How to calculate the area under a Weibull curve

[Talitha]

Hi all,

I'm practising my survival analysis skills and I'm trying to conduct a partitioned survival model by means of a Weibull distribution. I can easily manage to do so for exponential distributions, where the survival function is denoted as s(t)=EXP(-(EXP(-intercept)*t)). The area under the curve is then A(t)=(1-s(t))/EXP(-intercept). The intercept is derived from an analysis in R.

The survival curve for a Weibull distribution is S(t)=EXP(-EXP(-(intercept/EXP(log-scale)))*t^(1/EXP(log-scale))).
The intercept and log-scale are again derived from R. I do not have a formula to calculate an area under this survival curve, nor can I find one. Could anyone help me with this?

Thanks!

 

[shg]

Isn't it just 1 - the CDF of the distribution?

https://en.wikipedia.org/wiki/Weibull_distribution#Cumulative_distribution_function

 

[shg]

I retract that; the survival function is the complement of the CDF, not the PDF.

What's the useful interpretation of its integral?

 

[Fluff]

Cross posted https://www.excelforum.com/excel-fo...calculate-the-area-under-a-weibull-curve.html

While we do not prohibit Cross-Posting on this site, we do ask that you please mention you are doing so and provide links in each of the threads pointing to the other thread (see rule 13 here along with the explanation: Forum Rules).
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[Talitha]

The interpretation is usually used in partitioned survival analysis.
I am using it to grasp the probably costs in certain health states -> I calculate the surface under so called overall survival (OS) curves and progression free survival (PFS) curves. They are mutually exclusive curves/health states. Say, the surface under the overall survival curve at t=5 equals 4.5 and the surface under the progression free curve at t=5 equals 2.5. In the progression free disease state the costs per cycle (t=1) equal 1000 dollars and in the progressed disease state equal 2000 dollars. You then now that for an average patient you might expect (4.5-2.5)*2000+2.5*1000=6000 for costs.

 

[Talitha]

*probable, * know hahah

I figured now that the only info I am missing to use the excel function [FONT=&quot]WEIBULL.DIST(x,alpha,beta,cumulative) is beta.
Any idea how I can derive beta? [/FONT]

 

[Talitha]

This question was also asked at this forum: https://www.excelforum.com/excel-fo...calculate-the-area-under-a-weibull-curve.html