  The conventional nonparametric tests in survival analysis, such as the
log-rank test, assess the null hypothesis that the hazards are equal at all
times. However, hazards are hard to interpret causally, and other null
hypotheses are more relevant in many scenarios with survival outcomes. To allow
for a wider range of null hypotheses, we present a generic approach to define
test statistics. This approach utilizes the fact that a wide range of common
parameters in survival analysis can be expressed as solutions of differential
equations. Thereby we can test hypotheses based on survival parameters that
solve differential equations driven by cumulative hazards, and it is easy to
implement the tests on a computer. We present simulations, suggesting that our
tests perform well for several hypotheses in a range of scenarios. Finally, we
use our tests to evaluate the effect of adjuvant chemotherapies in patients
with colon cancer, using data from a randomised controlled trial.
