Predicting Overall Survival (OS) from Time to Recurrence (TTR) Using a Copula-Based Patient-Level Surrogacy Model with Parametric Marginal Survival Distributions: Application to Adjuvant Treatment of Patients with Colon Cancer
Author(s)
Andrea Berardi, MSc1, Dylan Maciel, MSc2, Liza Mastikhina, MSc2, Shannon Cope, MSc2;
1Precision AQ, London, United Kingdom, 2Precision AQ, Vancouver, BC, Canada
1Precision AQ, London, United Kingdom, 2Precision AQ, Vancouver, BC, Canada
OBJECTIVES: Cost-effectiveness analyses for health technology assessment require OS predictions over a lifetime horizon. When OS data are unavailable and trial-level surrogate relationships cannot be established, individual-level surrogacy relationships can be used. The study objective is to evaluate an individual-level surrogacy model versus a single hazard ratio (HR) approach to predict OS based on TTR in patients with colon cancer in the adjuvant setting.
METHODS: We used individual patient data from a three-arm randomized controlled trial investigating levamisole (L), L+fluoroacil (F) and observation (OBS) for stage III colon cancer (929 patients; median follow-up, 6.5 years). OS was assumed known for OBS, and unknown for L and L+F. Patient-level TTR-OS surrogacy was evaluated using the joint frailty-copula model following Wu-2020; baseline hazard functions were estimated using sex- and age-adjusted Weibull distributions. Patient-specific OS was simulated using the covariate-adjusted failure function, conditional on recurrence status, described by Berardi-2024. Individuals were censored when <5% of sample was at risk of events, reducing reliance on event-free tails. Simulations were performed assuming pre-recurrence death events were either known or unknown. The HR approach predicted L/L+F OS based on TTR and the TTR-OS HR estimated in the OBS arm. Performance was compared using area between simulated and observed OS (Δ OS).
RESULTS: TTR was associated with OS (Kendall’s tau: 0.67; 95%CI: 0.58-0.74). OS was predicted best by the surrogacy model with known pre-recurrence deaths (ΔOS-OBS: 1.42%, ΔOS-L: 2.61%, ΔOS-L+F: 2.69%) and unknown ones (ΔOS-OBS: 3.77%, ΔOS-L: 3.48%, ΔOS-L+F: 6.37%). The HR approach resulted in substantially greater differences (ΔOS-OBS: 9.25%, ΔOS-L: 8.09%, ΔOS-L+F: 7.08%). The individual-level surrogacy approach was able to capture the non-proportionality in hazards between OS and TTR, whereas the HR method could not.
CONCLUSIONS: In the adjuvant setting, where non-proportional hazards between time-to-event outcomes are likely, the predictive individual-level surrogacy may offer a credible methodology to predict OS.
METHODS: We used individual patient data from a three-arm randomized controlled trial investigating levamisole (L), L+fluoroacil (F) and observation (OBS) for stage III colon cancer (929 patients; median follow-up, 6.5 years). OS was assumed known for OBS, and unknown for L and L+F. Patient-level TTR-OS surrogacy was evaluated using the joint frailty-copula model following Wu-2020; baseline hazard functions were estimated using sex- and age-adjusted Weibull distributions. Patient-specific OS was simulated using the covariate-adjusted failure function, conditional on recurrence status, described by Berardi-2024. Individuals were censored when <5% of sample was at risk of events, reducing reliance on event-free tails. Simulations were performed assuming pre-recurrence death events were either known or unknown. The HR approach predicted L/L+F OS based on TTR and the TTR-OS HR estimated in the OBS arm. Performance was compared using area between simulated and observed OS (Δ OS).
RESULTS: TTR was associated with OS (Kendall’s tau: 0.67; 95%CI: 0.58-0.74). OS was predicted best by the surrogacy model with known pre-recurrence deaths (ΔOS-OBS: 1.42%, ΔOS-L: 2.61%, ΔOS-L+F: 2.69%) and unknown ones (ΔOS-OBS: 3.77%, ΔOS-L: 3.48%, ΔOS-L+F: 6.37%). The HR approach resulted in substantially greater differences (ΔOS-OBS: 9.25%, ΔOS-L: 8.09%, ΔOS-L+F: 7.08%). The individual-level surrogacy approach was able to capture the non-proportionality in hazards between OS and TTR, whereas the HR method could not.
CONCLUSIONS: In the adjuvant setting, where non-proportional hazards between time-to-event outcomes are likely, the predictive individual-level surrogacy may offer a credible methodology to predict OS.
Conference/Value in Health Info
2025-05, ISPOR 2025, Montréal, Quebec, CA
Value in Health, Volume 28, Issue S1
Code
P44
Topic
Methodological & Statistical Research
Topic Subcategory
Missing Data
Disease
SDC: Oncology