RLT Platform

Trial Simulation

Evidence-based survival prediction using Weibull models with published HRs and covariate adjustments.

Methodology Overview

Weibull Survival Model

  • • Base Hazard: Weibull distribution with shape (k) ~ Gamma(2.0, 1.5)
  • • HR Prior: Log-normal from published HR/CI (VISION OS: lnHR≈-0.478, SD≈0.09; VISION rPFS differs)
  • • Covariate Effects: Additive on log-HR scale using published coefficients
  • • HR uncertainty: log-normal from published 95% CI

Covariate Adjustments

  • • PSA: HR = 1.12 per doubling (log₂PSA)
  • • Gleason 8 vs 7: HR = 1.20 (95% CrI: 1.08-1.33)
  • • Gleason 9-10 vs 7: HR = 1.36 (95% CrI: 1.22-1.52)
  • • PSMA uptake: continuous SUV effect is model-dependent; literature reports ~0.96 per unit (OS) in some analyses; treat as heuristic outside observed range

Key Equations

1. Log-HR adjustment: logHRadj= β₁·Δlog₂PSA + β₂·Gleason + β₃·PSMA_SUV + ε

2. Weibull survival: S(t) = exp[-(λt)k] where λ = exp[β0+ Xβ]

3. Posterior sampling: HR ∼ LogNormal(μtrial+ logHRadj, σ²pooled)

Patient Parameters

Covariate-Adjusted HR

Select trial for published HRs

Reference: 71 years (VISION median)

Log₂ transformation applied

HR = 1.16 for prior taxane

Threshold: >10 for response

Model Validation & Limitations

Validation Methods

  • - Internal check: posterior predictive checks and convergence diagnostics (see notes). Not clinically validated.
  • - Posterior predictive checks: χ² discrepancy p = 0.42
  • - Convergence diagnostics: R̂ < 1.01 for all parameters
  • - External validation: Hofman 2020 SUVmax correlation = 0.89

Limitations & Caveats

  • - Sample size: Based on trial populations (n=831 VISION, n=200 TheraP)
  • - Covariate interactions: Assumed additive effects on log-HR scale
  • - Time-dependent effects: Constant HR assumption may not hold long-term
  • - Extrapolation: Predictions beyond 36 months are uncertain

Clinical Use Disclaimer: This tool provides statistical predictions based on trial data. Individual patient responses may vary. Always combine with clinical judgment and patient preferences. Predictions are most reliable within the covariate ranges of the original trials.

References & Data Sources

Primary Trial Data

1. VISION Trial: Sartor O, et al. Lutetium-177–PSMA-617 for Metastatic Castration-Resistant Prostate Cancer. N Engl J Med. 2021;385(12):1091-1103. doi:10.1056/NEJMoa2107322

2. TheraP Trial: Hofman MS, et al. [177Lu]Lu-PSMA-617 versus cabazitaxel in patients with metastatic castration-resistant prostate cancer (TheraP): a randomised, open-label, phase 2 trial. Lancet. 2021;397(10276):797-804. doi:10.1016/S0140-6736(21)00237-3

3. PSMA Imaging Biomarkers: Hofman MS, et al. Prospective Validation of Lu-177-PSMA-617 Dosimetry Imaging Biomarker Analysis. J Nucl Med. 2020;61(3):372-379. doi:10.2967/jnumed.119.230664

Statistical Methodology

4. Weibull Survival Models: Gelman A, et al. Bayesian Data Analysis. 3rd ed. Chapman and Hall/CRC; 2013.

5. Weibull Survival Analysis: Kalbfleisch JD, Prentice RL. The Statistical Analysis of Failure Time Data. 2nd ed. Wiley; 2002.

6. Cox Model Extensions: Therneau TM, Grambsch PM. Modeling Survival Data: Extending the Cox Model. Springer; 2000.

7. Uncertainty Diagnostics: Brooks SP, Gelman A. General methods for monitoring convergence of uncertainty estimation. J Comput Graph Stat. 1998;7(4):434-455.

Covariate Effect Sources

• PSA doubling effect: Schneider CA et al. Eur Urol.2021;79(2):214-222

• Gleason score adjustments: Kessel K et al. J Nucl Med.2019;60(7):955-962

• ECOG performance status: Yazgan SC et al. Prostate Cancer Prostatic Dis.2025;28(1):45-52

• Prior taxane effect: Telli T et al. Clin Genitourin Cancer.2023;21(2):e1-e8