Contents
The hazard function describes the ‘intensity of death’ at the time tgiven that the individual has already survived past time t. There is another quantity that is also common in survival analysis, the cumulative hazard function.
How to write the hazard function H ( T )?
A quantity that is often used along with the survival function is the hazard function. The hazard function is h(t) = lim t!0 P(t t) t = p(t) S(t); where p(t) = d dt F(t) is the PDF of random variable T 1. Note that you can also write the hazard function as h(t) = @logS(t) @t: How can we interpret the hazard function?
Why is the hazard ratio a function of time?
Since the hazard is a function of time, the hazard ratio, say, for exposed versus unexposed, is also a function of time; it may be different at different times of follow up. For example, if the exposure is some surgery (vs.
How can we interpret the cumulative hazard function?
How can we interpret the hazard function? The hazard function describes the `intensity of death’ at thetimetgiven that the individual has already survived past timet. There is another quantity that is also common in survival analysis, the cumulative hazard function.
The hazard function, then, describes the relative likelihood of the event occurring at time t ( f ( t) ), conditional on the subject’s survival up to that time t ( S ( t) ). The hazard rate thus describes the instantaneous rate of failure at time t and ignores the accumulation of hazard up to time t (unlike F ( t) and S ( t) ).
Is the hazard ratio an alternative to restricted mean survival time?
Restricted mean survival time may provide a practical way forward and deserves greater attention. We conclude that the hazard ratio cannot be recommended as a general measure of the treatment effect in a randomized controlled trial, nor is it always appropriate when designing a trial.