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Phase I Clinical Trial Designs: Backfill i3+3 (Bi3+3)

Clinical Trial Designs

What is the Bi3+3 Design?

Backfill i3+3 (Bi3+3) is a statistical design for dose finding in oncology clinical trials. It uses backfilling and Bayesian modeling to optimize dose selection in early phase oncology trials.

The goal of the Bi3+3 design is to collect information at different doses during dose escalation with the intent to help inform dose-optimization decisions.

Important distinctions with the Bi3+3 Design

The design allows patient enrollment during dose finding into both the current (main) dose cohort as well as lower doses (backfill) that have a demonstrated safety profile in patients. Information from patients enrolled in the main and backfill cohorts is used to guide dose escalation decisions for the subsequent main cohort.

Bi3+3 uses a dose escalation algorithm that combines the model-free i3+3 design approach with a Bayesian model-based probability of decision (POD) framework. The POD framework is applied to patients in the backfill cohorts for whom dose-limiting toxicity (DLT) outcomes are pending.


Explaining the Dose Escalation Process of the Bi3+3 Design

The dose escalation approach and algorithm for Bi3+3 is shown in Figure 1. Patients are first enrolled in the current dose level (main cohort). Once the main cohort has completed enrollment, patients are randomly allocated to backfill cohort doses which must be lower than the current dose level. To be considered eligible for backfill, doses must be considered safe as well as demonstrate sufficient efficacy. The design recommends use of a Bayesian model for evaluating efficacy that should be monitored continuously throughout trial conduct to update the doses to be considered for backfill.

After DLT outcomes in the main cohort are observed, a dosing decision for the next main cohort is made using the i3+3 design (to either escalate to the next dose, stay at the current dose, or de-escalate to a lower dose). Simultaneously (and prior to acting on the decision for the main cohort) the dosing decision for all the backfill doses is also determined. If none of the subjects in the backfill cohorts have pending DLT outcomes, the i3+3 design is used to make dosing decisions for the backfill doses.

If at least one subject has a pending DLT outcome, the POD framework is used to first determine if trial enrollment should be suspended for all doses. If trial enrollment is suspended, patients with pending DLT outcomes are followed up. Once sufficient DLT outcomes are observed such that trial enrollment is no longer suspended, the POD framework is then used to make dosing decisions for all the backfill doses.

Based on the findings from the backfill doses and main cohort, a dosing decision for the next main cohort is made. This process is continued until no doses are left either due to safety rules being met or the number of patients in the main cohort reaching a pre-determined maximum sample size.

Bi33-workflowFigure 1. Backfill i3+3 Design Workflow


Safety rules of the Bi3+3 Clinical Trial Design

The Bi3+3 incorporates two safety rules to prevent excessive toxicity:

1. Throughout the trial, when a new DLT outcome is observed at any dose and the current dose is evaluated as excessively toxic, the current and all higher doses are excluded from the remainder of the trial

2. If the current dose is considered excessively toxic and is the lowest dose, the trial is stopped for safety.

After trial enrollment is complete and all DLT and efficacy data have been obtained, the Bi3+3 design recommends using an isotonic regression and the pooled adjacent violators algorithm (PAVA) to select the maximum tolerated dose (MTD) and using a Bayesian four-parameter model using toxicity and efficacy data to select the optimal biologic dose (OBD).



By allowing backfill enrollment and using Bayesian modeling, the design collects richer data across multiple doses to help optimize selection of the maximum tolerated and optimal biologic doses. The integrated algorithm balances patient safety, efficacy, and operational efficiency.

Sponsors and clinical research organizations conducting dose-finding studies in oncology can benefit from the Bi3+3 design’s ability to escalate doses more swiftly while minimizing risk to accelerate development of potentially life-changing therapies.


1. Liu J, Yuan S, Bekele BN, Ji Y. The Backfill i3+ 3 Design for Dose-Finding Trials in Oncology. arXiv preprint arXiv:2303.15798. 2023 Mar 28.