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survival2.py
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survival2.py
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#Kaplan-Meier Estimator
import numpy as np
import numpy.linalg as la
import matplotlib.pyplot as plt
from scipy import stats
from statsmodels.iolib.table import SimpleTable
class KaplanMeier(object):
"""
KaplanMeier(...)
KaplanMeier(data, endog, exog=None, censoring=None)
Create an object of class KaplanMeier for estimating
Kaplan-Meier survival curves.
Parameters
----------
data: array_like
An array, with observations in each row, and
variables in the columns
endog: index (starting at zero) of the column
containing the endogenous variable (time)
exog: index of the column containing the exogenous
variable (must be catagorical). If exog = None, this
is equivalent to a single survival curve
censoring: index of the column containing an indicator
of whether an observation is an event, or a censored
observation, with 0 for censored, and 1 for an event
Attributes
-----------
censorings: List of censorings associated with each unique
time, at each value of exog
events: List of the number of events at each unique time
for each value of exog
results: List of arrays containing estimates of the value
value of the survival function and its standard error
at each unique time, for each value of exog
ts: List of unique times for each value of exog
Methods
-------
fit: Calcuate the Kaplan-Meier estimates of the survival
function and its standard error at each time, for each
value of exog
plot: Plot the survival curves using matplotlib.plyplot
summary: Display the results of fit in a table. Gives results
for all (including censored) times
test_diff: Test for difference between survival curves
Examples
--------
>>> import statsmodels.api as sm
>>> import matplotlib.pyplot as plt
>>> import numpy as np
>>> from statsmodels.sandbox.survival2 import KaplanMeier
>>> dta = sm.datasets.strikes.load()
>>> dta = dta.values()[-1]
>>> dta[range(5),:]
array([[ 7.00000000e+00, 1.13800000e-02],
[ 9.00000000e+00, 1.13800000e-02],
[ 1.30000000e+01, 1.13800000e-02],
[ 1.40000000e+01, 1.13800000e-02],
[ 2.60000000e+01, 1.13800000e-02]])
>>> km = KaplanMeier(dta,0)
>>> km.fit()
>>> km.plot()
Doing
>>> km.summary()
will display a table of the estimated survival and standard errors
for each time. The first few lines are
Kaplan-Meier Curve
=====================================
Time Survival Std. Err
-------------------------------------
1.0 0.983870967742 0.0159984306572
2.0 0.91935483871 0.0345807888235
3.0 0.854838709677 0.0447374942184
4.0 0.838709677419 0.0467104592871
5.0 0.822580645161 0.0485169952543
Doing
>>> plt.show()
will plot the survival curve
Mutliple survival curves:
>>> km2 = KaplanMeier(dta,0,exog=1)
>>> km2.fit()
km2 will estimate a survival curve for each value of industrial
production, the column of dta with index one (1).
With censoring:
>>> censoring = np.ones_like(dta[:,0])
>>> censoring[dta[:,0] > 80] = 0
>>> dta = np.c_[dta,censoring]
>>> dta[range(5),:]
array([[ 7.00000000e+00, 1.13800000e-02, 1.00000000e+00],
[ 9.00000000e+00, 1.13800000e-02, 1.00000000e+00],
[ 1.30000000e+01, 1.13800000e-02, 1.00000000e+00],
[ 1.40000000e+01, 1.13800000e-02, 1.00000000e+00],
[ 2.60000000e+01, 1.13800000e-02, 1.00000000e+00]])
>>> km3 = KaplanMeier(dta,0,exog=1,censoring=2)
>>> km3.fit()
Test for difference of survival curves
>>> log_rank = km3.test_diff([0.0645,-0.03957])
The zeroth element of log_rank is the chi-square test statistic
for the difference between the survival curves for exog = 0.0645
and exog = -0.03957, the index one element is the degrees of freedom for
the test, and the index two element is the p-value for the test
Groups with nan names
>>> groups = np.ones_like(dta[:,1])
>>> groups = groups.astype('S4')
>>> groups[dta[:,1] > 0] = 'high'
>>> groups[dta[:,1] <= 0] = 'low'
>>> dta = dta.astype('S4')
>>> dta[:,1] = groups
>>> dta[range(5),:]
array([['7.0', 'high', '1.0'],
['9.0', 'high', '1.0'],
['13.0', 'high', '1.0'],
['14.0', 'high', '1.0'],
['26.0', 'high', '1.0']],
dtype='|S4')
>>> km4 = KaplanMeier(dta,0,exog=1,censoring=2)
>>> km4.fit()
"""
def __init__(self, data, endog, exog=None, censoring=None):
self.exog = exog
self.censoring = censoring
cols = [endog]
self.endog = 0
if exog != None:
cols.append(exog)
self.exog = 1
if censoring != None:
cols.append(censoring)
if exog != None:
self.censoring = 2
else:
self.censoring = 1
data = data[:,cols]
if data.dtype == float or data.dtype == int:
self.data = data[~np.isnan(data).any(1)]
else:
t = (data[:,self.endog]).astype(float)
if exog != None:
evec = data[:,self.exog]
evec = evec[~np.isnan(t)]
if censoring != None:
cvec = (data[:,self.censoring]).astype(float)
cvec = cvec[~np.isnan(t)]
t = t[~np.isnan(t)]
if censoring != None:
t = t[~np.isnan(cvec)]
if exog != None:
evec = evec[~np.isnan(cvec)]
cvec = cvec[~np.isnan(cvec)]
cols = [t]
if exog != None:
cols.append(evec)
if censoring != None:
cols.append(cvec)
data = (np.array(cols)).transpose()
self.data = data
def fit(self):
"""
Calculate the Kaplan-Meier estimator of the survival function
"""
self.results = []
self.ts = []
self.censorings = []
self.event = []
if self.exog == None:
self.fitting_proc(self.data)
else:
groups = np.unique(self.data[:,self.exog])
self.groups = groups
for g in groups:
group = self.data[self.data[:,self.exog] == g]
self.fitting_proc(group)
def plot(self):
"""
Plot the estimated survival curves. After using this method
do
plt.show()
to display the plot
"""
plt.figure()
if self.exog == None:
self.plotting_proc(0)
else:
for g in range(len(self.groups)):
self.plotting_proc(g)
plt.ylim(ymax=1.05)
plt.ylabel('Survival')
plt.xlabel('Time')
def summary(self):
"""
Print a set of tables containing the estimates of the survival
function, and its standard errors
"""
if self.exog == None:
self.summary_proc(0)
else:
for g in range(len(self.groups)):
self.summary_proc(g)
def fitting_proc(self, group):
"""
For internal use
"""
t = ((group[:,self.endog]).astype(float)).astype(int)
if self.censoring == None:
events = np.bincount(t)
t = np.unique(t)
events = events[:,list(t)]
events = events.astype(float)
eventsSum = np.cumsum(events)
eventsSum = np.r_[0,eventsSum]
n = len(group) - eventsSum[:-1]
else:
censoring = ((group[:,self.censoring]).astype(float)).astype(int)
reverseCensoring = -1*(censoring - 1)
events = np.bincount(t,censoring)
censored = np.bincount(t,reverseCensoring)
t = np.unique(t)
censored = censored[:,list(t)]
censored = censored.astype(float)
censoredSum = np.cumsum(censored)
censoredSum = np.r_[0,censoredSum]
events = events[:,list(t)]
events = events.astype(float)
eventsSum = np.cumsum(events)
eventsSum = np.r_[0,eventsSum]
n = len(group) - eventsSum[:-1] - censoredSum[:-1]
(self.censorings).append(censored)
survival = np.cumprod(1-events/n)
var = ((survival*survival) *
np.cumsum(events/(n*(n-events))))
se = np.sqrt(var)
(self.results).append(np.array([survival,se]))
(self.ts).append(t)
(self.event).append(events)
def plotting_proc(self, g):
"""
For internal use
"""
survival = self.results[g][0]
t = self.ts[g]
e = (self.event)[g]
if self.censoring != None:
c = self.censorings[g]
csurvival = survival[c != 0]
ct = t[c != 0]
if len(ct) != 0:
plt.vlines(ct,csurvival+0.02,csurvival-0.02)
x = np.repeat(t[e != 0], 2)
y = np.repeat(survival[e != 0], 2)
if self.ts[g][-1] in t[e != 0]:
x = np.r_[0,x]
y = np.r_[1,1,y[:-1]]
else:
x = np.r_[0,x,self.ts[g][-1]]
y = np.r_[1,1,y]
plt.plot(x,y)
def summary_proc(self, g):
"""
For internal use
"""
if self.exog != None:
myTitle = ('exog = ' + str(self.groups[g]) + '\n')
else:
myTitle = "Kaplan-Meier Curve"
table = np.transpose(self.results[g])
table = np.c_[np.transpose(self.ts[g]),table]
table = SimpleTable(table, headers=['Time','Survival','Std. Err'],
title = myTitle)
print(table)
def test_diff(self, groups, rho=None, weight=None):
"""
test_diff(groups, rho=0)
Test for difference between survival curves
Parameters
----------
groups: A list of the values for exog to test for difference.
tests the null hypothesis that the survival curves for all
values of exog in groups are equal
rho: compute the test statistic with weight S(t)^rho, where
S(t) is the pooled estimate for the Kaplan-Meier survival function.
If rho = 0, this is the logrank test, if rho = 0, this is the
Peto and Peto modification to the Gehan-Wilcoxon test.
weight: User specified function that accepts as its sole arguement
an array of times, and returns an array of weights for each time
to be used in the test
Returns
-------
An array whose zeroth element is the chi-square test statistic for
the global null hypothesis, that all survival curves are equal,
the index one element is degrees of freedom for the test, and the
index two element is the p-value for the test.
Examples
--------
>>> import statsmodels.api as sm
>>> import matplotlib.pyplot as plt
>>> import numpy as np
>>> from statsmodels.sandbox.survival2 import KaplanMeier
>>> dta = sm.datasets.strikes.load()
>>> dta = dta.values()[-1]
>>> censoring = np.ones_like(dta[:,0])
>>> censoring[dta[:,0] > 80] = 0
>>> dta = np.c_[dta,censoring]
>>> km = KaplanMeier(dta,0,exog=1,censoring=2)
>>> km.fit()
Test for difference of survival curves
>>> log_rank = km3.test_diff([0.0645,-0.03957])
The zeroth element of log_rank is the chi-square test statistic
for the difference between the survival curves using the log rank test
for exog = 0.0645 and exog = -0.03957, the index one element
is the degrees of freedom for the test, and the index two element
is the p-value for the test
>>> wilcoxon = km.test_diff([0.0645,-0.03957], rho=1)
wilcoxon is the equivalent information as log_rank, but for the
Peto and Peto modification to the Gehan-Wilcoxon test.
User specified weight functions
>>> log_rank = km3.test_diff([0.0645,-0.03957], weight=np.ones_like)
This is equivalent to the log rank test
More than two groups
>>> log_rank = km.test_diff([0.0645,-0.03957,0.01138])
The test can be performed with arbitrarily many groups, so long as
they are all in the column exog
"""
groups = np.asarray(groups)
if self.exog == None:
raise ValueError("Need an exogenous variable for logrank test")
elif (np.in1d(groups,self.groups)).all():
data = self.data[np.in1d(self.data[:,self.exog],groups)]
t = ((data[:,self.endog]).astype(float)).astype(int)
tind = np.unique(t)
NK = []
N = []
D = []
Z = []
if rho != None and weight != None:
raise ValueError("Must use either rho or weights, not both")
elif rho != None:
s = KaplanMeier(data,self.endog,censoring=self.censoring)
s.fit()
s = (s.results[0][0]) ** (rho)
s = np.r_[1,s[:-1]]
elif weight != None:
s = weight(tind)
else:
s = np.ones_like(tind)
if self.censoring == None:
for g in groups:
dk = np.bincount((t[data[:,self.exog] == g]))
d = np.bincount(t)
if np.max(tind) != len(dk):
dif = np.max(tind) - len(dk) + 1
dk = np.r_[dk,[0]*dif]
dk = dk[:,list(tind)]
d = d[:,list(tind)]
dk = dk.astype(float)
d = d.astype(float)
dkSum = np.cumsum(dk)
dSum = np.cumsum(d)
dkSum = np.r_[0,dkSum]
dSum = np.r_[0,dSum]
nk = len(data[data[:,self.exog] == g]) - dkSum[:-1]
n = len(data) - dSum[:-1]
d = d[n>1]
dk = dk[n>1]
nk = nk[n>1]
n = n[n>1]
s = s[n>1]
ek = (nk * d)/(n)
Z.append(np.sum(s * (dk - ek)))
NK.append(nk)
N.append(n)
D.append(d)
else:
for g in groups:
censoring = ((data[:,self.censoring]).astype(float)).astype(int)
reverseCensoring = -1*(censoring - 1)
censored = np.bincount(t,reverseCensoring)
ck = np.bincount((t[data[:,self.exog] == g]),
reverseCensoring[data[:,self.exog] == g])
dk = np.bincount((t[data[:,self.exog] == g]),
censoring[data[:,self.exog] == g])
d = np.bincount(t,censoring)
if np.max(tind) != len(dk):
dif = np.max(tind) - len(dk) + 1
dk = np.r_[dk,[0]*dif]
ck = np.r_[ck,[0]*dif]
dk = dk[:,list(tind)]
ck = ck[:,list(tind)]
d = d[:,list(tind)]
dk = dk.astype(float)
d = d.astype(float)
ck = ck.astype(float)
dkSum = np.cumsum(dk)
dSum = np.cumsum(d)
ck = np.cumsum(ck)
ck = np.r_[0,ck]
dkSum = np.r_[0,dkSum]
dSum = np.r_[0,dSum]
censored = censored[:,list(tind)]
censored = censored.astype(float)
censoredSum = np.cumsum(censored)
censoredSum = np.r_[0,censoredSum]
nk = (len(data[data[:,self.exog] == g]) - dkSum[:-1]
- ck[:-1])
n = len(data) - dSum[:-1] - censoredSum[:-1]
d = d[n>1]
dk = dk[n>1]
nk = nk[n>1]
n = n[n>1]
s = s[n>1]
ek = (nk * d)/(n)
Z.append(np.sum(s * (dk - ek)))
NK.append(nk)
N.append(n)
D.append(d)
Z = np.array(Z)
N = np.array(N)
D = np.array(D)
NK = np.array(NK)
sigma = -1 * np.dot((NK/N) * ((N - D)/(N - 1)) * D
* np.array([(s ** 2)]*len(D))
,np.transpose(NK/N))
np.fill_diagonal(sigma, np.diagonal(np.dot((NK/N)
* ((N - D)/(N - 1)) * D
* np.array([(s ** 2)]*len(D))
,np.transpose(1 - (NK/N)))))
chisq = np.dot(np.transpose(Z),np.dot(la.pinv(sigma), Z))
df = len(groups) - 1
return np.array([chisq, df, stats.chi2.sf(chisq,df)])
else:
raise ValueError("groups must be in column exog")