Adaptive clinical trial design with delayed treatment effects using elicited prior distributions

Technical Summary: Adaptive Clinical Trial Design with Delayed Treatment Effects Using Elicited Prior Distributions

Problem Statement
Clinical trials utilizing time-to-event endpoints, such as overall survival (OS) or progression-free survival (PFS), are critical for evaluating new therapies, particularly in immuno-oncology. However, modern treatments like immunotherapies often exhibit delayed treatment effects (DTEs), where therapeutic benefits emerge only after a specific period. This phenomenon violates the proportional hazards (PH) assumption, which underpins standard statistical methods like the Cox model and the log-rank test. Consequently, traditional trial designs face significant risks:

1. Suboptimal Power: Standard methods may be inappropriate or suboptimal when PH is violated.
2. Premature Termination: Interim analyses conducted before the delay period has passed may underestimate the eventual treatment benefit, leading to incorrect futility decisions and the premature termination of potentially effective trials.
3. Uncertainty: Key parameters governing the delay (the onset time $T$ and the post-delay hazard ratio $HR^*$) are inherently uncertain at the design stage, making it difficult to design trials that are both adequately powered and robust.

Methodology
The authors propose a hybrid Bayesian-frequentist adaptive trial design framework that integrates elicited prior distributions from experts to address DTEs. The methodology consists of three main components:

1. Model Parameterisation and Priors:

   • The trial assumes a piecewise hazard model where the experimental group hazard matches the control group until a delay time $T$, after which a constant hazard ratio $HR^*$ applies.
   • Control group parameters ($\lambda_c, \gamma_c$) are derived from historical data.
   • Expert elicitation is used to define priors for:
     • $P_S$: The probability that survival curves separate (treatment effect exists).
     • $P_{DTE}$: The probability of a delay, conditional on an effect existing.
     • $D_{HR^*}$: The distribution of the post-delay hazard ratio.
     • $D_T$: The distribution of the delay duration.
   • This structure creates three clinically meaningful scenarios: no effect, immediate effect, and delayed effect.

2. Assurance with Interim Analyses:

   • The framework extends the concept of assurance (the prior-weighted probability of trial success) to adaptive designs.
   • Unlike traditional power calculated at a fixed alternative, assurance averages the probability of success over the joint prior distribution of parameters, accounting for uncertainty in $T$ and $HR^*$.
   • This is estimated via simulation, where trials are simulated under drawn parameter vectors, and stopping rules are applied at interim looks.

3. Predictive Probability (PP) for Futility Stopping:

   • A novel Predictive Probability (PP) framework is developed for interim futility decisions.
   • At an interim analysis, the elicited priors are updated with observed data using MCMC to obtain posterior distributions.
   • These posteriors are propagated forward to simulate unobserved future outcomes, reconstructing the final analysis to estimate the probability of ultimately rejecting the null hypothesis ($H_0$).
   • Key Innovation: The delay time $T$ is treated as a free parameter updated with data, rather than a fixed value, allowing the PP to account for uncertainty in the timing of the effect.
   • Stopping Rule: The trial stops for futility if the estimated PP falls below a pre-specified threshold $\lambda$. Efficacy stopping remains governed by standard group sequential boundaries (alpha-spending) to maintain Type I error control.

4. Calibration Procedure:

   • Timing Selection: The interim timing is chosen by simulating the distribution of PP values under the prior predictive distribution. The optimal time is selected when the PP distribution becomes sufficiently polarized (concentrated near 0 and 1) to distinguish promising from unpromising trials, ensuring the look is informative.
   • Threshold Selection: The futility threshold $\lambda$ is calibrated to balance Type I error control, power under alternative scenarios (including delayed effects), and the minimization of expected sample size under the null.

Key Contributions
The paper makes four specific contributions:

1. Extension of Assurance: It extends the assurance framework to adaptive designs with interim analyses, allowing trialists to evaluate how interim looks impact the overall probability of success under parameter uncertainty.
2. PP Framework for DTEs: It develops a Predictive Probability framework specifically for futility decision-making in the presence of delayed effects, utilizing elicited priors that are sequentially updated with trial data.
3. Calibration Methodology: It provides a practical, two-step calibration procedure for selecting the interim timing and the PP futility threshold, optimizing for operating characteristics such as expected sample size under the null while maintaining power.
4. Software Implementation: The authors developed a free, open-source R package (DTEAssurance) and a Shiny application to facilitate the implementation of this framework, enabling researchers to simulate, compare, and visualize adaptive trial designs.

Results
The framework was evaluated using a hypothetical Phase III trial in non-small-cell lung cancer (NSCLC) comparing an immunotherapy to docetaxel. The study compared four designs:

• D1: Fixed design (no interim).
• D2: Group Sequential Design (GSD) with efficacy-only looks.
• D3: Hybrid GSD with PP-based futility (the proposed method).
• D4: GSD with standard beta-spending futility boundaries.

Key Findings:

• Under the Null (No Effect): Both adaptive designs (D3 and D4) significantly reduced the expected sample size (from 1,200 to ~1,022) and trial duration by stopping ~69% of futile trials early, while maintaining Type I error at the nominal 2.5% level.
• Under Delayed Effect (Primary Scenario): The proposed PP design (D3) demonstrated superior performance compared to the standard beta-spending approach (D4). D3 stopped only 5.5% of delayed-effect trials for futility (power loss of 0.7% relative to D2), whereas D4 stopped 15.3% (power loss of 3.3%). This is because the standard log-rank statistic (used in D4) is attenuated by the delay, leading to premature futility, while the PP approach (D3) incorporates prior knowledge about the delay, remaining robust.
• Under Immediate Effect: Both adaptive designs performed similarly, with minimal power loss compared to fixed designs.
• Sensitivity: The results were robust to variations in the elicited prior probabilities ($P_S$ and $P_{DTE}$).

Significance and Claims
The paper claims that this framework provides a principled and practical approach to designing adaptive trials for therapies with delayed effects. By integrating elicited expert knowledge directly into the planning and decision-making process, the method:

• Enhances Robustness: It minimizes the risk of prematurely terminating trials with genuine but delayed benefits, a critical issue in immuno-oncology.
• Improves Efficiency: It reduces expected sample sizes and trial durations under the null hypothesis without sacrificing power under plausible alternative scenarios.
• Maintains Rigor: It preserves strict frequentist Type I error control for efficacy while using Bayesian methods for futility decisions.
• Facilitates Implementation: The accompanying software lowers the barrier to adoption, allowing trialists to visualize delay structures and communicate design choices effectively.

The authors position this work as a direct extension of their previous elicitation methodology, offering a coherent solution to the inferential and operational challenges posed by non-proportional hazards in modern clinical trials.