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import shutil
import tempfile
import numpy as N
from scipy.sandbox.models import survival, model
class discrete:
"""
A simple little class for working with discrete random vectors.
"""
def __init__(self, x, w=None):
self.x = N.squeeze(x)
if self.x.shape == ():
self.x = N.array([self.x])
self.n = self.x.shape[0]
if w is None:
w = N.ones(self.n, N.float64)
else:
if w.shape[0] != self.n:
raise ValueError, 'incompatible shape for weights w'
if N.any(N.less(w, 0)):
raise ValueError, 'weights should be non-negative'
self.w = w / w.sum()
def mean(self, f=None):
if f is None:
fx = self.x
else:
fx = f(self.x)
return (fx * self.w).sum()
def cov(self):
mu = self.mean()
dx = self.x - N.multiply.outer(mu, self.x.shape[1])
return N.dot(dx, N.transpose(dx))
class observation(survival.right_censored):
def __getitem__(self, item):
if self.namespace is not None:
return self.namespace[item]
else:
return getattr(self, item)
def __init__(self, time, delta, namespace=None):
self.namespace = namespace
survival.right_censored.__init__(self, time, delta)
def __call__(self, formula, time=None, **extra):
return formula(namespace=self, time=time, **extra)
class coxph(model.likelihood_model):
def __init__(self, subjects, formula, time_dependent=False):
self.subjects, self.formula = subjects, formula
self.time_dependent = time_dependent
self.initialize(self.subjects)
def initialize(self, subjects):
self.failures = {}
for i in range(len(subjects)):
s = subjects[i]
if s.delta:
if not self.failures.has_key(s.time):
self.failures[s.time] = [i]
else:
self.failures[s.time].append(i)
self.failure_times = self.failures.keys()
self.failure_times.sort()
def cache(self):
if self.time_dependent:
self.cachedir = tempfile.mkdtemp()
self.design = {}
self.risk = {}
first = True
for t in self.failures.keys():
if self.time_dependent:
d = N.array([s(self.formula, time=t)
for s in self.subjects]).astype('<f8')
dshape = d.shape
dfile = file(tempfile.mkstemp(dir=self.cachedir)[1], 'w')
d.tofile(dfile)
dfile.close()
del(d)
self.design[t] = N.memmap(dfile.name,
dtype=N.dtype('<f8'),
shape=dshape)
elif first:
d = N.array([s(self.formula, time=t)
for s in self.subjects]).astype(N.float64)
self.design[t] = d
else:
self.design[t] = d
self.risk[t] = N.compress([s.atrisk(t) for s in self.subjects],
N.arange(self.design[t].shape[0]),axis=-1)
def __del__(self):
shutil.rmtree(self.cachedir, ignore_errors=True)
def logL(self, b, ties='breslow'):
logL = 0
for t in self.failures.keys():
fail = self.failures[t]
d = len(fail)
risk = self.risk[t]
Zb = N.dot(self.design[t], b)
logL += Zb[fail].sum()
if ties == 'breslow':
s = N.exp(Zb[risk]).sum()
logL -= N.log(N.exp(Zb[risk]).sum()) * d
elif ties == 'efron':
s = N.exp(Zb[risk]).sum()
r = N.exp(Zb[fail]).sum()
for j in range(d):
logL -= N.log(s - j * r / d)
elif ties == 'cox':
raise NotImplementedError, 'Cox tie breaking method not implemented'
else:
raise NotImplementedError, 'tie breaking method not recognized'
return logL
def score(self, b, ties='breslow'):
score = 0
for t in self.failures.keys():
fail = self.failures[t]
d = len(fail)
risk = self.risk[t]
Z = self.design[t]
score += Z[fail].sum()
if ties == 'breslow':
w = N.exp(N.dot(Z, b))
rv = discrete(Z[risk], w=w[risk])
score -= rv.mean() * d
elif ties == 'efron':
w = N.exp(N.dot(Z, b))
score += Z[fail].sum()
for j in range(d):
efron_w = w
efron_w[fail] -= i * w[fail] / d
rv = discrete(Z[risk], w=efron_w[risk])
score -= rv.mean()
elif ties == 'cox':
raise NotImplementedError, 'Cox tie breaking method not implemented'
else:
raise NotImplementedError, 'tie breaking method not recognized'
return N.array([score])
def information(self, b, ties='breslow'):
info = 0
score = 0
for t in self.failures.keys():
fail = self.failures[t]
d = len(fail)
risk = self.risk[t]
Z = self.design[t]
if ties == 'breslow':
w = N.exp(N.dot(Z, b))
rv = discrete(Z[risk], w=w[risk])
info += rv.cov()
elif ties == 'efron':
w = N.exp(N.dot(Z, b))
score += Z[fail].sum()
for j in range(d):
efron_w = w
efron_w[fail] -= i * w[fail] / d
rv = discrete(Z[risk], w=efron_w[risk])
info += rv.cov()
elif ties == 'cox':
raise NotImplementedError, 'Cox tie breaking method not implemented'
else:
raise NotImplementedError, 'tie breaking method not recognized'
return score
if __name__ == '__main__':
import numpy.random as R
n = 100
X = N.array([0]*n + [1]*n)
b = 0.4
lin = 1 + b*X
Y = R.standard_exponential((2*n,)) / lin
delta = R.binomial(1, 0.9, size=(2*n,))
subjects = [observation(Y[i], delta[i]) for i in range(2*n)]
for i in range(2*n):
subjects[i].X = X[i]
import scipy.sandbox.models.formula as F
x = F.quantitative('X')
f = F.formula(x)
c = coxph(subjects, f)
c.cache()
# c.newton([0.4])
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