# A Method for Evaluating Robustness of Limited Sampling Strategies—Exemplified by Serum Iohexol Clearance for Determination of Measured Glomerular Filtration Rate

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Population Pharmacokinetics Model and Limited Sampling Strategy of Iohexol

#### 2.2. Semi-Parametric Simulation from Support Points

_{0-∞}). Simulated profiles with GFR < 15 mL/min or GFR > 115 mL/min were excluded, as they were outside the validated range of the LSS and will not be explored in this work. As such, both AUC and GFR are conversely evaluated in this work.

#### 2.3. Deviation from Optimal Sample Times

#### 2.4. Optimal Sample Windows

## 3. Results

#### 3.1. Simulated Profiles

#### 3.2. LSS Performance on Simulated Profiles

#### 3.3. Effect of Shifts in Sample Times on Estimated GFR

#### 3.4. Optimal Sample Windows

#### 3.5. Effect of Shifts in Sample Times on Model Parameters

_{0-inf}, changes in estimated model parameters were also evaluated. A graphical representation of the model-estimated parameter densities across all evaluated shifts is shown in Figure 6. When compared with the true parameter densities of the simulated data, the reference run with optimally timed samples achieved a relative error in mean population model parameter estimates in CL, V, Vp, and Q of 1.5%, 0.6%, 6.9%, and 3.8%, respectively. However, the mean individual relative errors in the same estimates in CL, V, Vp, and Q were 7.4%, 7.6%, 22.7%, and 495%.

## 4. Discussion

_{0-inf}. To our knowledge, this is the first work evaluating the robustness of LSS in such a setting. Overall, the 4-point LSS appears robust to shifts in both single and multiple sample times, especially for profiles with medium to good GFR, i.e., above 45 mL/min. An interesting finding is that the robustness is affected by patient absolute clearance or GFR, in this case, and that acceptable sample time deviations should be adapted also based on this information. This is especially useful in scenarios when a rough estimate of the patient clearance is known based on clinical history, but the exact mGFR is desired, e.g., for dose-adjustment of drugs.

_{0-∞}, here translated to mGFR. All runs exhibited exceptionally low mean prediction errors and relative root-mean-squared errors. This was observed during early method development and for this reason, iohexol serum clearance, and thus GFR, was calculated by dividing dose by AUC

_{0-∞}. This further highlights the need for a more robust evaluation of LSS, especially when model parameters are used directly. Our results demonstrate the clinical application of evaluating the robustness of BE-based LSS. Previously, the effect of a deviation in sample time was unknown but has now been quantified for the present model and population. With this information, one may look up the deviation in sample time for the relevant CKD stage and use this to decide on whether to include an additional sample, for example, which is likely to improve the accuracy of the parameter estimates. Such changes to the LSS are not possible in the case of multiple linear regression-based methods, where one is restricted to a pre-defined or binned sample space.

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

## References

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**Figure 1.**Kernel density estimates for the posterior (blue) and simulated (red) for (

**A**) clearance from the central compartment (CL), (

**B**) inter-compartmental clearance (Q), (

**C**) central volume (V), and (

**D**) peripheral volume (Vp). The overlap coefficient for empirical distributions between the posterior and simulated parameter distribution is shown in the top-right corner.

**Figure 2.**Mean absolute error in estimated GFR by the shift in sample time at point (

**A**) 10 min, (

**B**) 30 min, (

**C**) 2 h, and (

**D**) 5 h. Labels indicate the percentage of individuals with a relative error greater than 15% (P15).

**Figure 3.**Median absolute error in predicted mGFR by deviation in sample time at point (

**A**) 10 min, (

**B**) 30 min, (

**C**) 2 h, and (

**D**) 5 h, grouped by CKD stage.

**Figure 4.**The effect of shifts in time over multiple sample points, where the (

**A**) reference run is compared to when shifts in sample time are normally distributed around the optimal sample time with a relative standard deviation (RSD) of (

**B**) 5%, (

**C**) 10%, (

**D**) 15%, (

**E**) 20%, and (

**F**) 25%. Blue and red fill indicates an individual error greater than or less than 15%, respectively. The label in the upper-left corner denotes the proportion of individuals with a relative prediction error greater than 15% (P15) for each level of RSD.

**Figure 5.**Empirical estimates of optimal sample windows for (

**A**) deviations in individual sample times, assuming all other points are sampled optimally, resulting in mean error < 2 mL/min, and (

**B**) deviations across all sample times, normally distributed around each sample point with 25% RSD, resulting in a P15 = 8.3%.

**Figure 6.**Kernel density estimates for all empirical deviations in time (black), compared to the observed posterior (red) for (

**A**) clearance from the central compartment (CL), (

**B**) inter-compartmental clearance (Q), (

**C**) central volume (V), and (

**D**) peripheral volume (Vp).

**Table 1.**Weighted mean and weighted median (95% credibility interval) of the population pharmacokinetic model parameters support points for the original and simulated dataset.

Weighted Mean | Weighted Median (95% Credibility Interval) | |||
---|---|---|---|---|

Original | Simulated | Original | Simulated | |

CL (L/h) | 2.89 | 2.84 | 1.95 (1.54–2.60) | 2.42 (2.16–2.72) |

V (L) | 10.36 | 9.32 | 10.11 (9.19–10.91) | 8.98 (8.25–9.57) |

Vp (L) | 9.20 | 7.98 | 7.95 (7.23–8.60) | 7.46 (7.06–7.81) |

Q (L/h) | 10.65 | 11.37 | 8.03 (6.53–9.23) | 8.65 (7.50–9.72) |

**Table 2.**Limited sampling strategy performance on determining mGFR for the simulated profiles, presented as the absolute and relative error from the simulated “true” GFR. Data are presented as mean ± standard deviation.

Group | Absolute Error (mL/min) | Relative Error (%) | P15 (%) | n |
---|---|---|---|---|

All profiles | 1.5 ± 2.2 | 4.1 ± 5.5 | 5.3 | 339 |

CKD Stage 4 (15–29 mL/min) | 1.5 ± 1.3 | 6.3 ± 5.8 | 7.8 | 90 |

CKD Stage 3b (30–44 mL/min) | 1.9 ± 2.2 | 5.4 ± 6.0 | 8.0 | 100 |

CKD Stage 3a (45–59 mL/min) | 1.0 ± 1.6 | 2.2 ± 3.4 | 1.8 | 57 |

CKD Stage 2 (60–90 mL/min) | 1.3 ± 3.0 | 1.9 ± 4.4 | 2.7 | 73 |

CKD Stage 1 (90–115 mL/min) | 1.2 ± 2.2 | 1.2 ± 1.9 | 0.0 | 19 |

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**MDPI and ACS Style**

Hovd, M.; Robertsen, I.; Woillard, J.-B.; Åsberg, A.
A Method for Evaluating Robustness of Limited Sampling Strategies—Exemplified by Serum Iohexol Clearance for Determination of Measured Glomerular Filtration Rate. *Pharmaceutics* **2023**, *15*, 1073.
https://doi.org/10.3390/pharmaceutics15041073

**AMA Style**

Hovd M, Robertsen I, Woillard J-B, Åsberg A.
A Method for Evaluating Robustness of Limited Sampling Strategies—Exemplified by Serum Iohexol Clearance for Determination of Measured Glomerular Filtration Rate. *Pharmaceutics*. 2023; 15(4):1073.
https://doi.org/10.3390/pharmaceutics15041073

**Chicago/Turabian Style**

Hovd, Markus, Ida Robertsen, Jean-Baptiste Woillard, and Anders Åsberg.
2023. "A Method for Evaluating Robustness of Limited Sampling Strategies—Exemplified by Serum Iohexol Clearance for Determination of Measured Glomerular Filtration Rate" *Pharmaceutics* 15, no. 4: 1073.
https://doi.org/10.3390/pharmaceutics15041073