WeibullAFTFitter.predict_cumulative_hazard

[rsmita]

Hi,

I understand that predict_cumulative_hazard() function is to get the cumulative probability of failure. However I am unable to interpret the output from this function. I expected that highest probability would be 100%, howver I am getting highest failure probability as 2.35.

Can you please help interpreting the below output from predict_cumulative_hazard().

# Code
aft = WeibullAFTFitter()
aft.fit(df_refined, duration_col='Age', event_col='Failed', ancillary=df_refined)
X = df_refined.loc[0]
aft.predict_cumulative_hazard(X, ancillary=X)

#Output
0
6.358904 0.014141
6.917808 0.017875
7.939726 0.026225
8.345205 0.030122
10.000000 0.049824
... ...
37.000000 1.897246
38.000000 2.043352
39.000000 2.196473
39.200000 2.227952
40.000000 2.356753

Thank you,

[CamDavidsonPilon]

Cumulative hazards aren't probabilities. You can convert to probabilities by taking the negative exponential, eg: exp(-cum_haz(t)) is a probabilities, specifically the survival function, S(t)

[rsmita]

Hi, appreciate your response.

I guess cumulative Hazard function will not help to calculate probability of failure of an individual item at time,t.
I specifically need to predict:

1. Probability of machine failing at age t
2. How many machines will fail in next month, considering their current age.

Here for 1st one, can we use predict_survival_function() to get S(t) & calculate F(t) = 1-S(t) ?
Which function can help answer the 2nd point?

Thank you,

[CamDavidsonPilon]

1. F(t) will tell you has it not failed yet, not "failing at age t". "failing at age t" would be something like S(t) - S(t-1)

2. Try using something like https://lifelines.readthedocs.io/en/latest/Survival%20Regression.html#prediction-on-censored-subjects

[rsmita]

Thanks you, Had applied it on my data & got the survival prediction probability, but unable to interpret & answer to following: 1. What is the probability of failure at current age+ 6 months ( Would you be able to guide me on this part please. Thanks & Regards, Smita

…

On Tue, Aug 9, 2022 at 12:34 AM Cameron Davidson-Pilon < ***@***.***> wrote: 1. F(t) will tell you has it not failed *yet*, not "failing at age t". "failing at age t" would be something like S(t) - S(t-1) 2. Try using something like https://lifelines.readthedocs.io/en/latest/Survival%20Regression.html#prediction-on-censored-subjects — Reply to this email directly, view it on GitHub <#1445 (reply in thread)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/ANPQEONAQGBPMWBHSDM2DSDVYFK5XANCNFSM55RLNNRA> . You are receiving this because you authored the thread.Message ID: ***@***.*** com>

[rsmita]

Hi, Thank you for your response. In that case, can we calculate probability of failure as 1-probability of survival i.e. 1-S(t) Thanks, Smita

…

On Thu, Aug 4, 2022 at 8:30 PM Cameron Davidson-Pilon < ***@***.***> wrote: Cumulative hazards aren't probabilities. You can convert to probabilities by taking the negative exponential, eg: exp(-cum_haz(t)) is a probabilities, specifically the survival function, S(t) — Reply to this email directly, view it on GitHub <#1445 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/ANPQEOLQQN36JQ5EY2MGPL3VXPLJXANCNFSM55RLNNRA> . You are receiving this because you authored the thread.Message ID: ***@***.*** com>

[CamDavidsonPilon]

Yes, that's correct