# Estimating Similarity of Dose–Response Relationships in Phase I Clinical Trials—Case Study in Bridging Data Package

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## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Commensurability Distances

#### 2.2. Dose–Toxicity Model

## 3. Case Studies

## 4. Settings

^{2}for Erilubin, 900 mg/day for Lapatinib, 200 mg/day for Sorafenib, 30 mg/m

^{2}for Ixabepilone, 8 mg/m

^{2}for Edotecarin and 700 mg/m

^{2}for E7070.

## 5. Results

## 6. Discussion

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

bid | bis in die: twice a day |

BLRM | Bayesian Logistic Regression Model |

CRM | Continual reassessment method |

DLT | dose-limiting toxicity |

ICH | International Conference on Harmonisation of Technical Requirements for Registration of Pharmaceuticals for Human Use |

MTD | maximum tolerated dose |

PMDA | Pharmaceuticals and Medical Devices Agency |

## Appendix A. Bivariate Posterior Plots

**Figure A1.**Bivariate posterior distributions of ${\beta}_{0}$ and ${\beta}_{1}$ when using ${d}_{mod}$ for the three synthetic examples.

**Figure A2.**Bivariate posterior distributions of ${\beta}_{0}$ and ${\beta}_{1}$ when using ${d}_{mod}$ for the real case studies shown in Table 2.

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**Figure 1.**MTD posterior distributions for Erilubin, Ixabepilone, Lapatinib, Sorafenib, Edotecarin and E7070 case studies. Posterior medians are represented by a circle for Caucasian and a triangle for Japanese, while maximum a posteriori is represented by a dashed line for Caucasian and a two-dash line for Japanese.

**Figure 2.**MTD posterior distributions for the Synthetic-1, Synthetic-2 and Synthetic-3 examples. Posterior medians are represented by a circle for Caucasian and a triangle for Japanese, while maximum a posteriori by a dashed line for Caucasian and a two-dash line for Japanese.

**Figure 3.**Gradient plot representing the distance between dose–toxicity curves, ${d}_{mod}$ (y-axis), and maximum of the posterior MTD distribution, ${d}_{p2}$ (x-axis). The intensity of the color varies along with the increasing distance value and coherence. Small dose–toxicity distance and high MTD distance is incoherent, as such it is plotted in a darker color.

**Table 1.**Number of dose-limiting toxicity and total number of patients accrued at each dose for 1 Caucasian trial and 3 Japanese synthetic trials. In the first column, the trial population is specified. A dash (-) means that the dose was not tested in the specified population. A box denotes the dose that has been defined as maximum tolerated dose (MTD).

Doses | ||||||
---|---|---|---|---|---|---|

Example (mg/Day) | 100 | 200 | 400 | 500 | 600 | 800 |

Caucasian (DLTs/nb pt) | 0/3 | 0/3 | 0/6 | - | $\overline{)3/9}$ | 2/3 |

Japanese | ||||||

Synthetic-1 (DLTs/nb pt) | - | - | - | 1/10 | $\overline{)2/8}$ | 2/2 |

Synthetic-2 (DLTs/nb pt) | - | - | 0/3 | 0/9 | $\overline{)4/12}$ | 3/3 |

Synthetic-3 (DLTs/nb pt) | 0/3 | $\overline{)1/6}$ | 3/3 | - | - | - |

**Table 2.**Value of dose-limiting toxicity and total number of patients accrued at each dose for all trials analysed in this manuscript. In the first column, the trial population is specified. A dash (-) means that the dose was not tested in the specified population. A box denotes the dose that has been defined as MTD, if the MTD was reached in the trial. For Sorafenib, the doses were given twice daily (bid).

Investigated Drug | Doses | ||||||||
---|---|---|---|---|---|---|---|---|---|

Erilubin (mg/m^{2}) | 0.25 | 0.5 | 0.7 | 1.0 | 1.4 | 2 | 2.8 | 4 | |

Caucasian [16] (DLTs/nb pt) | 0/1 | 0/4 | - | 0/3 | - | $\overline{)1/7}$ | 2/3 | 3/3 | |

Japanese [17] (DLTs/nb pt) | - | - | 0/3 | 0/3 | 2/6 | $\overline{)3/3}$ | - | ||

Lapatinib (mg/day) | 500 | 650 | 900 | 1000 | 1200 | 1600 | 1800 | ||

Caucasian [18] (DLTs/nb pt) | 0/13 | 1/15 | 0/11 | 1/3 | 1/12 | 1/13 | - | ||

Japanese [19] (DLTs/nb pt) | - | - | 0/6 | - | 0/6 | 1/6 | $\overline{)1/6}$ | ||

Sorafenib (mg bid) | 100 | 200 | 400 | 600 | |||||

Caucasian [20] (DLTs/nb pt) | 0/3 | 1/6 | $\overline{)0/8}$ | 3/7 | |||||

Japanese [21] (DLTs/nb pt) | 0/3 | 1/12 | $\overline{)0/6}$ | 1/6 | |||||

Ixabepilone (mg/m^{2}) | 7.4 | 15 | 30 | 40 | 50 | 57 | 65 | ||

Caucasian [22] (DLTs/nb pt) | 0/3 | 0/3 | 0/3 | - | $\overline{)3/22}$ | 3/3 | 2/3 | ||

Japanese [23] (DLTs/nb pt) | - | 0/3 | 0/3 | 1/6 | $\overline{)2/2}$ | - | - | ||

Edotecarin (mg/m^{2}) | 6 | 8 | 11 | 13 | 15 | ||||

Caucasian [24] (DLTs/nb pt) | 0/3 | 0/3 | 0/6 | 1/9 | $\overline{)4/9}$ | ||||

Japanese [25] (DLTs/nb pt) | - | 0/3 | 1/6 | 1/9 | $\overline{)2/6}$2/6 | ||||

E7070 (mg/m^{2}) | 50 | 100 | 200 | 400 | 600 | 700 | 800 | 900 | 1000 |

Caucasian [26] (DLTs/nb pt) | 0/4 | 0/3 | 0/3 | 0/3 | 0/4 | $\overline{)2/7}$ | 2/4 | - | 3/3 |

Japanese [27] (DLTs/nb pt) | - | - | - | 0/3 | 0/3 | 0/6 | 1/6 | $\overline{)2/3}$ | - |

**Table 3.**Results in terms of d, ${d}_{mod}$, ${d}_{MTD}$, ${d}_{p1}$ and ${d}_{p2}$ for the synthetic examples and the real case studies. ${x}_{r}$ denotes the reference dose selected for the Bayesian Logistic Regression Model (BLRM).

Drug | d | ${\mathit{d}}_{\mathit{mod}}$ | ${\mathit{d}}_{\mathit{MTD}}$ | ${\mathit{d}}_{\mathit{p}1}$ | ${\mathit{d}}_{\mathit{p}2}$ |
---|---|---|---|---|---|

Synthetic-1 | 0.23 | 0.18 | 0.19 | 0 | 0 |

Synthetic-2 | 0.53 | 0.37 | 0.41 | 0.02 | 0.02 |

Synthetic-3 | 0.91 | 0.83 | 1.00 | 1.50 | 1.27 |

Erilubin | 0.92 | 0.83 | 0.91 | 0.47 | 0.43 |

Lapatinib | 0.58 | 0.39 | 0.50 | 7.29 | 0.35 |

Sorafenib | 0.45 | 0.43 | 0.57 | 10.07 | 0.75 |

Ixabepilone | 0.77 | 0.56 | 0.62 | 0.34 | 0.26 |

Edotecarin | 0.38 | 0.24 | 0.32 | 0.32 | 0.04 |

E7070 | 0.63 | 0.63 | 0.88 | 0.59 | 0.23 |

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**MDPI and ACS Style**

Ollier, A.; Zohar, S.; Morita, S.; Ursino, M.
Estimating Similarity of Dose–Response Relationships in Phase I Clinical Trials—Case Study in Bridging Data Package. *Int. J. Environ. Res. Public Health* **2021**, *18*, 1639.
https://doi.org/10.3390/ijerph18041639

**AMA Style**

Ollier A, Zohar S, Morita S, Ursino M.
Estimating Similarity of Dose–Response Relationships in Phase I Clinical Trials—Case Study in Bridging Data Package. *International Journal of Environmental Research and Public Health*. 2021; 18(4):1639.
https://doi.org/10.3390/ijerph18041639

**Chicago/Turabian Style**

Ollier, Adrien, Sarah Zohar, Satoshi Morita, and Moreno Ursino.
2021. "Estimating Similarity of Dose–Response Relationships in Phase I Clinical Trials—Case Study in Bridging Data Package" *International Journal of Environmental Research and Public Health* 18, no. 4: 1639.
https://doi.org/10.3390/ijerph18041639