Expected survival time

[cedricdeboom]

It would be nice to be able to compute the expected survival time from a fitted survival function. It should not be that hard actually, see: https://math.stackexchange.com/questions/642021/expected-value-as-integral-of-survival-function

Now I always do it manually, but it would make a nice addition to Lifelines!

[CamDavidsonPilon]

Agree! We currently have median_survival_time_, so a mean_survival_time_ makes sense too. I'll convert this to an issue.

[josegalelop1345]

PS: My goal is to compute the expected survival time from a fitted survival function

[cedricdeboom]

I did it like this, but I have not tested nor rigorously proven that this is a correct method. It could be that I am forgetting some factors, but my goal was to compare different models to each other, rather than have a near 100% correct absolute expected value. This is the code:

# Get the survival function
sf = kmf_full.survival_function_

# Calculate the approximate integral
integral = 0.0
previous_t = 0.0
previous_value = 1.0
for i, (j, r) in enumerate(sf.iterrows()):
    value = r['KM_estimate']
    t = r.name
    integral += previous_value * (t - previous_t)
    previous_t = t
    previous_value = value

integral += previous_value * 1.0
print(f"Expected survival time: {integral}")

[josegalelop1345]

@cedricdeboom Many thanks for this!

[CamDavidsonPilon]

I would suggest looking into scipy.integrate.trapezoid: https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.trapezoid.html

ev = trapezoid(km.survival_function_['KM_estimate'].values, km.survival_function_.index)

[cedricdeboom]

Even better!