T3 + 3: 3 + 3 Design With Delayed Outcomes.

Delayed outcome is common in phase I oncology clinical trials. It causes logistic difficulty, wastes resources, and prolongs the trial duration. This article investigates this issue and proposes the time-to-event 3 + 3 (T3 + 3) design, which utilizes the actual follow-up time for at-risk patients with pending toxicity outcomes. The T3 + 3 design allows continuous accrual without unnecessary trial suspension and is costless and implementable with pretabulated dose decision rules. Besides, the T3 + 3 design uses the isotonic regression to estimate the toxicity rates across dose levels and therefore can accommodate for any targeted toxicity rate for maximum tolerated dose (MTD). It dramatically facilitates the trial preparation and conduct without intensive computation and statistical consultation. The extension to other algorithm-based phase I dose-finding designs (e.g., i3 + 3 design) is also studied. Comprehensive computer simulation studies are conducted to investigate the performance of the T3 + 3 design under various dose-toxicity scenarios. The results confirm that the T3 + 3 design substantially shortens the trial duration compared with the conventional 3 + 3 design and yields much higher accuracy in MTD identification than the rolling six design. In summary, the T3 + 3 design addresses the delayed outcome issue while keeping the desirable features of the 3 + 3 design, such as simplicity, transparency, and costless implementation. It has great potential to accelerate early-phase drug development.

Modified isotonic regression based phase I/II clinical trial design identifying optimal biological dose.

Conventional phase I/II clinical trial designs often use complicated parametric models to characterize the dose-response relationships and conduct the trials. However, the parametric models are hard to justify in practice, and the misspecification of parametric models can lead to substantially undesirable performances in phase I/II trials. Moreover, it is difficult for the physicians conducting phase I/II trials to clinically interpret the parameters of these complicated models, and such significant learning costs impede the translation of novel statistical designs into practical trial implementation. To solve these issues, we propose a transparent and efficient phase I/II clinical trial design, referred to as the modified isotonic regression-based design (mISO), to identify the optimal biological doses for molecularly targeted agents and immunotherapy. The mISO design makes no parametric model assumptions on the dose-response relationship and yields desirable performances under any clinically meaningful dose-response curves. The concise, clinically interpretable dose-response models and dose-finding algorithm make the proposed designs highly translational from the statistical community to the clinical community. We further extend the mISO design and develop the mISO-B design to handle the delayed outcomes. Our comprehensive simulation studies show that the mISO and mISO-B designs are highly efficient in optimal biological dose selection and patients allocation and outperform many existing phase I/II clinical trial designs. We also provide a trial example to illustrate the practical implementation of the proposed designs. The software for simulation and trial implementation are available for free download.

CWL: A conditional weighted likelihood method to account for the delayed joint toxicity-efficacy outcomes for phase I/II clinical trials.

The delayed outcome issue is common in early phase dose-finding clinical trials. This problem becomes more intractable in phase I/II clinical trials because both toxicity and efficacy responses are subject to the delayed outcome issue. The existing methods applying for the phase I trials cannot be used directly for the phase I/II trial due to a lack of capability to model the joint toxicity-efficacy distribution. In this paper, we propose a conditional weighted likelihood (CWL) method to circumvent this issue. The key idea of the CWL method is to decompose the joint probability into the product of marginal and conditional probabilities and then weight each probability based on each patient's actual follow-up time. The CWL method makes no parametric model assumption on either the dose-response curve or the toxicity-efficacy correlation and therefore can be applied to any existing phase I/II trial design. Numerical trial applications show that the proposed CWL method yields desirable operating characteristics.

Enrollment and Stopping Rules for Managing Toxicity Requiring Long Follow-Up in Phase II Oncology Trials.

Monitoring of toxicity is often conducted in Phase II trials in oncology to avoid an excessive number of toxicities if the wrong dose is chosen for Phase II. Existing stopping rules for toxicity use information from patients who have already completed follow-up. We describe a stopping rule that uses all available data to determine whether to stop for toxicity or not when follow-up for toxicity is long. We propose an enrollment rule that prescribes the maximum number of patients that may be enrolled at any given point in the trial.

Outcome-adaptive randomization for a delayed outcome with a short-term predictor: imputation-based designs.

Delay in the outcome variable is challenging for outcome-adaptive randomization, as it creates a lag between the number of subjects accrued and the information known at the time of the analysis. Motivated by a real-life pediatric ulcerative colitis trial, we consider a case where a short-term predictor is available for the delayed outcome. When a short-term predictor is not considered, studies have shown that the asymptotic properties of many outcome-adaptive randomization designs are little affected unless the lag is unreasonably large relative to the accrual process. These theoretical results assumed independent identical delays, however, whereas delays in the presence of a short-term predictor may only be conditionally homogeneous. We consider delayed outcomes as missing and propose mitigating the delay effect by imputing them. We apply this approach to the doubly adaptive biased coin design (DBCD) for motivating pediatric ulcerative colitis trial. We provide theoretical results that if the delays, although non-homogeneous, are reasonably short relative to the accrual process similarly as in the iid delay case, the lag is also asymptotically ignorable in the sense that a standard DBCD that utilizes only observed outcomes attains target allocation ratios in the limit. Empirical studies, however, indicate that imputation-based DBCDs performed more reliably in finite samples with smaller root mean square errors. The empirical studies assumed a common clinical setting where a delayed outcome is positively correlated with a short-term predictor similarly between treatment arm groups. We varied the strength of the correlation and considered fast and slow accrual settings.