasma busulfan concentrations were assayed by HPLC-UV by a laboratory that participates in the proficiency testing program organized by PDL BioPharma [7]. The coefficient of variation of the assay is 7% to 12%. Busulfan AUC was calculated as described above.

The association between the AUC values calculated using all available data points and the AUC values predicted by each LSS that met the criteria for acceptability, which had been set in the development phase (ie, r² > 0.9; bias and precision <15%; limits of agreement for AUC ± 200 μM·min) was determined as described in the development phase. Again, based on a target AUC of 1300 μM·min, a theoretic adjusted busulfan dose was calculated using the AUC values calculated using each LSS that met the criteria for acceptability. The extent of agreement between the AUC7 values and those calculated by each acceptable LSS was determined using the methodology described in the development phase. The AUC that would have been achieved after simulated administration of the theoretic adjusted busulfan dose calculated using the AUC determined by each LSS was calculated using the AUC7 value. Patients who achieved an AUC <900 μM·min or >1500 μM·min under simulation were noted.

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Results 

Development Phase 

Forty-four children, 0.3 to 16 years of age, received i.v. busulfan at The Hospital for Sick Children during the study period and were included in this analysis. Demographic data and information regarding the busulfan dose administered are presented in Table 1.

Table 1. Demographic Data and Information Regarding the i.v. Busulfan Dose Administered to the Development and Validation Patient Groups

	Development Group	Validation Group
Number of patients	44	35
Mean age ± SD in years (median; range)	5.0 ± 5.21 (3.0; 0.3 to 16.2)	8.5 ± 6.14 (8.1; 0.4 to 18.3)
Underlying diagnosis (number of patients; %)
Acute myelogenous leukemia	10 (23)	12 (34)
Acute lymphoblastic leukemia	0	5 (14)
Immune deficiency syndrome	8 (18)	1 (3)
Histiocytosis	4 (9)	0
Chronic myelogenous leukemia	4 (9)	1 (3)
Hurler syndrome	4 (9)	3 (9)
Sickle cell anemia	0	4 (11)
Myelodysplastic syndrome	0	5 (14)
Beta-thalassemia	3 (7)	1 (3)
Medulloblastoma	2 (5)	0
Osteopetrosis	2 (5)	0
Wiskott-Aldrich syndrome	2 (5)	0
Other	5 (11)	3 (9)
Number of patients given phenytoin	44	7
Mean initial busulfan dose in mg/kg∗ (median; range)	1.02 ± 0.178 (1.01; 0.56 to 1.45)	0.82 ± 0.100 (0.80; 0.63 to 1.09)

SD indicates standard deviation.

Plasma busulfan concentrations drawn at every time point after the 2-hour infusion correlated strongly with AUC7 (Table 2; Spearman rho coefficient = 0.709-0.985). Details regarding the LSSs that met the criteria for acceptability (ie, adjusted r² > 0.9, mean bias <15% and precision <15%) are presented in Table 3. Mean AUC7 values and AUC values generated by each LSS are presented in Table 4.

Table 2. Development Phase: Spearman Rho Correlation Coefficients for AUC7 and Plasma Busulfan Concentrations at Time Points after the Start of a 2-Hour Infusion in 44 Patients

AUC7 indicates area under the busulfan concentration versus time curve calculated using 7 data points.

Table 3. Development Phase: Limited Sampling Strategies for i.v. Busulfan Determined by Multiple Regression Analysis

CI indicates confidence interval; C4, C5, C6, busulfan plasma concentration 4, 5, and 6 hours after the start of a 2-hour infusion, respectively.

Table 4. Mean Actual and Predicted AUC and Ideal Busulfan Dose Values (95% Confidence Interval) Generated during Development and Validation Phases

	Development Phase	Validation Phase
Mean AUC7	1268.6 (1182.2-1354.9)	880.2 (791.4-969.0)
Mean AUC: 1-point LSS	1268.6 (1183.6-1353.5)	892.4 (814.4-970.3)
Mean AUC: 2-point LSS	1268.6 (1182.8-1354.3)	850.2 (772.4-928.0)
Mean AUC: 3-point LSS	1268.6 (1182.6-1354.5)	857.9∗ (773.0-942.9)
Mean ideal busulfan dose (mg) based on:
AUC7	21.2 (16.7-25.7)	37.6 (30.3-44.9)
1-point LSS	21.1 (16.6-25.6)	36.9 (29.8-44.0)
2-point LSS	21.3 (16.7-25.9)	38.8 (31.3-46.3)
3-point LSS	21.2 (16.7-25.7)	39.9 (32.5-47.3)

AUC indicates area under the plasma busulfan versus time curve; AUC7, AUC calculated using 7 data points; LSS, limited sampling strategy.

When administration of the doses calculated using any of the 3 LSSs was simulated and the resulting AUC was calculated using the AUC7 value, all patients included in the development phase achieved an AUC within the target range (900-1500 μM·min).

Variance within the AUC7 and predicted AUC values was found to be equal (data not shown); log transformation of the data was not necessary. Excellent agreement (ICC 0.983-0.995; Table 5) was observed between AUC7 and the AUC values generated using the LSSs using 1, 2, and 3 plasma busulfan concentrations. The precision of these LSSs was <5% and mean bias was very small (−0.03%-0.17%). The BA plots for those LSSs that met the clinically acceptable limits of agreement set a priori (AUC ±15%) are presented in Figure 1.

Table 5. Extent of Agreement between AUC Values Predicted by the Limited Sampling Strategies and AUC7

ICC indicates parallel, 1-way random effect model intraclass correlation coefficient; CI, confidence interval; C4, C5, C6, busulfan concentration 4, 5, and 6 hours after the start of a 2-hour infusion, respectively.

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• Figure 1. 

  Development phase: BA plots of AUC7 versus AUC predicted by each limited sampling strategy (LSS). (A) 1-sample LSS; (B) 2-sample LSS; (C) 3-sample LSS.

Validation Phase 

Thirty-five children, aged 0.4 to 18.3 years of age, who received i.v. busulfan at CHU Ste-Justine during the study period were included in this analysis. Demographic data and information regarding the busulfan dose administered are presented in Table 1.

Mean AUC values calculated using all available data points and via all acceptable LSSs identified in the validation phase are presented in Table 4. Variance within the AUC7 and predicted AUC values was found to be equal (data not shown); log transformation of the data was not necessary. Excellent agreement was again observed between AUC7 and the AUC values predicted by the LSS strategies (ICC 0.957 to 0.970; Table 5) though the limits of agreement of the 1-sample LSS exceeded 15%. Again, the limits of agreement of the 1-sample LSS were −11.9% to 15.8%, and thus exceeded the limit of ±15% that had been set a priori. The BA plots comparing actual AUC7 and the AUC values predicted by the LSSs are presented in Figure 2.

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• Figure 2. 

  Validation phase: BA plots of AUC7 versus AUC predicted by each limited sampling strategy (LSS). (A) 1-point LSS; (B) 2-point LSS; (C) 3-point LSS.

The difference between the AUC7 and the AUC calculated using the 2- and 3-sample LSSs exceeded the limits of agreement of ±15% set a priori in a single patient. The difference between the AUC7 and the 2-point and 3-point AUCLSSs was 27% and 22%, respectively. This patient was an 8-year-old with myelodysplastic syndrome who weighed 94% of ideal body weight, received lorazepam for prophylaxis for busulfan-induced seizures, and exhibited a very short busulfan half-life (78 minutes). The difference between the AUC7 and the 2-sample and 3-sample AUCLSSs was 18% and 15%, respectively, in another patient. This patient was a 13.5-year-old with acute lymphoblastic leukemia who weighed 100% of ideal body weight, received midazolam for prophylaxis of busulfan-induced seizures and exhibited a very long busulfan half-life (258 minutes). No other distinguishing features of these patients were evident.

No patient achieved an AUC <900 μM·min when administration of the theoretic adjusted busulfan doses was simulated. Two patients achieved AUC values >1500 μM·min under each LSS (2-sample LSS: 1706 and 1550; 3-sample LSS: 1626 and 1511 μM·min, respectively). Both of these patients are described in the previous paragraph.

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Discussion 

We have developed and externally validated 2 LSSs using either 2 or 3 busulfan concentration-time points for calculating AUC in children receiving i.v. busulfan prior to HSCT. These LSSs predict AUC7 with good precision and little bias. The AUC values predicted by these LSSs and the adjusted busulfan doses derived using the LSSs have excellent agreement, both statistically and clinically, with those calculated using 7 data points.

Traditionally, the full assessment of AUC of a drug that displays 1-compartmental disposition such as busulfan, requires a minimum of 7 concentration-time points after the first dose. Evaluation of the AUC after the first dose allows us to assume that the initial concentration at time zero is 0; this constitutes the eighth data point. Assessment of AUC is therefore very labor intensive because nurses must obtain many samples that then must be analyzed. Delays in receiving results may delay administration of subsequent individualized 6 hourly busulfan doses. In our institutions, plasma busulfan concentrations are usually available 6 hours after the last sample is drawn and patients usually receive an adjusted dose by the fourth busulfan dose.

Other investigators have developed LSSs after i.v. busulfan administration to adults. Vaughan et al. [8] developed a LSS in 59 adults each of whom had 4 to 12 plasma busulfan concentrations determined after the first i.v. busulfan dose. Their approach was validated in 96 patients. AUC calculation using 4 or 5 samples was recommended because this number of samples accommodates the occasional pragmatic need to discard samples that have yielded questionable results. This analysis emphasized the number of data points required for AUC determination, not the ideal timing of sampling required for efficient and reliable determination of AUC. In addition, the performance of the LSS was evaluated using tests of differences between mean AUC, elimination half-life, and coefficient of variations rather than by an evaluation of the agreement between individual AUC or dose adjustment pairs. Precision and bias of the LSS were not specified. As noted by others, assessment of agreement using the correlation coefficient or comparisons of mean values is flawed [9].

Nguyen et al. [10] also developed a LSS in adults receiving i.v. busulfan using Bayesian methods: data from 103 and 24 patients were used to develop and validate the model, respectively. A 2-sample LSS using plasma busulfan concentrations obtained at 2.25 and 6 hours from the start of a 2-hour infusion predicted the AUC with no signficiant bias and good precision. The correlation coefficient was used to compare the predicted AUC based on the LSS and the AUC based on the complete data set. Application of this LSS requires use of Bayesian methodology.

Neither of the LSSs proposed to date are ideal. The first⁸ suffers from lack of demonstrated agreement with the results of the full data set, whereas the second¹⁰ requires the use of methodology that is not readily accessible to many clinicians. The LSSs we propose will reliably and accurately predict AUC in children receiving i.v. busulfan over 2 hours without the use of sophisticated computer modeling. Use of the LSSs described here is limited to the population used in their development and validation: children receiving the first of 16 2 hour busulfan infusions. As well, adherence to the timing of blood sampling must be rigorous. Determination of AUC using the traditional 7-point method should be considered for patients who exhibit extreme busulfan half-lives (very short or very long) because the LSS described here may not predict actual AUC accurately in such patients.

We recommend adoption of the 3-sample LSS so as to minimize complications should 1 of the samples yield questionable results and need to be discarded. Depending on which sample is forfeit, it may be possible to calculate AUC by means of the 2-sample LSS. In our institution, the adoption of the 3-sample LSS will not only reduce assay costs, nursing and laboratory technician workload, and patient inconvenience, but will also improve result turnover and permit dose adjustment by the third busulfan dose.

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Acknowledgments 

The authors thank Dr. Winnie Seto PharmD, Pharmacy Therapeutic Drug Monitoring Coordinator, the nurses, pharmacists, physicians, and other staff who care for hematopoietic stem cell transplant patients at The Hospital for Sick Children, Toronto and CHU Ste-Justine, Montréal.

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