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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).
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 | import lifelinesfrom lifelines.datasets import load_waltonsdf = load_waltons() # returns a Pandas DataFrameT = df['T']E = df['E']from lifelines import KaplanMeierFitterkmf = KaplanMeierFitter()kmf.fit(T, event_observed=E) # more succiently, kmf.fit(T,E)kmf.survival_function_'''Out[7]: KM_estimatetimeline 0.0 1.0000006.0 0.9938657.0 0.9877309.0 0.96921013.0 0.95069015.0 0.93834417.0 0.93217019.0 0.91365022.0 0.88895726.0 0.85809029.0 0.82722432.0 0.82105133.0 0.80253136.0 0.79018438.0 0.77783741.0 0.73462443.0 0.72845145.0 0.67289147.0 0.66666148.0 0.61681751.0 0.598125'''kmf.median_'''Out[8]: 56.0'''kmf.plot() |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 | import lifelinesfrom lifelines.datasets import load_waltonsfrom lifelines import KaplanMeierFitterdf = load_waltons() # returns a Pandas DataFramekmf = KaplanMeierFitter()T = df['T']E = df['E']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) |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 | import numpy as npimport matplotlib.pyplot as plt from lifelines.plotting import plot_lifetimesfrom numpy.random import uniform, exponentialN = 25current_time = 10actual_lifetimes = np.array([[exponential(12), exponential(2)][uniform()<0.5] for i in range(N)])observed_lifetimes = np.minimum(actual_lifetimes,current_time)observed= actual_lifetimes < current_timeplt.xlim(0,25)plt.vlines(10,0,30,lw=2, linestyles='--')plt.xlabel('time')plt.title('Births and deaths of our population, at $t=10$')plot_lifetimes(observed_lifetimes, event_observed=observed)print 'Observed lifetimes at time %d:\n'%(current_time), observed_lifetimes |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 | import pandas as pdimport lifelinesfrom lifelines import KaplanMeierFitterimport matplotlib.pyplot as pltdata = lifelines.datasets.load_dd()kmf = KaplanMeierFitter()T = data['duration']C = data['observed']kmf.fit(T, event_observed=C )plt.title('Survival function of political regimes')kmf.survival_function_.plot()kmf.plot()kmf.median_ |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 | import pandas as pdimport lifelinesfrom lifelines import KaplanMeierFitterimport matplotlib.pyplot as pltdata = lifelines.datasets.load_dd()kmf = KaplanMeierFitter()T = data['duration']C = data['observed']kmf.fit(T, event_observed=C )plt.title('Survival function of political regimes')kmf.survival_function_.plot()kmf.plot()ax = plt.subplot(111)dem = (data['democracy'] == 'Democracy')kmf.fit(T[dem], event_observed=C[dem], label='Democratic Regimes')kmf.plot(ax=ax, ci_force_lines=True)kmf.fit(T[~dem], event_observed=C[~dem], label='Non-democratic Regimes')plt.ylim(0,1);plt.title('Lifespans of different global regimes')kmf.plot(ax=ax, ci_force_lines=True) |
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具體文檔
http://lifelines.readthedocs.io/en/latest/
https://wenku.baidu.com/view/577041d3a1c7aa00b52acb2e.html?from=search
https://wenku.baidu.com/view/a5adff8b89eb172ded63b7d6.html?from=search
https://github.com/thomas-haslwanter/statsintro_python/tree/master/ISP/Code_Quantlets/10_SurvivalAnalysis/lifelinesDemo
測(cè)試代碼
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 | # -*- coding: utf-8 -*-# Import standard packagesimport numpy as npimport matplotlib.pyplot as pltfrom numpy.random import uniform, exponentialimport os# additional packagesfrom lifelines.plotting import plot_lifetimesimport syssys.path.append(os.path.join('..', '..', 'Utilities'))try:# Import formatting commands if directory 'Utilities' is available from ISP_mystyle import setFonts except ImportError:# Ensure correct performance otherwise def setFonts(*options): return # Generate some dummy datanp.set_printoptions(precision=2)N = 20study_duration = 12# Note: a constant dropout rate is equivalent to an exponential distribution!actual_subscriptiontimes = np.array([[exponential(18), exponential(3)][uniform()<0.5] for i in range(N)])observed_subscriptiontimes = np.minimum(actual_subscriptiontimes,study_duration)observed= actual_subscriptiontimes < study_duration# Show the datasetFonts(18)plt.xlim(0,24)plt.vlines(12, 0, 30, lw=2, linestyles='--')plt.xlabel('time')plt.title('Subscription Times, at $t=12$ months')plot_lifetimes(observed_subscriptiontimes, event_observed=observed)print('Observed subscription time at time %d:\n'%(study_duration), observed_subscriptiontimes) |
where k > 0 is the shape parameter and > 0 is the scale parameter of the
distribution. (It is one of the rare cases where we use a shape parameter different
from skewness and kurtosis.) Its complementary cumulative distribution function is
a stretched exponential function.
If the quantity x is a “time-to-failure,” theWeibull distribution gives a distribution
for which the failure rate is proportional to a power of time. The shape parameter, k,
is that power plus one, and so this parameter can be interpreted directly as follows:
· Avalueofk < 1 indicates that the failure rate decreases over time. This happens
if there is significant “infant mortality,” or defective items failing early and the
failure rate decreasing over time as the defective items are weeded out of the
population.
· Avalueofk D 1 indicates that the failure rate is constant over time. This might
suggest random external events are causing mortality, or failure.
· Avalueofk > 1 indicates that the failure rate increases with time. This happens
if there is an “aging” process, or parts that are more likely to fail as time goes on.
An example would be products with a built-in weakness that fail soon after the
warranty expires.
In the field of materials science, the shape parameter k of a distribution of
strengths is known as the Weibull modulus.
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