  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.
