A non-parametric proportional risk model to assess a treatment effect in time-to-event data

TL;DR

This paper introduces a non-parametric model for time-to-event data that estimates treatment effects without relying on proportional hazards assumptions, focusing on relative risk and number needed to treat for clearer interpretation.

Contribution

It proposes a novel non-parametric approach assuming proportional risks, offering direct estimation of relative risk and number needed to treat in survival analysis.

Findings

Model validated through simulation studies.

Applied to clinical trial data on dapagliflozin.

Provides an alternative to Cox's model under non-proportional hazards.

Abstract

Time-to-event analysis often relies on prior parametric assumptions, or, if a non-parametric approach is chosen, Cox's model. This is inherently tied to the assumption of proportional hazards, with the analysis potentially invalidated if this assumption is not fulfilled. In addition, most interpretations focus on the hazard ratio, that is often misinterpreted as the relative risk. In this paper, we introduce an alternative to current methodology for assessing a treatment effect in a two-group situation, not relying on the proportional hazards assumption but assuming proportional risks. Precisely, we propose a new non-parametric model to directly estimate the relative risk of two groups to experience an event under the assumption that the risk ratio is constant over time. In addition to this relative measure, our model allows for calculating the number needed to treat as an absolute measure, providing the possibility of an easy and holistic interpretation of the data. We demonstrate the validity of the approach by means of a simulation study and present an application to data from a large randomized controlled trial investigating the effect of dapagliflozin on the risk of first hospitalization for heart failure.