When dealing with Survival Analysis, we create models that estimate two properties:
Survival: Survival Probabilities tend to be more straightforward to understand. Survival Probabilities estimate the probability of surviving some "event" past a certain time, given that you have survived up until that time.
Hazard: On the other hand, Hazard Rate is said to represent the "instantaneous rate of experiencing the event" at any given time.
I have the following question: When we work with on Survival Analysis data, what kinds of problems are better answered using "Survival Probabilities" and what kinds of problems are better answered using "Hazard Rates"?
For instance, I could use Survival Probabilities to estimate out which cohorts of patients are more likely to survive a certain "event" (e.g. some disease) - and I could then use Hazard Rates to estimate which of these same cohorts are more likely to experience this "event" at different times. I am not a biomedical researcher by background, but both of these quantities seem equally important to me. But I was hoping someone could help me better understand this question.
Usually in biomedical studies, which of these two quantities tends to be "more important" - are we ever able to interpret both of these quantities simultaneously? In short, which kinds of problems are better answered using "Survival Probabilities" and what kinds of problems are better answered using "Hazard Rates"?