Adaptive Weighting for Time-to-Event Continual Reassessment Method: Improving Safety in Phase I Dose-Finding Through Data-Driven Delay Distribution Estimation

TL;DR

Adaptive weighting offers a practical way to improve Phase I trial safety while preserving MTD selection accuracy, and requires minimal computation and is ready for real-time use.

Abstract

Background: Phase I dose-finding trials increasingly encounter delayed-onset toxicities, especially with immunotherapies and targeted agents. The time-to-event continual reassessment method (TITE-CRM) handles incomplete follow-up using fixed linear weights, but this ad hoc approach doesn't reflect actual delay patterns and may expose patients to excessive risk during dose escalation. Methods: We replace TITE-CRM's fixed weights with adaptive weights, posterior predictive probabilities derived from the evolving toxicity delay distribution. Under a Weibull timing model, we get closed-form weight updates through maximum likelihood estimation, making real-time implementation straightforward. We tested our method (AW-TITE) against TITE-CRM and standard designs (3+3, mTPI, BOIN) across three dose-toxicity scenarios through simulation (N = 30 patients, 2,000 replications). We also examined robustness across varying accrual rates, sample sizes, shape parameters, observation windows, and priors. Results: Our AW-TITE reduced patient overdosing by 40.6% compared to TITE-CRM (mean fraction above MTD: 0.202 vs 0.340; 95% CI: -0.210 to -0.067, p < 0.001) while maintaining comparable MTD selection accuracy (mean difference: +0.023, p = 0.21). Against algorithm-based methods, AW-TITE achieved higher MTD identification: +32.6% vs mTPI, +19.8% vs 3+3, and +5.6% vs BOIN. Performance remained robust across all sensitivity analyses. Conclusions: Adaptive weighting offers a practical way to improve Phase I trial safety while preserving MTD selection accuracy. The method requires minimal computation and is ready for real-time use.

Figures (10)

• Figure 1: Graphical Abstract. Adaptive weighting replaces TITE-CRM's fixed linear weights with data-driven posterior predictive probabilities derived from the evolving toxicity delay distribution. This innovation reduces patient overdosing by 40.6% while maintaining MTD selection accuracy, computational simplicity, and practical implementability.
• Figure 2: Trial flowchart for AW-TITE implementation. At each decision point, patients with incomplete follow-up ($t_i < T_{\max}$) contribute through adaptive weights $w_i$ computed from the current estimate of the toxicity delay distribution. Under a Weibull model with shape $\gamma$, $\Delta_i = T_{\max}^{\gamma} - t_i^{\gamma}$ and $w_i = 1 - \exp\{-\widehat{\lambda}(d_i)\Delta_i\}$. Patients with observed DLTs receive $w_i=1$, and those with complete follow-up and no DLT receive $w_i=0$. The weighted likelihood updates the CRM posterior, which determines the next dose assignment; the process continues until $N$ patients are enrolled.
• Figure 3: Comprehensive comparison for Standard scenario (MTD = d3).Upper left: Safety comparison showing fraction of patients treated above the true MTD (lower is better). TITE-CRM shows excessive overdosing (0.417), while AW-MLE reduces this to 0.279, a 33.1% reduction. Upper right: MTD selection accuracy showing probability of correctly identifying dose 3 as the MTD (higher is better). AW-MLE (0.538) achieves comparable accuracy to TITE-CRM (0.552) while substantially improving safety. Lower left: DLT burden showing mean number of observed DLTs per trial (lower is better). AW-MLE reduces DLT burden from 7.74 (TITE) to 6.77. Lower right: Dose selection proportions showing the distribution of final dose recommendations across 2,000 simulated trials. The true MTD is d3 (toxicity probability 0.20, closest to target 0.25). Model-based methods (AW-MLE, AW-BAYES, TITE, BOIN) show concentrated selection at or near the MTD, while algorithm-based methods (mTPI, 3+3) show broader, less accurate distributions.
• Figure 4: Comprehensive comparison for Steep Curve scenario (MTD = d4).Upper left: Safety comparison. In this scenario with rapidly increasing toxicity, AW-MLE achieves the lowest overdosing rate among model-based methods (0.112), representing a 37.4% reduction compared to TITE-CRM (0.179). BOIN shows the best safety (0.097) due to its conservative design. Upper right: MTD selection accuracy. AW-MLE achieves the highest accuracy (0.741), outperforming TITE-CRM (0.696), BOIN (0.730), and substantially outperforming algorithm-based methods (mTPI: 0.296, 3+3: 0.498). Lower left: DLT burden. AW-MLE shows moderate DLT burden (7.27) between conservative methods (3+3: 2.85) and TITE-CRM (7.87). Lower right: Dose selection proportions. The true MTD is d4 (toxicity probability 0.25, exact target). The steep dose-toxicity relationship (0.02, 0.05, 0.10, 0.25, 0.50) creates clear differentiation between doses. AW-MLE and BOIN show highly concentrated selection at the correct dose, while mTPI struggles with this scenario, frequently under-escalating to lower doses.
• Figure 5: Comprehensive comparison for Flat Curve scenario (MTD = d4).Upper left: Safety comparison. This challenging scenario with minimal dose separation shows the largest safety advantage for AW-MLE. TITE-CRM overdoses 42.3% of patients, while AW-MLE reduces this to 21.3%, a 49.6% reduction the largest improvement across all scenarios. Upper right: MTD selection accuracy. Despite the difficulty of discriminating between similarly toxic doses (0.10, 0.15, 0.20, 0.25, 0.30), AW-MLE achieves the highest accuracy (0.378), outperforming TITE-CRM (0.341), BOIN (0.255), and particularly mTPI (0.104) which struggles severely in this scenario. Lower left: DLT burden remains moderate for AW-MLE (7.07) compared to TITE-CRM (7.90). Lower right: Dose selection proportions show the challenge of this scenario. The true MTD is d4. No method achieves highly concentrated selection due to the minimal differences between doses. Algorithm-based methods show particularly poor discrimination, with mTPI heavily over-selecting the lowest dose (d1) in 60% of trials. AW-MLE shows the most appropriate balance, with primary selections at d3 and d4.