# Source code for convoys.single

import numpy
from scipy.special import expit, logit
import scipy.stats
import warnings

__all__ = ['KaplanMeier']

class SingleModel:
pass  # TODO

[docs]class KaplanMeier(SingleModel):
''' Implementation of the Kaplan-Meier nonparametric method. '''
[docs]    def fit(self, B, T):
''' Fits the model

:param B: numpy vector of shape :math:n
:param T: numpy vector of shape :math:n
'''
# See https://www.math.wustl.edu/~sawyer/handouts/greenwood.pdf
BT = [(b, t) for b, t in zip(B, T)
if t >= 0 and 0 <= float(b) <= 1]
if len(BT) < len(B):
n_removed = len(B) - len(BT)
warnings.warn('Warning! Removed %d/%d entries from inputs where '
'T < 0 or B not 0/1' % (n_removed, len(B)))
B, T = ([z[i] for z in BT] for i in range(2))
n = len(T)
self._ts = [0.0]
self._ss = [1.0]
self._vs = [0.0]
sum_var_terms = 0.0
prod_s_terms = 1.0
for t, b in sorted(zip(T, B)):
d = float(b)
self._ts.append(t)
prod_s_terms *= 1 - d/n
self._ss.append(prod_s_terms)
if d == n == 1:
sum_var_terms = float('inf')
else:
sum_var_terms += d / (n*(n-d))
if sum_var_terms > 0:
self._vs.append(1 / numpy.log(prod_s_terms)**2 * sum_var_terms)
else:
self._vs.append(0)
n -= 1

# Just prevent overflow warning when computing the confidence interval
eps = 1e-9
self._ss_clipped = numpy.clip(self._ss, eps, 1.0-eps)

def _get_value_at(self, j, ci):
if ci:
z_lo, z_hi = scipy.stats.norm.ppf([(1-ci)/2, (1+ci)/2])
return (
1 - self._ss[j],
1 - numpy.exp(-numpy.exp(
numpy.log(-numpy.log(self._ss_clipped[j]))
+ z_hi * self._vs[j]**0.5)),
1 - numpy.exp(-numpy.exp(
numpy.log(-numpy.log(self._ss_clipped[j]))
+ z_lo * self._vs[j]**0.5))
)
else:
return 1 - self._ss[j]

def cdf(self, t, ci=None):
t = numpy.array(t)
res = numpy.zeros(t.shape + (3,) if ci else t.shape)
for indexes, value in numpy.ndenumerate(t):
j = numpy.searchsorted(self._ts, value, side='right') - 1
if j >= len(self._ts) - 1:
# Make the plotting stop at the last value of t
res[indexes] = [float('nan')]*3 if ci else float('nan')
else:
res[indexes] = self._get_value_at(j, ci)
return res