In Survival Analysis, is there some "method" (e.g. an estimator) which can be used to "jointly interpret" (i.e. weighted average, aggregate) the information from the survival curves and the hazard curves?
For example, the Survival Function is used to estimate the probability of an individual (usually at the cohort level) surviving past a certain time. The Survival Function is strictly decreasing:
On the other hand, the Hazard Function (also called "failure" or "mortality") is used to estimate the instantaneous rate of surviving at any given time. Unlike the Survival Function, the Hazard Function is not strictly decreasing - it can increase and decrease throughout time, and is useful for modelling phenomena such as human mortality (e.g. humans have a relatively higher mortality rate when they are infants, this mortality rate steadily decreases and then increases in old age):
The Survival Function and the Hazard Function both describe different aspects within the data. For instance, in the following paper (see references) the authors used both the Survival Function (Right) and the Hazard Function (Left) to study the efficacy of malaria treatments in clinical trials:
My Question: In Survival Analysis, are there any methods or estimators that combine information from both the survival estimates and the hazard estimates - which in turn can help analysts make decisions using both estimates at the same time, instead of individually using these estimates?