TWICEBEE: A Two-stage Intra-patient Curve-free Bayesian Decision-Theoretic Dose Escalation Design

1. Problem Statement

Phase I clinical trials traditionally aim to identify a single Maximum Tolerated Dose (MTD) based on the assumption that dose assignment occurs once at enrollment and toxicity outcomes are static across treatment cycles. However, this assumption fails for multi-cycle immunotherapies (e.g., CAR T-cell therapy), where:

• Intra-patient dose escalation is clinically desirable to increase drug exposure over time.
• Toxicity patterns are dynamic: For many immunotherapies, toxicity at a fixed dose is highest in the initial cycle and decreases in subsequent cycles due to mechanisms like immune adaptation or reduced tumor burden.
• Existing limitations: Current intra-patient designs (e.g., BaSyc, DIETE, IP-CRM) either assume constant toxicity, target a single MTD for the entire trial, or are limited to a small number of cycles. They fail to account for the specific "non-increasing cycle-specific toxicity" pattern where the MTD effectively increases as the patient progresses through cycles.

2. Methodology: The TWICEBEE Design

The authors propose TWICEBEE (TWo-stage Intra-patient Curve-frEe Bayesian dEcision-thEoretic dose escalation), a two-stage design tailored for settings where toxicity decreases over cycles at a fixed dose.

A. Core Conceptual Shift

The design treats the treatment cycle as a second dimension alongside dose level. Unlike standard two-agent designs where toxicity increases with both dimensions, TWICEBEE assumes:

• Dose Dimension: Toxicity increases with dose ($p_{j,c} \le p_{j+1,c}$).
• Cycle Dimension: Toxicity decreases with cycle number ($p_{j,c} \ge p_{j,c+1}$).

B. The "C Partial Order"

To accommodate the reversed toxicity trend in the cycle dimension, the authors modify the curve-free Bayesian decision-theoretic (c-CFBD) framework:

• They define a C partial order where a dose-cycle combination $(j, c)$ is considered less toxic than $(j', c')$ if $j \le j'$ (lower dose) AND $c' \le c$ (earlier cycle).
• This allows the model to propagate information: observing a DLT at a high dose/early cycle informs the safety of lower doses or later cycles, while observing safety at a low dose/early cycle informs the safety of higher doses or later cycles.
• Calibration: The design uses effective sample size (ESS) calibration to prevent over-extrapolation, ensuring that pseudo-data propagation does not artificially inflate sample sizes.

C. Two-Stage Structure

1. Stage 1: Accelerated Titration (AT)

   • Goal: Rapidly explore dose levels.
   • Mechanism: All patients start at a prespecified dose. If no DLT occurs, the dose escalates by one level in the next cycle.
   • Transition: The trial moves to Stage 2 upon observing the first DLT or reaching a prespecified maximum initial sample size ($n_{start}$).
   • Data Usage: Even during Stage 1, the modified c-CFBD model updates hyperparameters for all dose-cycle combinations to prepare for Stage 2.

2. Stage 2: Modified c-CFBD

   • Goal: Refine dose assignments and estimate cycle-specific MTDs (MTDC).
   • Mechanism: Uses a One-Step-Look-Ahead (OSLA) utility function to select the optimal dose for the next cycle.
   • Decision Rules:
     • New Patients: Starting dose is selected based on the current posterior distribution for Cycle 1.
     • Ongoing Patients: The next dose is determined by taking the minimum of two recommendations: (1) the dose recommended for the specific patient based on their history, and (2) the lowest dose recommended for the most recent cohort of patients who completed that cycle. This prevents aggressive "dose jumps."
     • DLT Handling: If a patient experiences a DLT, they are de-escalated by one level (or stay at the lowest level).
   • Stopping Rule: The trial stops enrolling new patients if the probability that the next higher dose exceeds the target toxicity rate ($p_T + \delta$) is high.

3. Key Contributions

• Novel Framework: Introduces the first design specifically modeling decreasing toxicity over cycles for intra-patient dose escalation, moving beyond the single-MTD paradigm.
• C Partial Order: Adapts the c-CFBD design by redefining the partial ordering structure to reflect the inverse relationship between cycle number and toxicity.
• Cycle-Specific MTDs: Instead of a single MTD, the design outputs a sequence of MTDCs (Maximum Tolerated Doses per Cycle), providing a more granular and clinically relevant dosing schedule.
• Hybrid Approach: Combines the speed of Accelerated Titration (Stage 1) with the statistical rigor of Bayesian decision theory (Stage 2).

4. Results (Simulation Studies)

The authors evaluated TWICEBEE against three competitors: DIETE, IP-CRM, and a variant called 2S-i3+3 (TWICEBEE with i3+3 in Stage 2). Simulations were run across 10 scenarios with varying toxicity profiles (independent and dependent cycles).

• Accuracy: TWICEBEE accurately identified the true MTDC trajectory in most scenarios, closely matching the true MTD/MAD for each cycle.
• Patient Allocation: It allocated a higher proportion of patients to the correct (optimal) dose levels compared to the 2S-i3+3 variant, which tended to be overly conservative (subtherapeutic).
• Comparison to Competitors:
  • vs. DIETE/IP-CRM: Unlike DIETE (which finds two MTDs: pre- and post-adaptation) or IP-CRM (which finds one MTD for all cycles), TWICEBEE successfully identified a unique MTD for every cycle, reflecting the dynamic nature of the therapy.
  • vs. 2S-i3+3: TWICEBEE was more aggressive in finding higher doses when safe, whereas the i3+3 variant often stuck to lower, safer doses.
• Efficiency: TWICEBEE required the smallest expected sample size among all compared designs, inheriting this efficiency from the c-CFBD foundation.
• Robustness: The design maintained favorable operating characteristics even under scenarios with intra-patient dependence (where a DLT in one cycle increases the risk in the next).

5. Significance and Implications

• Clinical Relevance: The design addresses a critical gap in CAR T-cell and other immunotherapy trials where patients can tolerate higher doses in later cycles. It provides a statistically rigorous method to implement intra-patient dose escalation, potentially improving efficacy without compromising safety.
• Regulatory Alignment: The approach aligns with recent FDA guidance encouraging intra-patient dose optimization and model-informed drug development.
• Broader Applicability: While motivated by intracranial CAR T-cell therapy for brain tumors, the framework is applicable to other multi-cycle regimens (e.g., bispecific T-cell engagers) where immune-mediated toxicity attenuates over time.
• Future Directions: The authors note that the current design relies solely on toxicity. Future work aims to incorporate efficacy outcomes and handle toxicity patterns that may accumulate rather than decrease.

In summary, TWICEBEE represents a significant methodological advancement in Phase I trial design, offering a tailored solution for the complex, dynamic toxicity profiles inherent in modern cellular immunotherapies.