Model-free Approach to Evaluate a Censored Intermediate Outcome as a Surrogate for Overall Survival

TL;DR

This paper introduces a non-parametric, model-free method to evaluate censored surrogate outcomes for overall survival in clinical trials, enabling more flexible and assumption-light analysis of time-to-event data.

Contribution

It proposes a novel approach to estimate the proportion of treatment effect explained by a censored surrogate outcome, relaxing parametric assumptions and applicable to time-to-event data.

Findings

Method performs well in simulations

Application to colorectal cancer data demonstrates utility

Provides a flexible alternative to existing methods

Abstract

Clinical trials or studies oftentimes require long-term and/or costly follow-up of participants to evaluate a novel treatment/drug/vaccine. There has been increasing interest in the past few decades in using short-term surrogate outcomes as a replacement of the primary outcome i.e., in using the surrogate outcome, which can potentially be observed sooner, to make inference about the treatment effect on the long-term primary outcome. Very few of the available statistical methods to evaluate a surrogate are applicable to settings where both the surrogate and the primary outcome are time-to-event outcomes subject to censoring. Methods that can handle this setting tend to require parametric assumptions or be limited to assessing only the restricted mean survival time. In this paper, we propose a non-parametric approach to evaluate a censored surrogate outcome, such as time to progression, when the primary outcome is also a censored time-to-event outcome, such as time to death, and the treatment effect of interest is the difference in overall survival. Specifically, we define the proportion of the treatment effect on the primary outcome that is explained (PTE) by the censored surrogate outcome in this context, and estimate this proportion by defining and deriving an optimal transformation of the surrogate information. Our approach provides the added advantage of relaxed assumptions to guarantee that the true PTE is within (0,1), along with being model-free. Finite sample performance of our estimators are illustrated via extensive simulation studies and a real data application examining progression-free survival as a surrogate for overall survival for patients with metastatic colorectal cancer.