# Carboplatin Dosing in Children Using Estimated Glomerular Filtration Rate: Equation Matters

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## Abstract

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## Simple Summary

## Abstract

## 1. Introduction

^{51}Chromium ethylenediamine tetraacetic acid (

^{51}Cr-EDTA) clearance and technetium-99 m diethylenetriaminepentacetic acid (

^{99}mTc-DTPA) clearance). Although highly accurate, these methods are not widely available and often too invasive and time-consuming for routine measurement of GFR [15]. Therefore, current guidelines in clinical nephrology advise the use of estimated GFR (eGFR) based on the serum concentrations of creatinine or cystatin C [16,17]. Carboplatin dosing using eGFR may therefore be a more practical alternative to calculate the appropriate carboplatin dose. This has been studied extensively in adults [18,19].

## 2. Materials and Methods

#### 2.1. Patients and Treatment

^{2}(in children ≥10 kg) or 18.7 mg/kg (in children <10 kg) during one hour. Concomitant chemotherapeutic drugs were vincristine 1.5 mg/m

^{2}and etoposide 150 mg/m

^{2}, administration of which are part of the local standard treatment protocol.

#### 2.2. Ethical Approval

#### 2.3. Carboplatin Administration, Blood Sampling and Platinum Analysis

#### 2.4. Renal Function

_{crea}[29], Brandt [30] and Millisor [15] equations and the cystatin C-based Schwartz

_{cys}[29], FAS

_{cys}[31] and Berg [32] equations. Details of these equations can be found in Table 1. Choice of equations was based on performance in validation studies using gold standard GFR measurements [33]. Of note, both the Brandt and Millisor equations were derived in pediatric oncology patients.

#### 2.5. Pharmacokinetic and Statistical Analysis

^{-1}and 0.215 h

^{-1}, respectively. This model was implemented in MWPharm++ 1.35 (Mediware a.s., Praha, Czech Republic). The volume of distribution was allometrically scaled to corrected lean body mass. Pharmacokinetic parameters were assumed to be distributed log-normally. Residual error was assumed to be distributed normally with a standard deviation according to SD = 0.1 × C, in which C is platinum plasma concentration. Individual clearance was calculated for each patient and cycle using an iterative Bayesian procedure. The Marquardt method was used with a stop criterion of 1.00 × 10

^{−6}.

^{2}GFR was converted to absolute GFR in mL/min before use in the Newell formula. Body surface area (BSA) was calculated according to Mosteller [35]. Predicted and measured carboplatin clearance were used to calculate predicted and measured drug exposure by means of the area under the concentration time curve (AUC).

- The percentage prediction error (%PE), defined as: $\frac{\left(\mathrm{observed}\mathrm{AUC}-\mathrm{predicted}\mathrm{AUC}\right)}{\mathrm{observed}\mathrm{AUC}}\times 100\%$ which is a measure of bias;
- The absolute percentage prediction error (APE) $\left|\frac{\left(\mathrm{observed}\mathrm{AUC}-\mathrm{predicted}\mathrm{AUC}\right)}{\mathrm{observed}\mathrm{AUC}}\right|\times 100\%$, which is a measure of imprecision;
- Accuracy assessed by calculating the proportion of predicted AUC values within ± 30% of measured AUC (P
_{30}accuracy), a commonly used accuracy measure in the evaluation of eGFR equations [20].

_{−10 to +25}) in analogy to the study by Millisor et al [15]. Since the local standard retinoblastoma treatment protocol used anthropometric dosing based on BSA for children over 10 kg and on body weight for smaller children to achieve a carboplatin exposure within the target AUC, this approach was evaluated by comparing target AUC and measured AUC using the parameters described above (%PE, APE and accuracy). The target AUC of carboplatin used in this study was 7.42 mg/mL.min and was based on previously published data by Newell et al [6].

## 3. Results

#### 3.1. Patients

#### 3.2. Pharmacokinetics and Comparison of Equations

_{crea}equation. Observed carboplatin clearance ranged from 11.68 mL/min to 57 mL/min (median 33.42 mL/min), and observed AUC ranged from 3.56 mg/mL.min to 12.81 mg/mL.min (median 7.29 mg/mL.min). After visual inspection of the concentration–time curves there was an adequate goodness of fit of the final model and no bias was observed. In line with the eGFR data, observed carboplatin clearance differed between both age groups even when normalized for BSA (84.5 mL/min/1.73 m

^{2}in the younger versus 116.7 mL/min/1.73 m

^{2}in the older patients).

_{cys}equation performed best both in terms of bias and accuracy. In the infant group, Schwartz

_{cys}and FAS

_{cys}had strikingly high accuracy, while the Brandt equation, which was developed specifically for young children, did not outperform the other creatinine-based equations. In the older children, Schwartz

_{crea}, Schwartz

_{cys}and Millisor had the least bias and highest precision and yielded high P

_{30}accuracy. Combining a cystatin C- and a creatinine-based eGFR yielded similar results. Of note, anthropometric dosing had lower %PE, APE and higher accuracy when compared to a number of the eGFR equations.

_{cys}resulted in the flattest waterfall plot indicating that this is the most balanced method. In Figure 2, %PE in anthropometric dosing appears to be directly related to body weight, leading to significant underdosing in the youngest children, while %PE is mostly positive in studies above 10 kg. This was not observed with any of the eGFR-based dosing methods.

## 4. Discussion

_{cys}equation led to more accurate carboplatin exposure than the other cystatin C- or creatinine-based eGFR methods. While anthropometric dosing based on BSA or weight performed reasonably well overall, we observed significant underdosing of carboplatin in studies performed at a bodyweight below 10 kg, although patient numbers were small.

^{51}Cr-EDTA,

^{99}Tc-DTPA,

^{125}I-iothalamate or iohexol [14,36,37] are invasive, costly and cumbersome, thereby precluding widespread use in clinical practice. Therefore, current international guidelines advocate the use of eGFR based on endogenous markers for drug dosing [38] and the detection, evaluation, and management of kidney disease [16,17]. This has led to the development of a wide range of pediatric eGFR equations based on creatinine and cystatin C in recent years [20].

_{crea}equation and had higher %PE values than Schwartz

_{cys}, indicating overestimation of GFR. The Brandt equation had the highest positive bias of all creatinine-based equations. This was also observed in Millisor’s paper, where the Brandt equation systematically overestimated GFR [15]. The cystatin C-based equations performed slightly better than the creatinine-based equations, in particular in younger children. This is remarkable as both Schwartz

_{cys}and FAS

_{cys}were developed in children above the age of one [29,42], while the youngest patient in the cohort of Brandt et al. was 2.8 months of age [30] and 1 month in Millisor’s cohort [15].

_{creat}and 60% eGFR

_{cys}has been suggested to be optimal for patients with malignancy [43]. Still, this did not improve accuracy of carboplatin exposure in the present study because all equations had a positive bias.

^{2}/kg in our cohort) are inversely related to age. Therefore, weight-based dosing will result in lower carboplatin exposure in small children, as observed here.

^{2}introduces the potential for bias. It would therefore be useful to recalibrate the Newell equation in children using eGFR instead of measured GFR and also re-evaluate the extra-renal clearance of carboplatin. This could be a most welcome follow-up study.

_{30}accuracy of carboplatin exposure prediction using FAS

_{cys}and Schwartz

_{cys}was well above the 80% benchmark used for eGFR equations [33]. Second, the GFR in our patients was normal, which may have reduced the potential benefit of kidney function-based dosing when compared to anthropometric dosing. In a study in adults, Ekhart et al. [50] found no advantage of eGFR-based dosing in patients with a GFR above 50 mL/min. Veal et al. [10] demonstrated that GFR-based dosing can lead to overdosing in children with hyperfiltration, a not uncommon finding in patients with malignancy undergoing hyperhydration [51]. Still, none of the patients here showed hyperfiltration as all eGFR measurements were below 140 mL/min/1.73 m

^{2}.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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Equations Based on Creatinine | |

Equation 1 | $eGFR-Schwartzcreatinine(\mathrm{mL}/\mathrm{min}/1.73{\mathrm{m}}^{2})=42.3\times {\left(\frac{height\left(\mathrm{m}\right)}{creatinine\left(\mathrm{mg}/\mathrm{dL}\right)}\right)}^{0.79}$ |

Equation 2 | $eGFR-Brandt\left(\frac{\mathrm{mL}}{\mathrm{min}}\right)=k\times \sqrt{\frac{\left(age\left(months\right)+6\right)\times \left(weight\left(\mathrm{kg}\right)\right)}{creatinine\left(\frac{\mathrm{mg}}{\mathrm{dL}}\right)}}$ |

$k=0.95\left(females\right)and1.05\left(males\right)$ | |

Equation 3 | $eGFR-Millisor\left(\mathrm{mL}/\mathrm{min}/1.73{\mathrm{m}}^{2}\right)=0.33\times \left(\frac{height\left(\mathrm{cm}\right)}{creatinine\left(\mathrm{mg}/\mathrm{dL}\right)}\right)$ |

Equations Based on Cystatin C | |

Equation 4 | $eGFR-SchwartzcystatinC\left(\mathrm{mL}/\mathrm{min}/1.73{\mathrm{m}}^{2}\right)=40.6\times {\left(\frac{1.8}{cystatinC(\mathrm{mg}/\mathrm{L}}\right)}^{0.93}$ |

Equation 5 | $eGFR-FAScystatinC\left(\mathrm{mL}/\mathrm{min}/1.73{\mathrm{m}}^{2}\right)=107.3\xf7\left(\frac{cystatinC\left(\mathrm{mg}/\mathrm{L}\right)}{0.82}\right)$ |

Equation 6 | $eGFR-Berg=91\times cystatinC{\left(\mathrm{mg}/\mathrm{L}\right)}^{-1.213}$ |

Number of Clearance Studies | Total 38 | <2 Years 18 | >2 Years 20 | p-Value |
---|---|---|---|---|

Age, years | 2.2 [0.5–3.3] | 0.5 [0.4–1.0] | 3.3 [3.0–4.0] | <0.001 |

Body weight, kg | 13.5 [8.8–15.7] | 8.6 [6.2–9.5] | 15.6 [14.8–16.5] | <0.001 |

BSA, m^{2} | 0.60 [0.41–0.66] | 0.40 [0.33–0.43] | 0.65 [0.63–0.67] | <0.001 |

BMI, kg/m^{2} | 15.9 [15.1–18.6] | 17.9 [14.7–18.9] | 15.6 [15.1–16.4] | 0.11 |

Creatinine, mg/dL ^{a} | 0.27 [0.22–0.32] | 0.25 [0.18–0.29] | 0.31 [0.24–0.33] | 0.008 |

Cystatin C, mg/L | 0.80 [0.74–0.97] | 0.97 [0.86–1.09] | 0.75 [0.69–0.79] | <0.001 |

eGFR-Schwartz_{crea} (mL/min/1.73 m^{2}) | 104.3 [92.8–120.7] | 95.2 [82.6–116.7] | 108.9 [99.9–125.3] | <0.001 |

eGFR-Schwartz_{crea} abs (mL/min) | 36.0 [21.7–43.0] | 21.7 [19.1–26.6] | 42.7 [39.3–44.9] | <0.001 |

eGFR-Brandt (mL/min/1.73 m^{2}) | 115.4 [97.9–128.7] | 97.8 [85.2–106.0] | 128.6 [123.4–138.9] | <0.001 |

eGFR-Brandt abs (mL/min) | 43.5 [22.1–49.4] | 22.0 [18.6–24.0] | 49.2 [46.9–52.1] | <0.001 |

eGFR-Millisor (mL/min/1.73 m^{2}) | 103.4 [89.2–124.5] | 92.2 [76.9–119.3] | 109.2 [98.0–130.5] | <0.001 |

eGFR-Millisor abs (mL/min) | 35.8 [21.7–43.3] | 21.3 [18.2–26.9] | 42.6 [37.8–46.4] | <0.001 |

eGFR-Schwartz_{cys} (mL/min/1.73 m^{2}) | 99.7 [84.1–107.4] | 83.8 [75.3–94.2] | 106.6 [100.9–114.7] | <0.001 |

eGFR-Schwartz_{cys} abs (mL/min) | 33.6 [18.1–40.9] | 18.0 [13.8–24.4] | 40.6 [38.0–44.0] | <0.001 |

eGFR-FAScys (mL/min/1.73 m^{2}) | 109.4 [91.1–118.5] | 90.7 [80.8–102.9] | 117.6 [110.8–127.1] | <0.001 |

eGFR-FAScys abs (mL/min) | 37.2 [19.6–45.2] | 19.4 [14.7–26.7] | 44.8 [41.7–48.7] | <0.001 |

eGFR-Berg (mL/min/1.73 m^{2}) | 118.5 [94.9–130.6] | 94.5 [82.1–110.1] | 129.3 [120.3–142.2] | <0.001 |

eGFR-Berg abs (mL/min) | 41.3 [20.2–49.9] | 20.1 [14.8–28.5] | 49.2 [45.0–54.6] | <0.001 |

Observed carboplatin clearance (mL/min/1.73 m^{2}) | 104.3 [83.6–122.9] | 84.5 [75.3–106.2] | 116.7 [90.3–136.1] | 0.002 |

Observed carboplatin clearance abs (mL/min) | 33.4 [18.8–45.4] | 18.7 [15.9–27.9] | 44.4 [37.3–49.3] | <0.001 |

Observed carboplatin AUC (mg/mL.min) | 7.9 [7.0–8.6] | 7.7 [6.4–8.5] | 8.2 [7.3–10.7] | 0.09 |

^{a}To convert to µmol/L multiply by 88.4. BMI: body mass index, BSA: body surface area, eGFR: estimated glomerular filtration rate.

**Table 3.**Performance of predicted carboplatin AUC values based on different estimates of GFR and anthropometric dosing. Data for infants (<2 years) and older children are displayed separately.

Bias (mg/mL.min) | %PE (%) | APE (%) | Accuracy (±30%) | Accuracy (−10 to 25%) | ||
---|---|---|---|---|---|---|

Schwartz_{crea} | Total N = 38 | 1.1 [0.1 to 2.5] | 14.2 [1.7 to 27.6] | 20.1 [5.5 to 28.8] | 78.9 | 57.9 |

Brandt | 1.5 [0.6 to 2.4] | 18.3 [8.8 to 29.7] | 18.5 [9.7 to 29.7] | 76.3 | 63.2 | |

Millisor | 1.0 [0.2 to 2.3] | 13.6 [2.3 to 27.4] | 18.4 [6.3 to 29.8] | 76.3 | 57.9 | |

Schwartz_{cys} | 0.4 [−0.5 to 1.6] | 5.7 [−6.3 to 18.9] | 10.9 [5.7 to 23.4] | 89.5 | 65.8 | |

FAScys | 1.1 [0.1 to 2.0] | 13.1 [1.6 to 24.5] | 13.9 [8.1 to 26.9] | 84.2 | 68.4 | |

Berg | 1.3 [0.4 to 2.3] | 18.5 [6.3 to 27.9] | 19.3 [11.0 to 27.9] | 76.3 | 71.1 | |

Anthropometric dosing | 0.4 [−0.4 to 1.2] | 5.6 [−5.9 to 13.6] | 12.0 [5.2 to 20.1] | 81.6 | 55.3 | |

Schwartz_{crea} | Infants N = 18 | 1.7 [0.6 to 2.5] | 21.0 [8.2 to 30.2] | 22.3 [17.4 to 34.8] | 72.2 | 50.0 |

Brandt | 1.4 [0.5 to 2.0] | 17.0 [6.9 to 26.4] | 17.6 [8.9 to 29.2] | 77.8 | 66.7 | |

Millisor | 1.3 [0.4 to 2.4] | 16.9 [4.5 to 33.0] | 21.6 [14.3 to 36.1] | 66.7 | 55.6 | |

Schwartz_{cys} | 0.7 [−0.1 to 1.5] | 8.8 [−1.5 to 18.9] | 10.9 [6.4 to 22.5] | 94.4 | 77.8 | |

FAS_{cys} | 1.1 [0.3 to 1.9] | 14.1 [3.7 to 24.0] | 14.6 [8.4 to 26.9] | 94.4 | 66.7 | |

Berg | 1.3 [0.1 to 2.2] | 16.3 [1.0 to 25.3] | 18.2 [11.0 to 25.3] | 77.8 | 72.2 | |

Anthropometric dosing | 0.3 [−1.0 to 1.0] | 3.6 [−15.1 to 12.2] | 12.7 [4.7 to 17.0] | 88.9 | 55.6 | |

Schwartz_{crea} | Older children N = 20 | 0.3 [−0.1 to 2.4] | 4.1 [−0.7 to 23.7] | 11.1 [3.0 to 26.3] | 85.0 | 65.0 |

Brandt | 1.5 [0.7 to 3.7] | 19.0 [9.5 to 35.3] | 19.0 [10.4 to 35.3] | 75.0 | 60.0 | |

Millisor | 0.4 [−0.1 to 2.4] | 6.1 [−1.1 to 24.8] | 11.3 [4.8 to 27.5] | 85.0 | 60.0 | |

Schwartz_{cys} | 0.4 [−0.7 to 2.4] | 4.3 [−9.4 to 22.9] | 11.7 [4.8 to 25.0] | 85.0 | 55.0 | |

FAS_{cys} | 1.0 [−0.0 to 3.1] | 12.3 [−0.4 to 29.2] | 12.7 [7.3 to 29.2] | 75.0 | 70.0 | |

Berg | 1.6 [0.5 to 3.7] | 19.3 [7.9 to 34.7] | 19.3 [8.6 to 34.7] | 75.0 | 70.0 | |

Anthropometric dosing | 0.8 [−0.2 to 3.3] | 9.7 [−2.1 to 30.9] | 10.7 [5.7 to 30.9] | 75.0 | 55.0 |

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**MDPI and ACS Style**

van de Velde, M.E.; den Bakker, E.; Blufpand, H.N.; Kaspers, G.L.; Abbink, F.C.H.; Kors, A.W.A.; Wilhelm, A.J.; Honeywell, R.J.; Peters, G.J.; Stoffel-Wagner, B.;
et al. Carboplatin Dosing in Children Using Estimated Glomerular Filtration Rate: Equation Matters. *Cancers* **2021**, *13*, 5963.
https://doi.org/10.3390/cancers13235963

**AMA Style**

van de Velde ME, den Bakker E, Blufpand HN, Kaspers GL, Abbink FCH, Kors AWA, Wilhelm AJ, Honeywell RJ, Peters GJ, Stoffel-Wagner B,
et al. Carboplatin Dosing in Children Using Estimated Glomerular Filtration Rate: Equation Matters. *Cancers*. 2021; 13(23):5963.
https://doi.org/10.3390/cancers13235963

**Chicago/Turabian Style**

van de Velde, Mirjam E., Emil den Bakker, Hester N. Blufpand, Gertjan L. Kaspers, Floor C. H. Abbink, Arjenne W. A. Kors, Abraham J. Wilhelm, Richard J. Honeywell, Godefridus J. Peters, Birgit Stoffel-Wagner,
and et al. 2021. "Carboplatin Dosing in Children Using Estimated Glomerular Filtration Rate: Equation Matters" *Cancers* 13, no. 23: 5963.
https://doi.org/10.3390/cancers13235963