Finding Hazard Function from Survival Function

[izzah]

Anyone know how to find the hazard function when given the survival function. I am able to calculate the cumulative hazard function, but cannot find a formula for just the hazard function. survival function is:
S(t)=e^(-at-bt2)

 

[NateTG]

http://mathworld.wolfram.com/HazardFunction.html

Seems to indicate you need a probability function as well.

 

[PerennialII]

Or if you don't have them available for, say, a specific distribution, go with numerical approximations.

 

[artbio]

The hazard function is:

$$h(t)=- \frac{d Ln[S(t)]}{dt}$$

The cumulative hazard function is:

$$H(t)=-Ln[S(t)]$$

 

[blue_raver22]

There are a few ways to approach finding the hazard function from a given survival function. One method is to use the relationship between the survival function and the hazard function, which states that the hazard function is equal to the negative derivative of the natural logarithm of the survival function. In this case, we can use the given survival function, S(t) = e^(-at-bt2), to calculate the hazard function, h(t) = -d/dt[ln(S(t))] = a+2bt. Another approach is to use the relationship between the survival function and the cumulative hazard function, which states that the hazard function is equal to the derivative of the cumulative hazard function. In this case, we can use the given survival function to calculate the cumulative hazard function, H(t) = -ln(S(t)) = at+bt2, and then take the derivative to find the hazard function, h(t) = a+2bt. Both methods result in the same hazard function, which is a constant value of a+2bt. I hope this helps in your calculations.