pip install lifelines
Kaplan-Meier and Nelson-Aalen¶
Let’s start by importing some data. We need the durations that individuals are observed for, and whether they “died” or not.
from lifelines.datasets import load_waltons df = load_waltons() # returns a Pandas DataFrame print df.head() """ T E group 0 6 1 miR-137 1 13 1 miR-137 2 13 1 miR-137 3 13 1 miR-137 4 19 1 miR-137 """ T = df['T'] E = df['E']
T is an array of durations,
E is a either boolean or binary array representing whether the “death” was observed (alternatively an individual can be censored).
By default, lifelines assumes all “deaths” are observed.
from lifelines import KaplanMeierFitter kmf = KaplanMeierFitter() kmf.fit(T, event_observed=E) # more succiently, kmf.fit(T,E)
After calling the
fit method, we have access to new properties like
survival_function_ and methods like
plot(). The latter is a wrapper around Pandas internal plotting library.
kmf.survival_function_ kmf.median_ kmf.plot()
groups = df['group'] ix = (groups == 'miR-137') kmf.fit(T[~ix], E[~ix], label='control') ax = kmf.plot() kmf.fit(T[ix], E[ix], label='miR-137') kmf.plot(ax=ax)
Similar functionality exists for the
from lifelines import NelsonAalenFitter naf = NelsonAalenFitter() naf.fit(T, event_observed=E)
but instead of a
survival_function_ being exposed, a
Similar to Scikit-Learn, all statistically estimated quantities append an underscore to the property name.
Getting Data in The Right Format¶
Often you’ll have data that looks like:
Lifelines has some utility functions to transform this dataset into durations and censorships:
from lifelines.utils import datetimes_to_durations # start_times is a vector of datetime objects # end_times is a vector of (possibly missing) datetime objects. T, C = datetimes_to_durations(start_times, end_times, freq='h')
Alternatively, perhaps you are interested in viewing the survival table given some durations and censorship vectors.
from lifelines.utils import survival_table_from_events table = survival_table_from_events(T, E) print table.head() """ removed observed censored entrance at_risk event_at 0 0 0 0 163 163 6 1 1 0 0 163 7 2 1 1 0 162 9 3 3 0 0 160 13 3 3 0 0 157 """
While the above
NelsonAalenFitter are useful, they only give us an “average” view of the population. Often we have specific data at the individual level, either continuous or categorical, that we would like to use. For this, we turn to survival regression, specifically
from lifelines.datasets import load_regression_dataset regression_dataset = load_regression_dataset() regression_dataset.head()
The input of the
fit method’s API on
AalenAdditiveFitter is different than above. All the data, including durations, censorships and covariates must be contained in a Pandas DataFrame (yes, it must be a DataFrame). The duration column and event occured column must be specified in the call to
from lifelines import AalenAdditiveFitter, CoxPHFitter # Using Cox Proportional Hazards model cf = CoxPHFitter() cf.fit(regression_dataset, 'T', event_col='E') cf.print_summary() # Using Aalen's Additive model aaf = AalenAdditiveFitter(fit_intercept=False) aaf.fit(regression_dataset, 'T', event_col='E')
After fitting, you’ll have access to properties like
cumulative_hazards_ and methods like
predict_survival_function. The latter two methods require an additional argument of individual covariates:
x = regression_dataset[regression_dataset.columns - ['E','T']] aaf.predict_survival_function(x.ix[10:12]).plot() #get the unique survival functions of the first two subjects
Like the above estimators, there is also a built-in plotting method: