Interval events

Thanks for the awesome work.

I am trying to do some survival analysis where the observations are done on fixed intervals. Is there anyway to handle these types of information?

The following is an example of such data

    Start   Stop  Censored
0    4640    NaN      True
1    4640    NaN      True
2    4640    NaN      True
3    4640    NaN      True
4    4640    NaN      True
..    ...    ...       ...
15    215  464.0     False
16      0    1.0     False
17   4640    NaN      True
18   4640    NaN      True
19   4640    NaN      True

Here, if the Stop column is NaN then the data is censored, but if the Stop has a number then the event happened between Start time and Stop time.

Thanks for the help

[CamDavidsonPilon]

So version 0.21.0 (just released) has initial support for parametric models of interval censoring. Here’s an example: https://dataorigami.net/blogs/napkin-folding/counting-and-interval-censoring

Next is to do non and semi parametric models, but that’s for the medium-term future.

Your example can be modelled something like:

from lifelines import LogLogisticFitter

df['stop'] = df['stop'].fillna(np.inf)

llf = LogLogisticFitter().fit(df['start'], df['stop'])
llf.plot_survival_function()

I believe that’s it! I’m treating your right censored as interval censored (with an endpoint at infinity).

[CamDavidsonPilon]

It’s not hard to write down the likelihood for this data (assuming a parametric model). It would be a combination of eq (2) and (3) in this paper: https://cran.r-project.org/web/packages/flexsurv/vignettes/flexsurv.pdf