Nonparametric Analysis of Delayed Treatment Effects using Single-Crossing Constraints

TL;DR

This paper introduces a flexible nonparametric method for analyzing survival data with crossing treatment effects, especially useful in immuno-oncology trials where delayed effects violate proportional hazards assumptions.

Contribution

It proposes a novel approach that constrains survival curves to cross at most once, providing estimates of crossing time and interpretable treatment benefit measures without strong parametric assumptions.

Findings

Method accurately estimates crossing time in simulations

Effectively analyzes real immuno-oncology trial data

Provides interpretable measures of treatment benefit

Abstract

Clinical trials involving novel immuno-oncology (IO) therapies frequently exhibit survival profiles which violate the proportional hazards assumption due to a delay in treatment effect, and in such settings, the survival curves in the two treatment arms may have a crossing before the two curves eventually separate. To flexibly model such scenarios, we describe a nonparametric approach for estimating the treatment arm-specific survival functions which constrains these two survival functions to cross at most once without making any additional assumptions about how the survival curves are related. A main advantage of our approach is that it provides an estimate of a crossing time if such a crossing exists, and moreover, our method generates interpretable measures of treatment benefit including crossing-conditional survival probabilities and crossing-conditional estimates of restricted residual mean life. We demonstrate the use and effectiveness of our approach with a large simulation study and an analysis of reconstructed outcomes from a recent combination-therapy trial.