def smoothed_hazard_confidence_intervals_(self, bandwidth, hazard_=None):
"""
Parameter:
bandwidth: the bandwith to use in the Epanechnikov kernel.
hazard_: a computed (n,) numpy array of estimated hazard rates. If none, uses naf.smoothed_hazard_
"""
if hazard_ == None:
hazard_ = self.smoothed_hazard_(bandwidth).values[:, 0]
timeline = self.timeline
alpha2 = inv_normal_cdf(1 - (1 - self.alpha) / 2)
name = "smoothed-" + self.cumulative_hazard_.columns[0]
self._cumulative_sq.iloc[0] = 0
var_hazard_ = self._cumulative_sq.diff().fillna(self._cumulative_sq.iloc[0])
C = var_hazard_.values != 0.0 # only consider the points with jumps
std_hazard_ = np.sqrt(
1.0
/ (2 * bandwidth ** 2)
* np.dot(
epanechnikov_kernel(timeline[:, None], timeline[C][None, :], bandwidth) ** 2, var_hazard_.values[C]
)
)
values = {
"%s_upper_%.2f" % (name, self.alpha): hazard_ * np.exp(alpha2 * std_hazard_ / hazard_),
"%s_lower_%.2f" % (name, self.alpha): hazard_ * np.exp(-alpha2 * std_hazard_ / hazard_),
}
return pd.DataFrame(values, index=timeline)
def smoothed_hazards_(self, bandwidth=1):
"""
Using the epanechnikov kernel to smooth the hazard function, with sigma/bandwidth
"""
return pd.DataFrame(np.dot(epanechnikov_kernel(self.timeline[:, None], self.timeline, bandwidth), self.hazards_.values),
columns=self.hazards_.columns, index=self.timeline)
def smoothed_hazards_(self, bandwith=1):
"""
Using the epanechnikov kernel to smooth the hazard function, with sigma/bandwith
"""
C = self.censorship.astype(bool)
return pd.DataFrame( np.dot(epanechnikov_kernel(self.timeline[:,None], self.timeline[C],bandwith), self.hazards_.values[C,:]),
columns=self.hazards_.columns, index=self.timeline)
def smoothed_hazards_(self, bandwidth=1):
"""
Using the epanechnikov kernel to smooth the hazard function, with sigma/bandwidth
"""
return pd.DataFrame(np.dot(
epanechnikov_kernel(self.timeline[:, None], self.timeline,
bandwidth), self.hazards_.values),
columns=self.hazards_.columns,
index=self.timeline)
def smoothed_hazard_(self, bandwidth):
"""
bandwidth: the bandwith used in the Epanechnikov kernel.
"""
timeline = self.timeline
cumulative_hazard_name = self.cumulative_hazard_.columns[0]
hazard_name = "smoothed-" + cumulative_hazard_name
hazard_ = self.cumulative_hazard_.diff().fillna(self.cumulative_hazard_.iloc[0] )
C = (hazard_[cumulative_hazard_name] != 0.0).values
return pd.DataFrame( 1./(2*bandwidth)*np.dot(epanechnikov_kernel(timeline[:,None], timeline[C][None,:],bandwidth), hazard_.values[C,:]),
columns=[hazard_name], index=timeline)
def smoothed_hazard_(self, bandwidth):
"""
Parameters:
bandwidth: the bandwith used in the Epanechnikov kernel.
Returns:
a DataFrame of the smoothed hazard
"""
timeline = self.timeline
cumulative_hazard_name = self.cumulative_hazard_.columns[0]
hazard_name = "differenced-" + cumulative_hazard_name
hazard_ = self.cumulative_hazard_.diff().fillna(self.cumulative_hazard_.iloc[0])
C = (hazard_[cumulative_hazard_name] != 0.0).values
return pd.DataFrame(1. / bandwidth * np.dot(epanechnikov_kernel(timeline[:, None], timeline[C][None, :], bandwidth), hazard_.values[C, :]),
columns=[hazard_name], index=timeline)
def smoothed_hazard_confidence_intervals_(self, bandwidth, hazard_=None):
"""
Parameter:
bandwidth: the bandwith to use in the Epanechnikov kernel.
hazard_: a computed (n,) numpy array of estimated hazard rates. If none, uses naf.smoothed_hazard_
"""
if hazard_ is None:
hazard_ = self.smoothed_hazard_(bandwidth).values[:, 0]
timeline = self.timeline
alpha2 = inv_normal_cdf(1 - (1 - self.alpha) / 2)
self._cumulative_sq.iloc[0] = 0
var_hazard_ = self._cumulative_sq.diff().fillna(self._cumulative_sq.iloc[0])
C = (var_hazard_.values != 0.0) # only consider the points with jumps
std_hazard_ = np.sqrt(1. / (bandwidth ** 2) * np.dot(epanechnikov_kernel(timeline[:, None], timeline[C][None, :], bandwidth) ** 2, var_hazard_.values[C]))
values = {
self.ci_labels[0]: hazard_ * np.exp(alpha2 * std_hazard_ / hazard_),
self.ci_labels[1]: hazard_ * np.exp(-alpha2 * std_hazard_ / hazard_)
}
return pd.DataFrame(values, index=timeline)
