Relative survival analysis deals with a competing risks survival model where the cause of death is unknown. This lack of information occurs regularly in population-based cancer studies. Non-parametric estimation of the net survival is possible through the Pohar Perme estimator, taking other causes of mortality into account. Derived similarly to Kaplan-Meier, it nevertheless relies on untestable independence assumptions. We propose here to relax these assumptions and provide a generalized estimator that works for other dependence structures, by leveraging the underlying counting process and martingales. Our approach provides a new perspective on the Pohar Perme estimator and the acceptability of this assumption. We showcase the difference between the two estimators on population-based colorectal cancer registry, and discuss potential extensions of the methodology.