Survival analysis in Python, including Kaplan Meier, Nelson Aalen and regression
Project description
lifelines
=========
`What is survival analysis and why should I learn
it? <http://lifelines.readthedocs.org/en/latest/Survival%20Analysis%20intro.html>`__
Survival analysis was originally developed and applied heavily by the
actuarial and medical community. Its purpose was to answer *why do
events occur now versus later* under uncertainity (where *events* might
refer to deaths, disease remission, etc.). This is great for researchers
who are interested in measuring lifetimes: they can answer questions
like *what factors might influence deaths?*
But outside of medicine and actuarial science, there are many other
interesting and exciting applications of this lesser-known technique,
for example: - SaaS providers are interested in measuring customer
lifetimes, or time to first behaviours. - sociologists are interested in
measure political parties lifetimes, or relationships, or marriages -
Businesses are interested in what variables affect lifetime value
*lifelines* is a pure Python implementation of the best parts of
survival analysis. We'd love to hear if you are using *lifelines*,
please ping me at [@cmrn\_dp](https://twitter.com/Cmrn\_DP) and let me
know your thoughts on the library.
Installation:
-------------
Dependencies:
^^^^^^^^^^^^^
The usual Python data stack: Numpy, Scipy, Pandas (a modern version
please), Matplotlib
Installing
^^^^^^^^^^
You can install *lifelines* using
::
pip install lifelines
Or getting the bleeding edge version with:
::
pip install git+https://github.com/CamDavidsonPilon/lifelines.git
or upgrade with
::
pip install --upgrade git+https://github.com/CamDavidsonPilon/lifelines.git
from the command line.
Intro to *lifelines* and survival analysis
------------------------------------------
Situation: 500 random individuals are born at time 0, currently it is
time 12, so we have possibly not observed all death events yet.
::
# Create lifetimes, but censor all lifetimes after time 12
censor_after = 12
actual_lifetimes = np.random.exponential(10, size=500)
observed_lifetimes = np.minimum( actual_lifetimes, censor_after*np.ones(500) )
C = (actual_lifetimes < censor_after) #boolean array
Non-parametrically fit the *survival curve*:
::
from lifelines import KaplanMeierFitter
kmf = KaplanMeierFitter()
kmf.fit(observed_lifetimes, censorship=C)
# fitter methods have an internal plotting method.
# plot the curve with the confidence intervals
kmf.plot()
.. figure:: http://i.imgur.com/Bq73IfN.png
:alt: kmf
kmf
It looks like 50% of all individuals are dead before time 7.
::
print kmf.survival_function_.head()
time KM-estimate
0.000000 1.000
0.038912 0.998
0.120667 0.996
0.125719 0.994
0.133778 0.992
Non-parametrically fit the *cumulative hazard curve*:
::
from lifelines import NelsonAalenFitter
naf = NelsonAalenFitter()
naf.fit(observed_lifetimes, censorship=C)
#plot the curve with the confidence intervals
naf.plot()
.. figure:: http://i.imgur.com/2L7arWX.png
:alt: naf
naf
::
print naf.cumulative_hazard_.head()
time NA-estimate
0.000000 0.000000
0.038912 0.002000
0.120667 0.004004
0.125719 0.006012
0.133778 0.008024
Compare two populations using the logrank test:
::
from lifelines.statistics import logrank_test
other_lifetimes = np.random.exponential(3, size=500)
summary, p_value, results = logrank_test(observed_lifetimes, other_lifetimes, alpha=0.95)
print summary
Results
df: 1
alpha: 0.95
t 0: -1
test: logrank
null distribution: chi squared
__ p-value ___|__ test statistic __|__ test results __
0.00000 | 268.465 | True
(Less Quick) Intro to *lifelines* and survival analysis
-------------------------------------------------------
If you are new to survival analysis, wondering why it is useful, or are
interested in *lifelines* examples and syntax, please check out the
`Documentation and Tutorials
page <http://lifelines.readthedocs.org/en/latest/index.html>`__
Alternatively, you can **use the IPython notebooks tutorials**, located
in the main directory of the repo:
1. `Introduction to survival
analysis <http://nbviewer.ipython.org/github/CamDavidsonPilon/lifelines/blob/master/Survival%20Analysis%20intro.ipynb>`__
2. `Using lifelines on real
data <http://nbviewer.ipython.org/github/CamDavidsonPilon/lifelines/blob/master/Intro%20to%20lifelines.ipynb>`__
More examples
^^^^^^^^^^^^^
There are some IPython notebook files in the repo, and you can view them
online here.
- `Divorce
data <http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/lifelines/master/datasets/Divorces%2520Rates.ipynb>`__
- `Gehan's survival
dataset <http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/lifelines/master/datasets/The%2520Gehan%2520Survival%2520Data.ipynb>`__
.. figure:: http://i.imgur.com/QXW71zA.png
:alt: lifelines
lifelines
License
-------
The Feedback MIT License (FMIT)
Copyright (c) 2013, Cameron Davidson-Pilon
Permission is hereby granted, free of charge, to any person obtaining a
copy of this software and associated documentation files (the
"Software"), to deal in the Software without restriction, including
without limitation the rights to use, copy, modify, merge, publish,
distribute, sublicense, and/or sell copies of the Software, and to
permit persons to whom the Software is furnished to do so, subject to
the following conditions:
1. The above copyright notice and this permission notice shall be
included in all copies or substantial portions of the Software.
2. Person obtaining a copy must return feedback to the authors.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
*lifelines* logo designed by Pulse designed by TNS from the Noun Project
=========
`What is survival analysis and why should I learn
it? <http://lifelines.readthedocs.org/en/latest/Survival%20Analysis%20intro.html>`__
Survival analysis was originally developed and applied heavily by the
actuarial and medical community. Its purpose was to answer *why do
events occur now versus later* under uncertainity (where *events* might
refer to deaths, disease remission, etc.). This is great for researchers
who are interested in measuring lifetimes: they can answer questions
like *what factors might influence deaths?*
But outside of medicine and actuarial science, there are many other
interesting and exciting applications of this lesser-known technique,
for example: - SaaS providers are interested in measuring customer
lifetimes, or time to first behaviours. - sociologists are interested in
measure political parties lifetimes, or relationships, or marriages -
Businesses are interested in what variables affect lifetime value
*lifelines* is a pure Python implementation of the best parts of
survival analysis. We'd love to hear if you are using *lifelines*,
please ping me at [@cmrn\_dp](https://twitter.com/Cmrn\_DP) and let me
know your thoughts on the library.
Installation:
-------------
Dependencies:
^^^^^^^^^^^^^
The usual Python data stack: Numpy, Scipy, Pandas (a modern version
please), Matplotlib
Installing
^^^^^^^^^^
You can install *lifelines* using
::
pip install lifelines
Or getting the bleeding edge version with:
::
pip install git+https://github.com/CamDavidsonPilon/lifelines.git
or upgrade with
::
pip install --upgrade git+https://github.com/CamDavidsonPilon/lifelines.git
from the command line.
Intro to *lifelines* and survival analysis
------------------------------------------
Situation: 500 random individuals are born at time 0, currently it is
time 12, so we have possibly not observed all death events yet.
::
# Create lifetimes, but censor all lifetimes after time 12
censor_after = 12
actual_lifetimes = np.random.exponential(10, size=500)
observed_lifetimes = np.minimum( actual_lifetimes, censor_after*np.ones(500) )
C = (actual_lifetimes < censor_after) #boolean array
Non-parametrically fit the *survival curve*:
::
from lifelines import KaplanMeierFitter
kmf = KaplanMeierFitter()
kmf.fit(observed_lifetimes, censorship=C)
# fitter methods have an internal plotting method.
# plot the curve with the confidence intervals
kmf.plot()
.. figure:: http://i.imgur.com/Bq73IfN.png
:alt: kmf
kmf
It looks like 50% of all individuals are dead before time 7.
::
print kmf.survival_function_.head()
time KM-estimate
0.000000 1.000
0.038912 0.998
0.120667 0.996
0.125719 0.994
0.133778 0.992
Non-parametrically fit the *cumulative hazard curve*:
::
from lifelines import NelsonAalenFitter
naf = NelsonAalenFitter()
naf.fit(observed_lifetimes, censorship=C)
#plot the curve with the confidence intervals
naf.plot()
.. figure:: http://i.imgur.com/2L7arWX.png
:alt: naf
naf
::
print naf.cumulative_hazard_.head()
time NA-estimate
0.000000 0.000000
0.038912 0.002000
0.120667 0.004004
0.125719 0.006012
0.133778 0.008024
Compare two populations using the logrank test:
::
from lifelines.statistics import logrank_test
other_lifetimes = np.random.exponential(3, size=500)
summary, p_value, results = logrank_test(observed_lifetimes, other_lifetimes, alpha=0.95)
print summary
Results
df: 1
alpha: 0.95
t 0: -1
test: logrank
null distribution: chi squared
__ p-value ___|__ test statistic __|__ test results __
0.00000 | 268.465 | True
(Less Quick) Intro to *lifelines* and survival analysis
-------------------------------------------------------
If you are new to survival analysis, wondering why it is useful, or are
interested in *lifelines* examples and syntax, please check out the
`Documentation and Tutorials
page <http://lifelines.readthedocs.org/en/latest/index.html>`__
Alternatively, you can **use the IPython notebooks tutorials**, located
in the main directory of the repo:
1. `Introduction to survival
analysis <http://nbviewer.ipython.org/github/CamDavidsonPilon/lifelines/blob/master/Survival%20Analysis%20intro.ipynb>`__
2. `Using lifelines on real
data <http://nbviewer.ipython.org/github/CamDavidsonPilon/lifelines/blob/master/Intro%20to%20lifelines.ipynb>`__
More examples
^^^^^^^^^^^^^
There are some IPython notebook files in the repo, and you can view them
online here.
- `Divorce
data <http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/lifelines/master/datasets/Divorces%2520Rates.ipynb>`__
- `Gehan's survival
dataset <http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/lifelines/master/datasets/The%2520Gehan%2520Survival%2520Data.ipynb>`__
.. figure:: http://i.imgur.com/QXW71zA.png
:alt: lifelines
lifelines
License
-------
The Feedback MIT License (FMIT)
Copyright (c) 2013, Cameron Davidson-Pilon
Permission is hereby granted, free of charge, to any person obtaining a
copy of this software and associated documentation files (the
"Software"), to deal in the Software without restriction, including
without limitation the rights to use, copy, modify, merge, publish,
distribute, sublicense, and/or sell copies of the Software, and to
permit persons to whom the Software is furnished to do so, subject to
the following conditions:
1. The above copyright notice and this permission notice shall be
included in all copies or substantial portions of the Software.
2. Person obtaining a copy must return feedback to the authors.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
*lifelines* logo designed by Pulse designed by TNS from the Noun Project
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