Identifying candidate secondary endpoints in semi-competing risk time-to-event data using an integrated analytical framework

TY - JOUR

T1 - Identifying candidate secondary endpoints in semi-competing risk time-to-event data using an integrated analytical framework

AU - Tripathy, Abhipsa

AU - Vishwakarma, Gajendra K.

AU - Bhattacharjee, Atanu

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2026.

PY - 2026/4

Y1 - 2026/4

N2 - Secondary or intermediate time-to-event endpoints are often used to supplement overall survival, yet their statistical validation remains limited in single-trial settings. Most surrogate endpoint methodologies were developed for multi-trial analyses, while existing single-trial approaches from earlier literature do not adequately accommodate covariate-dependent dependence structures in modern survival data. We address this gap by proposing a unified framework for surrogate evaluation under a semi-competing risks structure, with explicit attention to identifiability and inference in a single trial. Dependence between intermediate and terminal events is modelled using a joint frailty copula approach, allowing estimation of association while accounting for unobserved heterogeneity. Because surrogate assessment in a single trial is inherently non-identifiable without additional structure, we integrate time-dependent mediation analysis with the proportion of treatment effect explained to formalise indirect effects through the intermediate endpoint. Simulation studies demonstrate reliable estimation of both marginal and mediated treatment effects under realistic semi-competing risks scenarios, supporting the robustness and practical applicability of the proposed framework.

AB - Secondary or intermediate time-to-event endpoints are often used to supplement overall survival, yet their statistical validation remains limited in single-trial settings. Most surrogate endpoint methodologies were developed for multi-trial analyses, while existing single-trial approaches from earlier literature do not adequately accommodate covariate-dependent dependence structures in modern survival data. We address this gap by proposing a unified framework for surrogate evaluation under a semi-competing risks structure, with explicit attention to identifiability and inference in a single trial. Dependence between intermediate and terminal events is modelled using a joint frailty copula approach, allowing estimation of association while accounting for unobserved heterogeneity. Because surrogate assessment in a single trial is inherently non-identifiable without additional structure, we integrate time-dependent mediation analysis with the proportion of treatment effect explained to formalise indirect effects through the intermediate endpoint. Simulation studies demonstrate reliable estimation of both marginal and mediated treatment effects under realistic semi-competing risks scenarios, supporting the robustness and practical applicability of the proposed framework.

KW - Joint frailty copula model

KW - Proportion treatment effect

KW - Secondary endpoint

KW - Semi-competing risk model

KW - Time-dependent mediation

UR - https://www.scopus.com/pages/publications/105030443979

U2 - 10.1007/s00362-026-01816-z

DO - 10.1007/s00362-026-01816-z

M3 - Article

AN - SCOPUS:105030443979

SN - 0932-5026

VL - 67

JO - Statistical Papers

JF - Statistical Papers

IS - 2

M1 - 32

ER -