Phase I clinical trials in oncology aim to evaluate the toxicity risk of new therapies and identify a safe but also effective dose for future studies. Traditional Phase I trials of chemotherapies focus on estimating the maximum tolerated dose (MTD). The rationale for finding the MTD is that better therapeutic effects are expected at higher dose levels as long as the risk of severe toxicity is acceptable. With the advent of a new generation of cancer treatments such as the molecularly targeted agents (MTAs) and immunotherapies, higher dose levels no longer guarantee increased therapeutic effects, and the focus has shifted to estimating the optimal biological dose (OBD). The OBD is a dose level with the highest biologic activity with acceptable toxicity. The search for OBD requires joint evaluation of toxicity and efficacy. Although several seamleass phase I/II designs have been published in recent years, there is not a consensus regarding an optimal design and further improvement is needed for some designs to be widely used in practice. In this dissertation, we propose a modification to an existing seamless phase I/II design by Wages and Tait (2015) for locating the OBD based on binary outcomes, and extend it to time to event (TITE) endpoints. While the original design showed promising results, we hypothesized that performance could be improved by replacing the original adaptive randomization stage with a different randomization strategy. We proposed to calculate dose assigning probabilities by averaging all candidate models that fit the observed data reasonably well, as opposed to the original design that based all calculations on one best-fit model. We proposed three different strategies to select and average among candidate models, and simulations are used to compare the proposed strategies to the original design. Under most scenarios, one of the proposed strategies allocates more patients to the optimal dose while improving accuracy in selecting the final optimal dose without increasing the overall risk of toxicity. We further extend this design to TITE endpoints to address a potential issue of delayed outcomes. The original design is most appropriate when both toxicity and efficacy outcomes can be observed shortly after the treatment, but delayed outcomes are common, especially for efficacy endpoints. The motivating example for this TITE extension is a Phase I/II study evaluating optimal dosing of all-trans retinoic acid (ATRA) in combination with a fixed dose of daratumumab in the treatment of relapsed or refractory multiple myeloma. The toxicity endpoint is observed in one cycle of therapy (i.e., 4 weeks) while the efficacy endpoint is assessed after 8 weeks of treatment. The difference in endpoint observation windows causes logistical challenges in conducting the trial, since it is not acceptable in practice to wait until both outcomes for each participant have been observed before sequentially assigning the dose of a newly eligible participant. The result would be a delay in treatment for patients and undesirably long trial duration. To address this issue, we generalize the time-to-event continual reassessment method (TITE-CRM) to bivariate outcomes with potentially non-monotonic dose-efficacy relationship. Simulation studies show that the proposed TITE design maintains similar probability in selecting the correct OBD comparing to the binary original design, but the number of patients treated at the OBD decreases as the rate of enrollment increases. We also develop an R package for the proposed methods and document the R functions used in this research. The functions in this R package assist implementation of the proposed randomization strategy and design. The input and output format of these functions follow similar formatting of existing R packages such as "dfcrm" or "pocrm" to allow direct comparison of results. Input parameters include efficacy skeletons, prior distribution of any model parameters, escalation restrictions, design method, and observed data. Output includes recommended dose level for the next patient, MTD, estimated model parameters, and estimated probabilities of each set of skeletons. Simulation functions are included in this R package so that the proposed methods can be used to design a trial based on certain parameters and assess performance. Parameters of these scenarios include total sample size, true dose-toxicity relationship, true dose-efficacy relationship, patient recruit rate, delay in toxicity and efficacy responses.

Cette thèse est consacrée aux méthodes statistiques d’extrapolation dans les essais de recherche de dose en pédiatrie. Dans un premier temps, nous réalisons une revue systématique de la littérature sur le sujet. Elle met en évidence la nécessité de proposer de nouvelles méthodes pour la conception des études d’escalade de dose chez l’enfant. Nous apportons des réponses à cette problématique en exploitant l’information disponible chez l’adulte. Dans une première série de travaux, nous étudions l’intérêt de la prédiction des paramètres pharmacocinétiques (PK) en pédiatrie à l’aide de méthodes d’extrapolation : l’allométrie et la maturation. Cette évaluation est réalisée à partir de données PK chez l’adulte et l’enfant pour la méfloquine. Faisant appel aux paramètres prédits, nous développons une approche pour choisir les temps de prélèvements (design) d’une étude PK. Nous recommandons un design obtenu par optimisation grâce à la méthode de D-optimalité en utilisant le logiciel PFIM. Ce design est ensuite validé à l’aide de simulations sur différents modèles. Une seconde série de travaux nous amène à proposer des recommandations pour la planification d’un essai de recherche de dose. Nous avançons d’abord des techniques pour choisir les doses à tester grâce à l’utilisation des données adultes et de l’extrapolation. Nous proposons ensuite une méthode proche de la méta-analyse pour prédire les probabilités de toxicités pour chaque dose. Enfin, nous employons la méthode de l’Effective sample size afin de construire une loi a priori lors de l’utilisation d’une estimation bayésienne. Nous validons ces recommandations sur une étude de cas en utilisant une méthode d’escalade de dose, la méthode de réévaluation séquentielle bivariée, pour laquelle nous évaluons à la fois la toxicité et l’efficacité. A partir de l’exemple de la molécule erlotinib, nous effectuons une série de simulations sur plusieurs scénarios afin d’illustrer les performances de la planification. / This thesis addresses extrapolation techniques for statistical models for dose-finding studies in pediatrics. After a litterature review on these clinical trials, we observed the need of methodological propositions for the planification of dose- finding studies in pediatrics. We deal with this issue using information from the adult population. In a first research, the objectives are to design a pharmacokinetic (PK) study by using information from adults and evaluate the robustness of the recommended design through a case study of mefloquine. Pediatric PK parameters are predicted from adult PK using extrapolation functions such as allometry and maturation. A D-optimal design for children is obtained with PFIM by assuming the extrapolated design. The robustness of the recommended design is evaluated in a simulation study with four different models and is compared to the empirical design used for the pediatric data. In a second research, we propose a global approach to conduct a pediatric dose-finding clinical trial using extrapolation from adult information. First, we extrapolate the dose-range from adults using allometry and maturation. Then, using an approach to meta-analysis, we choose the initial probabilities of toxicity for each dose. Finally, we use the effective sample size method to choose the prior distribution of parameters in a Bayesian setting. We perform a simulation study based on the molecule erlotinib to evaluate the performances of this global approach.