  Time to event outcomes are often evaluated on the hazard scale, but
interpreting hazards may be difficult. Recently, there has been concern in the
causal inference literature that hazards actually have a built in
selection-effect that prevents simple causal interpretations. This is even a
problem in randomized controlled trials, where hazard ratios have become a
standard measure of treatment effects. Modeling on the hazard scale is
nevertheless convenient, e.g. to adjust for covariates. Using hazards for
intermediate calculations may therefore be desirable. Here, we provide a
generic method for transforming hazard estimates consistently to other scales
at which these built in selection effects are avoided. The method is based on
differential equations, and generalize a well known relation between the
Nelson-Aalen and Kaplan-Meier estimators. Using the martingale central limit
theorem we also find that covariances can be estimated consistently for a large
class of estimators, thus allowing for rapid calculations of confidence
intervals. Hence, given cumulative hazard estimates based on e.g. Aalen's
additive hazard model, we can obtain many other parameters without much more
effort. We present several examples and associated estimators. Coverage and
convergence speed is explored using simulations, suggesting that reliable
estimates can be obtained in real-life scenarios.
