Hybrid Non-informative and Informative Prior Model-assisted Designs for Mid-trial Dose Insertion

1. Problem Statement

In oncology Phase I clinical trials, model-assisted designs (e.g., Bayesian Optimal Interval [BOIN]) are widely used for dose escalation due to their operational simplicity and ability to accurately select the Maximum Tolerated Dose (MTD). However, a common practical challenge arises when initial dose levels, selected based on nonclinical data, prove inadequate. Specifically, if a lower dose shows no efficacy and a higher dose shows excessive toxicity, there is a clinical need to insert an intermediate dose level mid-trial.

Existing methods for dose insertion (e.g., TEAMS, general frameworks for combination trials) often lack a principled approach to constructing prior information for the newly inserted dose. They fail to effectively leverage the substantial safety and efficacy data already accumulated at adjacent dose levels. The core problem addressed is how to improve dose assignment and MTD/OBD (Optimal Biological Dose) selection when a new dose is added, by intelligently borrowing information from neighboring doses without compromising the robustness of non-informative designs.

2. Methodology

The authors propose a Hybrid Design framework that integrates non-informative model-assisted designs (BOIN/BOIN-ET) with informative extensions (iBOIN/iBOIN-ET) specifically for the newly inserted dose.

A. Core Hybrid Strategy

• Non-informative for Existing Doses: The original dose levels continue to be governed by standard non-informative designs (BOIN or BOIN-ET), preserving their simplicity and transparency.
• Informative for Inserted Dose: The newly added dose ($d^*$) utilizes an informative prior constructed from data accumulated at adjacent doses ($d_{j-1}, d_{j+1}$).

B. Construction of Informative Priors

To apply the informative extension, the authors define two key components for the inserted dose: the Skeleton (prior distribution of toxicity/efficacy probabilities) and the Effective Sample Size (ESS).

1. Skeleton Estimation:
   • Toxicity: A Bayesian Logistic Regression Model (BLRM) is fitted to the toxicity data of existing doses to estimate the toxicity probability at $d^*$.
   • Efficacy: A second-degree fractional polynomial logistic regression model is used to capture potential non-monotonic efficacy curves. Optimal power parameters are selected using binomial deviance.
2. ESS Calculation:
   • Instead of a fixed Prior Effective Sample Size (PESS), the authors propose a data-dependent ESS.
   • The posterior distribution of the toxicity/efficacy probability at $d^*$ (derived from the BLRM/fractional polynomial) is approximated by a Beta distribution.
   • The ESS is calculated as $n^* = \frac{\mu(1-\mu)}{v} - 1$, where $\mu$ and $v$ are the posterior mean and variance.
   • A scaling factor $\gamma \in (0, 1]$ is applied to prevent excessive borrowing, and the ESS is truncated to ensure it does not exceed the maximum sample size of the adjacent doses.

C. Adaptive Extensions for Skeleton Misspecification

To address the risk that the initial skeleton (based on pre-insertion data) may not align with the true toxicity profile of the new dose, two adaptive approaches are proposed:

1. Online-Weighting Approach (Hedge Algorithm):
   • Treats skeleton selection as an online learning problem.
   • Compares the initially specified skeleton ($r_0$) with an updated skeleton ($r_1$) derived from data collected after the dose insertion.
   • Uses exponentially weighted averaging (Hedge algorithm) to assign weights to the two candidates based on logarithmic loss, creating a convex combination for the next decision.
2. Bayesian-Mixture Approach:
   • Combines three candidate skeletons: (1) The BLRM-based estimate, (2) The toxicity probability of the dose immediately above, and (3) The toxicity probability of the dose immediately below.
   • Uses a Dirichlet prior on mixing weights and updates them based on the predictive likelihood of observed data at the new dose.

D. Safety Control Mechanism

A threshold $c$ is introduced to prevent inappropriate borrowing. If the observed toxicity probability at the new dose ($\hat{p}_T$) exceeds the skeleton-based estimate ($\hat{p}_{T, borrowing}$) by more than $c$ (i.e., $\hat{p}_T - \hat{p}_{T, borrowing} > c$), the informative prior is discarded, and the design reverts to non-informative rules for that dose.

3. Key Contributions

1. First Hybrid Framework: This is the first study to propose a hybrid strategy that seamlessly integrates non-informative and informative model-assisted designs specifically for mid-trial dose insertion in Phase I oncology.
2. Data-Driven ESS: Moves beyond fixed PESS recommendations by deriving a dynamic, data-dependent ESS that reflects the actual information available from adjacent doses.
3. Robustness Mechanisms: Introduces online learning and Bayesian mixture approaches to mitigate the risks of skeleton misspecification, a critical issue when sample sizes at new doses are small.
4. Extension to Efficacy: Generalizes the approach to BOIN-ET, addressing the modern shift toward selecting Optimal Biological Doses (OBD) based on both toxicity and efficacy.

4. Simulation Results

The methods were evaluated via simulation studies under Fixed Scenarios (intuitive, specific toxicity/efficacy profiles) and Random Scenarios (stochastically generated profiles).

• Fixed Scenarios (BOIN):
  • When the inserted dose was safe or moderately toxic (at or below Target Toxicity Level, TTL), the hybrid methods significantly outperformed standard BOIN in correct MTD selection rates.
  • When the inserted dose was highly toxic, setting the threshold $c=0$ allowed the hybrid method to perform comparably to standard BOIN, effectively avoiding the selection of overly toxic doses.
  • The Bayesian-mixture approach demonstrated superior robustness, improving MTD selection while controlling excessive toxicity across various settings.
• Fixed Scenarios (BOIN-ET):
  • Similar trends were observed for OBD selection. The hybrid designs generally outperformed standard BOIN-ET, particularly when the inserted dose offered a better balance of efficacy and safety.
  • The online-weighting approach showed some instability in efficacy updating, whereas the mixture approach remained stable.
• Random Scenarios:
  • The proposed methods did not perform worse than the original designs. While the improvement in correct selection rates was not always substantial, the methods maintained safety profiles comparable to or better than the benchmarks.
  • Under unimodal efficacy curves, the hybrid approach showed good performance.

5. Significance

This paper addresses a critical gap in the operationalization of Phase I trials where dose insertion is necessary but statistically challenging. By proposing a hybrid design, the authors provide a solution that:

• Enhances Efficiency: Leverages existing data to make better decisions for the new dose, potentially accelerating the identification of the MTD/OBD.
• Maintains Safety: The adaptive mechanisms (thresholds, mixture models) ensure that if the new dose behaves unexpectedly (e.g., is more toxic than predicted), the design reverts to safe, non-informative rules.
• Preserves Simplicity: Unlike fully model-based designs that require complex real-time model fitting for all doses, this approach only applies complex modeling to the single inserted dose, keeping the overall trial operationally simple and transparent.
• Aligns with Modern Standards: The extension to BOIN-ET supports the "Project Optimus" initiative, facilitating the selection of doses that optimize the benefit-risk ratio rather than just maximizing dose intensity.

In conclusion, the proposed hybrid design offers a principled, robust, and flexible framework for handling mid-trial dose insertions, balancing the benefits of information borrowing with the safety requirements of early-phase oncology trials.