def KM_median(array,
upper_lim_flags,
left_censor=True,
return_type='percentile'):
kmf = KaplanMeierFitter()
if upper_lim_flags is not None:
if left_censor == True:
kmf.fit_left_censoring(array, upper_lim_flags)
else:
kmf.fit(array, event_observed=upper_lim_flags) #right censoring
else:
kmf.fit(array, upper_lim_flags)
median = median_survival_times(kmf.survival_function_)
if return_type == 'percentile':
upper_perc = kmf.percentile(0.25)
lower_perc = kmf.percentile(0.75)
print(
f'median and 1st/3rd quartiles: {median}, {lower_perc}, {upper_perc}'
)
return median, upper_perc, lower_perc
elif return_type == 'ci':
median_ci = median_survival_times(kmf.confidence_interval_).values
print(f'median and CI: {median}, {median_ci}')
return median, median_ci[0][0], median_ci[0][1]
elif return_type == 'median':
return median
def fit(self, durations, event_observed=None, timeline=None, entry=None, label='KM_estimate',
alpha=None, left_censorship=False, ci_labels=None):
"""
Parameters:
duration: an array, or pd.Series, of length n -- duration subject was observed for
timeline: return the best estimate at the values in timelines (postively increasing)
event_observed: an array, or pd.Series, of length n -- True if the the death was observed, False if the event
was lost (right-censored). Defaults all True if event_observed==None
entry: an array, or pd.Series, of length n -- relative time when a subject entered the study. This is
useful for left-truncated (not left-censored) observations. If None, all members of the population
were born at time 0.
label: a string to name the column of the estimate.
alpha: the alpha value in the confidence intervals. Overrides the initializing
alpha for this call to fit only.
left_censorship: True if durations and event_observed refer to left censorship events. Default False
ci_labels: add custom column names to the generated confidence intervals
as a length-2 list: [<lower-bound name>, <upper-bound name>]. Default: <label>_lower_<alpha>
Returns:
self, with new properties like 'survival_function_'.
"""
# if the user is interested in left-censorship, we return the cumulative_density_, no survival_function_,
estimate_name = 'survival_function_' if not left_censorship else 'cumulative_density_'
v = _preprocess_inputs(durations, event_observed, timeline, entry)
self.durations, self.event_observed, self.timeline, self.entry, self.event_table = v
self._label = label
alpha = alpha if alpha else self.alpha
log_survival_function, cumulative_sq_ = _additive_estimate(self.event_table, self.timeline,
self._additive_f, self._additive_var,
left_censorship)
if entry is not None:
# a serious problem with KM is that when the sample size is small and there are too few early
# truncation times, it may happen that is the number of patients at risk and the number of deaths is the same.
# we adjust for this using the Breslow-Fleming-Harrington estimator
n = self.event_table.shape[0]
net_population = (self.event_table['entrance'] - self.event_table['removed']).cumsum()
if net_population.iloc[:int(n / 2)].min() == 0:
ix = net_population.iloc[:int(n / 2)].argmin()
raise StatError("""There are too few early truncation times and too many events. S(t)==0 for all t>%.1f. Recommend BreslowFlemingHarringtonFitter.""" % ix)
# estimation
setattr(self, estimate_name, pd.DataFrame(np.exp(log_survival_function), columns=[self._label]))
self.__estimate = getattr(self, estimate_name)
self.confidence_interval_ = self._bounds(cumulative_sq_[:, None], alpha, ci_labels)
self.median_ = median_survival_times(self.__estimate)
# estimation methods
self.predict = self._predict(estimate_name, label)
self.subtract = self._subtract(estimate_name)
self.divide = self._divide(estimate_name)
# plotting functions
self.plot = self._plot_estimate(estimate_name)
setattr(self, "plot_" + estimate_name, self.plot)
self.plot_loglogs = plot_loglogs(self)
return self
def __init__(self, time, events, label=None, color=None):
self._kmf = KaplanMeierFitter().fit(time.astype(np.float64),
events.astype(np.float64))
self._label: str = label
self.color: List[int] = color
# refactor this
time, survival = self._kmf.survival_function_.reset_index(
).values.T.tolist()
lower, upper = self._kmf.confidence_interval_.values.T.tolist()
self.x, self.y = self.generate_curve_coordinates(time, survival)
_, self.lower_bound = self.generate_curve_coordinates(time, lower)
_, self.upper_bound = self.generate_curve_coordinates(time, upper)
# Estimated function curve
self.estimated_fun = pg.PlotDataItem(self.x,
self.y,
pen=self.get_pen())
# Lower and upper confidence intervals
pen = self.get_pen(width=1, alpha=70)
self.lower_conf_limit = pg.PlotDataItem(self.x,
self.lower_bound,
pen=pen)
self.upper_conf_limit = pg.PlotDataItem(self.x,
self.upper_bound,
pen=pen)
self.confidence_interval = pg.FillBetweenItem(
self.upper_conf_limit,
self.lower_conf_limit,
brush=self.get_color(alpha=50))
self.selection = pg.PlotDataItem(
pen=mkPen(color=QColor(Qt.yellow), width=4))
self.selection.hide()
self.median_survival = median = np.round(
median_survival_times(
self._kmf.survival_function_.astype(np.float32)), 1)
self.median_vertical = pg.PlotDataItem(
x=(median, median),
y=(0, 0.5),
pen=pg.mkPen(**MEDIAN_LINE_PEN_STYLE))
censored_data = self.get_censored_data()
self.censored_data = pg.ScatterPlotItem(
x=censored_data[:, 0],
y=censored_data[:, 1],
brush=QBrush(Qt.black),
pen=self.get_pen(width=1, alpha=255),
symbol=create_line_symbol(),
size=15,
)
self.censored_data.setZValue(10)
self.num_of_samples = len(events)
self.num_of_censored_samples = len(censored_data)
def fit(self, durations, event_observed=None, timeline=None, entry=None, label='KM_estimate',
alpha=None, left_censorship=False, ci_labels=None):
"""
Parameters:
duration: an array, or pd.Series, of length n -- duration subject was observed for
timeline: return the best estimate at the values in timelines (postively increasing)
event_observed: an array, or pd.Series, of length n -- True if the the death was observed, False if the event
was lost (right-censored). Defaults all True if event_observed==None
entry: an array, or pd.Series, of length n -- relative time when a subject entered the study. This is
useful for left-truncated (not left-censored) observations. If None, all members of the population
were born at time 0.
label: a string to name the column of the estimate.
alpha: the alpha value in the confidence intervals. Overrides the initializing
alpha for this call to fit only.
left_censorship: True if durations and event_observed refer to left censorship events. Default False
ci_labels: add custom column names to the generated confidence intervals
as a length-2 list: [<lower-bound name>, <upper-bound name>]. Default: <label>_lower_<alpha>
Returns:
self, with new properties like 'survival_function_'.
"""
# if the user is interested in left-censorship, we return the cumulative_density_, no survival_function_,
estimate_name = 'survival_function_' if not left_censorship else 'cumulative_density_'
v = _preprocess_inputs(durations, event_observed, timeline, entry)
self.durations, self.event_observed, self.timeline, self.entry, self.event_table = v
self._label = label
alpha = alpha if alpha else self.alpha
log_survival_function, cumulative_sq_ = _additive_estimate(self.event_table, self.timeline,
self._additive_f, self._additive_var,
left_censorship)
if entry is not None:
# a serious problem with KM is that when the sample size is small and there are too few early
# truncation times, it may happen that is the number of patients at risk and the number of deaths is the same.
# we adjust for this using the Breslow-Fleming-Harrington estimator
n = self.event_table.shape[0]
net_population = (self.event_table['entrance'] - self.event_table['removed']).cumsum()
if net_population.iloc[:int(n / 2)].min() == 0:
ix = net_population.iloc[:int(n / 2)].argmin()
raise StatError("""There are too few early truncation times and too many events. S(t)==0 for all t>%.1f. Recommend BreslowFlemingHarringtonFitter.""" % ix)
# estimation
setattr(self, estimate_name, pd.DataFrame(np.exp(log_survival_function), columns=[self._label]))
self.__estimate = getattr(self, estimate_name)
self.confidence_interval_ = self._bounds(cumulative_sq_[:, None], alpha, ci_labels)
self.median_ = median_survival_times(self.__estimate)
# estimation methods
self.predict = self._predict(estimate_name, label)
self.subtract = self._subtract(estimate_name)
self.divide = self._divide(estimate_name)
# plotting functions
self.plot = self._plot_estimate(estimate_name)
setattr(self, "plot_" + estimate_name, self.plot)
return self
def fit(self,
durations,
event_observed=None,
timeline=None,
entry=None,
label='BFH_estimate',
alpha=None,
ci_labels=None):
"""
Parameters:
duration: an array, or pd.Series, of length n -- duration subject was observed for
timeline: return the best estimate at the values in timelines (postively increasing)
event_observed: an array, or pd.Series, of length n -- True if the the death was observed, False if the event
was lost (right-censored). Defaults all True if event_observed==None
entry: an array, or pd.Series, of length n -- relative time when a subject entered the study. This is
useful for left-truncated observations, i.e the birth event was not observed.
If None, defaults to all 0 (all birth events observed.)
label: a string to name the column of the estimate.
alpha: the alpha value in the confidence intervals. Overrides the initializing
alpha for this call to fit only.
ci_labels: add custom column names to the generated confidence intervals
as a length-2 list: [<lower-bound name>, <upper-bound name>]. Default: <label>_lower_<alpha>
Returns:
self, with new properties like 'survival_function_'.
"""
self._label = label
alpha = alpha if alpha is not None else self.alpha
naf = NelsonAalenFitter(alpha)
naf.fit(durations,
event_observed=event_observed,
timeline=timeline,
label=label,
entry=entry,
ci_labels=ci_labels)
self.durations, self.event_observed, self.timeline, self.entry, self.event_table = \
naf.durations, naf.event_observed, naf.timeline, naf.entry, naf.event_table
# estimation
self.survival_function_ = np.exp(-naf.cumulative_hazard_)
self.confidence_interval_ = np.exp(-naf.confidence_interval_)
self.median_ = median_survival_times(self.survival_function_)
# estimation methods
self.predict = self._predict("survival_function_", label)
self.subtract = self._subtract("survival_function_")
self.divide = self._divide("survival_function_")
# plotting functions
self.plot = self._plot_estimate("survival_function_")
self.plot_survival_function = self.plot
return self
def predict_50(conditioned_sf):
# Predict the month number where the survival chance of customer is 50%
# This can also be modified as predictions_50 = qth_survival_times(.50, conditioned_sf),
# where the percentile can be modified depending on our requirement
predictions_50 = median_survival_times(conditioned_sf)
'''
### predictions_50
Predicting the month at which the survival chance of the customer is 50%
'''
st.write(predictions_50[[customer]])
return predictions_50
def fit(self, durations, event_observed=None, timeline=None, entry=None,
label='BFH_estimate', alpha=None, ci_labels=None):
"""
Parameters:
duration: an array, or pd.Series, of length n -- duration subject was observed for
timeline: return the best estimate at the values in timelines (postively increasing)
event_observed: an array, or pd.Series, of length n -- True if the the death was observed, False if the event
was lost (right-censored). Defaults all True if event_observed==None
entry: an array, or pd.Series, of length n -- relative time when a subject entered the study. This is
useful for left-truncated observations, i.e the birth event was not observed.
If None, defaults to all 0 (all birth events observed.)
label: a string to name the column of the estimate.
alpha: the alpha value in the confidence intervals. Overrides the initializing
alpha for this call to fit only.
ci_labels: add custom column names to the generated confidence intervals
as a length-2 list: [<lower-bound name>, <upper-bound name>]. Default: <label>_lower_<alpha>
Returns:
self, with new properties like 'survival_function_'.
"""
self._label = label
alpha = alpha if alpha is not None else self.alpha
naf = NelsonAalenFitter(alpha)
naf.fit(durations, event_observed=event_observed, timeline=timeline, label=label, entry=entry, ci_labels=ci_labels)
self.durations, self.event_observed, self.timeline, self.entry, self.event_table = \
naf.durations, naf.event_observed, naf.timeline, naf.entry, naf.event_table
# estimation
self.survival_function_ = np.exp(-naf.cumulative_hazard_)
self.confidence_interval_ = np.exp(-naf.confidence_interval_)
self.median_ = median_survival_times(self.survival_function_)
# estimation methods
self.predict = self._predict("survival_function_", label)
self.subtract = self._subtract("survival_function_")
self.divide = self._divide("survival_function_")
# plotting functions
self.plot = self._plot_estimate("survival_function_")
self.plot_survival_function = self.plot
return self
def predict_50(conditioned_sf):
# Predict the month number where the survival chance of customer is 50%
# This can also be modified as predictions_50 = qth_survival_times(.50, conditioned_sf),
# where the percentile can be modified depending on our requirement
predictions_50 = median_survival_times(conditioned_sf)
return predictions_50
def fit(
self,
durations,
event_observed=None,
timeline=None,
entry=None,
label="KM_estimate",
alpha=None,
left_censorship=False,
ci_labels=None,
weights=None,
): # pylint: disable=too-many-arguments,too-many-locals
"""
Parameters
----------
duration: an array, or pd.Series, of length n -- duration subject was observed for
timeline: return the best estimate at the values in timelines (postively increasing)
event_observed: an array, or pd.Series, of length n -- True if the the death was observed, False if the event
was lost (right-censored). Defaults all True if event_observed==None
entry: an array, or pd.Series, of length n -- relative time when a subject entered the study. This is
useful for left-truncated (not left-censored) observations. If None, all members of the population
were born at time 0.
label: a string to name the column of the estimate.
alpha: the alpha value in the confidence intervals. Overrides the initializing
alpha for this call to fit only.
left_censorship: True if durations and event_observed refer to left censorship events. Default False
ci_labels: add custom column names to the generated confidence intervals
as a length-2 list: [<lower-bound name>, <upper-bound name>]. Default: <label>_lower_<alpha>
weights: n array, or pd.Series, of length n, if providing a weighted dataset. For example, instead
of providing every subject as a single element of `durations` and `event_observed`, one could
weigh subject differently.
Returns
-------
self: KaplanMeierFitter
self with new properties like 'survival_function_'.
"""
check_nans_or_infs(durations)
if event_observed is not None:
check_nans_or_infs(event_observed)
if weights is not None:
if (weights.astype(int) != weights).any():
warnings.warn(
"""It looks like your weights are not integers, possibly prospenity scores then?
It's important to know that the naive variance estimates of the coefficients are biased. Instead use Monte Carlo to
estimate the variances. See paper "Variance estimation when using inverse probability of treatment weighting (IPTW) with survival analysis"
or "Adjusted Kaplan-Meier estimator and log-rank test with inverse probability of treatment weighting for survival data."
""",
StatisticalWarning,
)
# if the user is interested in left-censorship, we return the cumulative_density_, no survival_function_,
estimate_name = "survival_function_" if not left_censorship else "cumulative_density_"
v = _preprocess_inputs(durations, event_observed, timeline, entry,
weights)
self.durations, self.event_observed, self.timeline, self.entry, self.event_table = v
self._label = label
alpha = alpha if alpha else self.alpha
log_survival_function, cumulative_sq_ = _additive_estimate(
self.event_table, self.timeline, self._additive_f,
self._additive_var, left_censorship)
if entry is not None:
# a serious problem with KM is that when the sample size is small and there are too few early
# truncation times, it may happen that is the number of patients at risk and the number of deaths is the same.
# we adjust for this using the Breslow-Fleming-Harrington estimator
n = self.event_table.shape[0]
net_population = (self.event_table["entrance"] -
self.event_table["removed"]).cumsum()
if net_population.iloc[:int(n / 2)].min() == 0:
ix = net_population.iloc[:int(n / 2)].idxmin()
raise StatError(
"""There are too few early truncation times and too many events. S(t)==0 for all t>%.1f. Recommend BreslowFlemingHarringtonFitter."""
% ix)
# estimation
setattr(
self, estimate_name,
pd.DataFrame(np.exp(log_survival_function), columns=[self._label]))
self.__estimate = getattr(self, estimate_name)
self.confidence_interval_ = self._bounds(cumulative_sq_[:, None],
alpha, ci_labels)
self.median_ = median_survival_times(self.__estimate,
left_censorship=left_censorship)
# estimation methods
self._estimation_method = estimate_name
self._estimate_name = estimate_name
self._predict_label = label
self._update_docstrings()
# plotting functions
setattr(self, "plot_" + estimate_name, self.plot)
return self
# print(df)
print(df.head(),'\n')
print(df['T'].min(), df['T'].max(),'\n')
print(df['E'].value_counts(),'\n')
print(df['group'].value_counts(),'\n')
kmf = KaplanMeierFitter()
kmf.fit(df['T'], event_observed=df['E'])
# kmf.plot_survival_function()
ax=kmf.survival_function_.plot()
#共享一个画布
ax=kmf.plot(ax=ax)
median_ = kmf.median_survival_time_
median_confidence_interval_ = median_survival_times(kmf.confidence_interval_)
print(median_confidence_interval_)
groups = df['group']
ix = (groups == 'largeAmount')
kmf.fit(df['T'][ix], df['E'][ix], label='largeAmount')
ax=kmf.survival_function_.plot(ax=ax)
ax = kmf.plot(ax=ax)
# plt.show()
treatment_median_confidence_interval_ = median_survival_times(kmf.confidence_interval_)
print("使用量基数较大的音乐存活50%对应的存活时间95%置信区间：'\n'", treatment_median_confidence_interval_, '\n')
kmf.fit(df['T'][~ix], df['E'][~ix], label='smallAmount')
ax=kmf.survival_function_.plot(ax=ax)
ax = kmf.plot(ax=ax)
# plt.show()
def fit_interval_censoring(
self,
lower_bound,
upper_bound,
event_observed=None,
timeline=None,
label=None,
alpha=None,
ci_labels=None,
entry=None,
weights=None,
tol: float = 1e-5,
show_progress: bool = False,
**kwargs,
) -> "KaplanMeierFitter":
"""
Fit the model to a interval-censored dataset using non-parametric MLE. This estimator is
also called the Turnbull Estimator.
Currently, only closed interval are supported. However, it's easy to create open intervals by adding (or subtracting) a very small
value from the lower-bound (or upper bound). For example, the following turns closed intervals into open intervals.
>>> left, right = df['left'], df['right']
>>> KaplanMeierFitter().fit_interval_censoring(left + 0.00001, right - 0.00001)
Note
------
This is new and experimental, and many features are missing.
Parameters
----------
lower_bound: an array, list, pd.DataFrame or pd.Series
length n -- lower bound of observations
upper_bound: an array, list, pd.DataFrame or pd.Series
length n -- upper bound of observations
event_observed: an array, list, pd.DataFrame, or pd.Series, optional
True if the the death was observed, False if the event was lost (right-censored). This can be computed from
the lower_bound and upper_bound, and can be left blank.
timeline: an array, list, pd.DataFrame, or pd.Series, optional
return the best estimate at the values in timelines (positively increasing)
entry: an array, list, pd.DataFrame, or pd.Series, optional
relative time when a subject entered the study. This is useful for left-truncated (not left-censored) observations. If None, all members of the population
entered study when they were "born".
label: string, optional
a string to name the column of the estimate.
alpha: float, optional
the alpha value in the confidence intervals. Overrides the initializing alpha for this call to fit only.
ci_labels: tuple, optional
add custom column names to the generated confidence intervals as a length-2 list: [<lower-bound name>, <upper-bound name>]. Default: <label>_lower_<1-alpha/2>
weights: an array, list, pd.DataFrame, or pd.Series, optional
if providing a weighted dataset. For example, instead
of providing every subject as a single element of `durations` and `event_observed`, one could
weigh subject differently.
tol: float, optional
minimum difference in log likelihood changes for iterative algorithm.
show_progress: bool, optional
display information during fitting.
Returns
-------
self: KaplanMeierFitter
self with new properties like ``survival_function_``, ``plot()``, ``median_survival_time_``
"""
if entry is not None:
raise NotImplementedError("entry is not supported yet")
if weights is None:
weights = np.ones_like(upper_bound)
self.weights = np.asarray(weights)
self.upper_bound = np.atleast_1d(
pass_for_numeric_dtypes_or_raise_array(upper_bound))
self.lower_bound = np.atleast_1d(
pass_for_numeric_dtypes_or_raise_array(lower_bound))
check_nans_or_infs(self.lower_bound)
self.event_observed = self.lower_bound == self.upper_bound
self.timeline = coalesce(
timeline,
np.unique(np.concatenate((self.upper_bound, self.lower_bound))))
if (self.upper_bound < self.lower_bound).any():
raise ValueError(
"All upper_bound times must be greater than or equal to lower_bound times."
)
if event_observed is None:
event_observed = self.upper_bound == self.lower_bound
if ((self.lower_bound == self.upper_bound) != event_observed).any():
raise ValueError(
"For all rows, lower_bound == upper_bound if and only if event observed = 1 (uncensored). Likewise, lower_bound < upper_bound if and only if event observed = 0 (censored)"
)
self._label = coalesce(label, self._label, "NPMLE_estimate")
results = npmle(self.lower_bound,
self.upper_bound,
verbose=show_progress,
tol=tol,
weights=weights,
**kwargs)
self.survival_function_ = reconstruct_survival_function(
*results, self.timeline, label=self._label).loc[self.timeline]
self.cumulative_density_ = 1 - self.survival_function_
self._median = median_survival_times(self.survival_function_)
"""
self.confidence_interval_ = npmle_compute_confidence_intervals(self.lower_bound, self.upper_bound, self.survival_function_, self.alpha)
self.confidence_interval_survival_function_ = self.confidence_interval_
self.confidence_interval_cumulative_density_ = 1 - self.confidence_interval_
"""
# estimation methods
self._estimation_method = "survival_function_"
self._estimate_name = "survival_function_"
return self
def fit_interval_censoring(
self,
lower_bound,
upper_bound,
event_observed=None,
timeline=None,
label=None,
alpha=None,
ci_labels=None,
show_progress=False,
entry=None,
weights=None,
tol=1e-7,
) -> "KaplanMeierFitter":
"""
Fit the model to a interval-censored dataset using non-parametric MLE. This estimator is
also called the Turball Estimator.
Note
------
This is new and experimental, and many feature are missing.
Parameters
----------
lower_bound: an array, list, pd.DataFrame or pd.Series
length n -- lower bound of observations
upper_bound: an array, list, pd.DataFrame or pd.Series
length n -- upper bound of observations
event_observed: an array, list, pd.DataFrame, or pd.Series, optional
True if the the death was observed, False if the event was lost (right-censored). This can be computed from
the lower_bound and upper_bound, and can be left blank.
timeline: an array, list, pd.DataFrame, or pd.Series, optional
return the best estimate at the values in timelines (positively increasing)
entry: an array, list, pd.DataFrame, or pd.Series, optional
relative time when a subject entered the study. This is useful for left-truncated (not left-censored) observations. If None, all members of the population
entered study when they were "born".
label: string, optional
a string to name the column of the estimate.
alpha: float, optional
the alpha value in the confidence intervals. Overrides the initializing alpha for this call to fit only.
ci_labels: tuple, optional
add custom column names to the generated confidence intervals as a length-2 list: [<lower-bound name>, <upper-bound name>]. Default: <label>_lower_<1-alpha/2>
weights: an array, list, pd.DataFrame, or pd.Series, optional
if providing a weighted dataset. For example, instead
of providing every subject as a single element of `durations` and `event_observed`, one could
weigh subject differently.
Returns
-------
self: KaplanMeierFitter
self with new properties like ``survival_function_``, ``plot()``, ``median_survival_time_``
"""
warnings.warn(
"This is new and experimental, many feature are missing and accuracy is not reliable",
UserWarning)
if entry is not None or weights is not None:
raise NotImplementedError("entry / weights is not supported yet")
self.weights = np.ones_like(upper_bound)
self.upper_bound = np.atleast_1d(
pass_for_numeric_dtypes_or_raise_array(upper_bound))
self.lower_bound = np.atleast_1d(
pass_for_numeric_dtypes_or_raise_array(lower_bound))
check_nans_or_infs(self.lower_bound)
self.event_observed = self.lower_bound == self.upper_bound
self.timeline = coalesce(
timeline,
np.unique(np.concatenate((self.upper_bound, self.lower_bound))))
if (self.upper_bound < self.lower_bound).any():
raise ValueError(
"All upper_bound times must be greater than or equal to lower_bound times."
)
if event_observed is None:
event_observed = self.upper_bound == self.lower_bound
if ((self.lower_bound == self.upper_bound) != event_observed).any():
raise ValueError(
"For all rows, lower_bound == upper_bound if and only if event observed = 1 (uncensored). Likewise, lower_bound < upper_bound if and only if event observed = 0 (censored)"
)
self._label = coalesce(label, self._label, "NPMLE_estimate")
probs, t_intervals = npmle(self.lower_bound,
self.upper_bound,
verbose=show_progress)
self.survival_function_ = reconstruct_survival_function(
probs, t_intervals, self.timeline,
label=self._label).loc[self.timeline]
self.cumulative_density_ = 1 - self.survival_function_
self._median = median_survival_times(self.survival_function_)
self.percentile = functools.partial(
qth_survival_time,
model_or_survival_function=self.survival_function_)
"""
self.confidence_interval_ = npmle_compute_confidence_intervals(self.lower_bound, self.upper_bound, self.survival_function_, self.alpha)
self.confidence_interval_survival_function_ = self.confidence_interval_
self.confidence_interval_cumulative_density_ = 1 - self.confidence_interval_
"""
# estimation methods
self._estimation_method = "survival_function_"
self._estimate_name = "survival_function_"
self._update_docstrings()
return self
def test_median_accepts_series():
sv = pd.Series(1 - np.linspace(0, 1, 1000))
assert utils.median_survival_times(sv) == 500
def _fit(
self,
durations,
event_observed=None,
timeline=None,
entry=None,
label="KM_estimate",
alpha=None,
ci_labels=None,
weights=None,
): # pylint: disable=too-many-arguments,too-many-locals
"""
Parameters
----------
durations: an array, list, pd.DataFrame or pd.Series
length n -- duration subject was observed for
event_observed: an array, list, pd.DataFrame, or pd.Series, optional
True if the the death was observed, False if the event was lost (right-censored). Defaults all True if event_observed==None
timeline: an array, list, pd.DataFrame, or pd.Series, optional
return the best estimate at the values in timelines (postively increasing)
entry: an array, list, pd.DataFrame, or pd.Series, optional
relative time when a subject entered the study. This is useful for left-truncated (not left-censored) observations. If None, all members of the population
entered study when they were "born".
label: string, optional
a string to name the column of the estimate.
alpha: float, optional
the alpha value in the confidence intervals. Overrides the initializing alpha for this call to fit only.
left_censorship: bool, optional (default=False)
True if durations and event_observed refer to left censorship events. Default False
ci_labels: tuple, optional
add custom column names to the generated confidence intervals as a length-2 list: [<lower-bound name>, <upper-bound name>]. Default: <label>_lower_<1-alpha/2>
weights: an array, list, pd.DataFrame, or pd.Series, optional
if providing a weighted dataset. For example, instead
of providing every subject as a single element of `durations` and `event_observed`, one could
weigh subject differently.
Returns
-------
self: KaplanMeierFitter
self with new properties like ``survival_function_``, ``plot()``, ``median``
"""
self._check_values(durations)
if event_observed is not None:
self._check_values(event_observed)
self._label = label
if weights is not None:
weights = np.asarray(weights)
if (weights.astype(int) != weights).any():
warnings.warn(
"""It looks like your weights are not integers, possibly propensity scores then?
It's important to know that the naive variance estimates of the coefficients are biased. Instead use Monte Carlo to
estimate the variances. See paper "Variance estimation when using inverse probability of treatment weighting (IPTW) with survival analysis"
or "Adjusted Kaplan-Meier estimator and log-rank test with inverse probability of treatment weighting for survival data."
""",
StatisticalWarning,
)
# if the user is interested in left-censorship, we return the cumulative_density_, no survival_function_,
is_left_censoring = CensoringType.is_left_censoring(self)
primary_estimate_name = "survival_function_" if not is_left_censoring else "cumulative_density_"
secondary_estimate_name = "cumulative_density_" if not is_left_censoring else "survival_function_"
self.durations, self.event_observed, self.timeline, self.entry, self.event_table = _preprocess_inputs(
durations, event_observed, timeline, entry, weights
)
alpha = alpha if alpha else self.alpha
log_estimate, cumulative_sq_ = _additive_estimate(
self.event_table, self.timeline, self._additive_f, self._additive_var, is_left_censoring
)
if entry is not None:
# a serious problem with KM is that when the sample size is small and there are too few early
# truncation times, it may happen that is the number of patients at risk and the number of deaths is the same.
# we adjust for this using the Breslow-Fleming-Harrington estimator
n = self.event_table.shape[0]
net_population = (self.event_table["entrance"] - self.event_table["removed"]).cumsum()
if net_population.iloc[: int(n / 2)].min() == 0:
ix = net_population.iloc[: int(n / 2)].idxmin()
raise StatError(
"""There are too few early truncation times and too many events. S(t)==0 for all t>%g. Recommend BreslowFlemingHarringtonFitter."""
% ix
)
# estimation
setattr(self, primary_estimate_name, pd.DataFrame(np.exp(log_estimate), columns=[self._label]))
setattr(self, secondary_estimate_name, pd.DataFrame(1 - np.exp(log_estimate), columns=[self._label]))
self.__estimate = getattr(self, primary_estimate_name)
self.confidence_interval_ = self._bounds(cumulative_sq_[:, None], alpha, ci_labels)
self.median_ = median_survival_times(self.__estimate, left_censorship=is_left_censoring)
self._cumulative_sq_ = cumulative_sq_
setattr(self, "confidence_interval_" + primary_estimate_name, self.confidence_interval_)
setattr(self, "confidence_interval_" + secondary_estimate_name, 1 - self.confidence_interval_)
# estimation methods
self._estimation_method = primary_estimate_name
self._estimate_name = primary_estimate_name
self._update_docstrings()
return self
ax.spines['right'].set_visible(False) ax.spines['top'].set_visible(False) add_at_risk_counts(12, kmf_overall, labels=None) leg_1 = Line2D([0], [0], color='grey', ls='--') leg_2 = Line2D([0], [0], color='blue', marker='|', ms=10) leg = [leg_1, leg_2] leg_lab = ['Due Date', 'Censored'] plt.legend(leg, leg_lab, fontsize=20) #plt.savefig(parent + '/Figures/survival_with_censor.png') # - #This provides the values for the 95% CI at the median from lifelines.utils import median_survival_times median_survival_times(kmf_overall.confidence_interval_) # + #The proportion reported any day can be checked by running this code and editing the value in loc[]: print(kmf_overall.survival_function_.loc[796]['KM_estimate']) print(kmf_overall.survival_function_.loc[815]['KM_estimate']) #If you are interested in the full data produced by the survival function you can view it here: surv_func = kmf_overall.survival_function_ surv_func.head() # - #Similarly, the upper and lower condifence interval values can be checked by editing the value in loc[]: kmf_overall.confidence_interval_survival_function_.loc[412] # +
from lifelines.datasets import load_waltons from lifelines import KaplanMeierFitter from lifelines.utils import median_survival_times df = load_waltons() print(df.head(),'\n') print(df['T'].min(), df['T'].max(),'\n') print(df['E'].value_counts(),'\n') print(df['group'].value_counts(),'\n') kmf = KaplanMeierFitter() kmf.fit(df['T'], event_observed=df['E']) kmf.plot_survival_function() median_ = kmf.median_survival_time_ median_confidence_interval_ = median_survival_times(kmf.confidence_interval_) print(median_confidence_interval_)
def test_median():
sv = pd.DataFrame(1 - np.linspace(0, 1, 1000))
assert utils.median_survival_times(sv) == 500
def median_(self):
"""
Return the unique time point, t, such that S(t) = 0.5. This is the "half-life" of the population, and a
robust summary statistic for the population, if it exists.
"""
return median_survival_times(self.survival_function_)
def _fit(self,
durations,
event_observed=None,
timeline=None,
entry=None,
label=None,
alpha=None,
ci_labels=None,
weights=None): # pylint: disable=too-many-arguments,too-many-locals
"""
Parameters
----------
durations: an array, list, pd.DataFrame or pd.Series
length n -- duration subject was observed for
event_observed: an array, list, pd.DataFrame, or pd.Series, optional
True if the the death was observed, False if the event was lost (right-censored). Defaults all True if event_observed==None
timeline: an array, list, pd.DataFrame, or pd.Series, optional
return the best estimate at the values in timelines (positively increasing)
entry: an array, list, pd.DataFrame, or pd.Series, optional
relative time when a subject entered the study. This is useful for left-truncated (not left-censored) observations. If None, all members of the population
entered study when they were "born".
label: string, optional
a string to name the column of the estimate.
alpha: float, optional
the alpha value in the confidence intervals. Overrides the initializing alpha for this call to fit only.
ci_labels: tuple, optional
add custom column names to the generated confidence intervals as a length-2 list: [<lower-bound name>, <upper-bound name>]. Default: <label>_lower_<1-alpha/2>
weights: an array, list, pd.DataFrame, or pd.Series, optional
if providing a weighted dataset. For example, instead
of providing every subject as a single element of `durations` and `event_observed`, one could
weigh subject differently.
Returns
-------
self: KaplanMeierFitter
self with new properties like ``survival_function_``, ``plot()``, ``median_survival_time_``
"""
durations = np.asarray(durations)
self._check_values(durations)
if event_observed is not None:
event_observed = np.asarray(event_observed)
self._check_values(event_observed)
self._label = coalesce(label, self._label, "KM_estimate")
if weights is not None:
weights = np.asarray(weights)
if (weights.astype(int) != weights).any():
warnings.warn(
"""It looks like your weights are not integers, possibly propensity scores then?
It's important to know that the naive variance estimates of the coefficients are biased. Instead use Monte Carlo to
estimate the variances. See paper "Variance estimation when using inverse probability of treatment weighting (IPTW) with survival analysis"
or "Adjusted Kaplan-Meier estimator and log-rank test with inverse probability of treatment weighting for survival data."
""",
StatisticalWarning,
)
else:
weights = np.ones_like(durations, dtype=float)
# if the user is interested in left-censorship, we return the cumulative_density_, no survival_function_,
is_left_censoring = CensoringType.is_left_censoring(self)
primary_estimate_name = "survival_function_" if not is_left_censoring else "cumulative_density_"
secondary_estimate_name = "cumulative_density_" if not is_left_censoring else "survival_function_"
(self.durations, self.event_observed, self.timeline, self.entry,
self.event_table,
self.weights) = _preprocess_inputs(durations, event_observed,
timeline, entry, weights)
alpha = alpha if alpha else self.alpha
log_estimate, cumulative_sq_ = _additive_estimate(
self.event_table, self.timeline, self._additive_f,
self._additive_var, is_left_censoring)
if entry is not None:
# a serious problem with KM is that when the sample size is small and there are too few early
# truncation times, it may happen that is the number of patients at risk and the number of deaths is the same.
# we adjust for this using the Breslow-Fleming-Harrington estimator
n = self.event_table.shape[0]
net_population = (self.event_table["entrance"] -
self.event_table["removed"]).cumsum()
if net_population.iloc[:int(n / 2)].min() == 0:
ix = net_population.iloc[:int(n / 2)].idxmin()
raise StatError(
"""There are too few early truncation times and too many events. S(t)==0 for all t>%g. Recommend BreslowFlemingHarringtonFitter."""
% ix)
# estimation
setattr(self, primary_estimate_name,
pd.DataFrame(np.exp(log_estimate), columns=[self._label]))
setattr(self, secondary_estimate_name,
pd.DataFrame(1 - np.exp(log_estimate), columns=[self._label]))
self.__estimate = getattr(self, primary_estimate_name)
self.confidence_interval_ = self._bounds(
cumulative_sq_.values[:, None], alpha, ci_labels)
self._median = median_survival_times(self.survival_function_)
self._cumulative_sq_ = cumulative_sq_
setattr(self, "confidence_interval_" + primary_estimate_name,
self.confidence_interval_)
setattr(self, "confidence_interval_" + secondary_estimate_name,
1 - self.confidence_interval_)
# estimation methods
self._estimation_method = primary_estimate_name
self._estimate_name = primary_estimate_name
return self
add_at_risk_counts(kmf_train, kmf_test, ax=ax, fontsize=12)
ax.set_xlabel('Time (months)', fontsize=12, fontweight='bold')
ax.set_ylabel('Survival probability', fontsize=12, fontweight='bold')
ax.legend(fontsize=12)
ax.text(10, 0.75, 'p=0.85', fontsize=12, fontweight='bold')
# In[27]:
print(kmf_train.median_survival_time_)
print(kmf_test.median_survival_time_)
# In[28]:
print(median_survival_times(kmf_train.confidence_interval_))
print(median_survival_times(kmf_test.confidence_interval_))
# In[29]:
print(kmf_train.event_table)
print(kmf_test.event_table)
# In[30]:
print('Survival probability for t=60 for train set: ', kmf_train.predict(60))
print('Survival probability for t=60 for test set: ', kmf_test.predict(60))
# In[31]:
results = logrank_test(train['PFS'],
def test_median():
sv = pd.DataFrame(1 - np.linspace(0, 1, 1000))
assert utils.median_survival_times(sv) == 500
dfn = pd.DataFrame(
d, columns=["ID", "KM", "DEAD", "ENGINE", "MOUNTAIN", "CITY", "MONDAY"])
print(dfn)
censored_subjects = censored_subjects.append(dfn, ignore_index=True)
print(censored_subjects)
unconditioned_sf = cph.predict_survival_function(censored_subjects)
print(unconditioned_sf)
from lifelines.utils import median_survival_times, qth_survival_times
predictions_75 = qth_survival_times(0.75, unconditioned_sf)
predictions_25 = qth_survival_times(0.25, unconditioned_sf)
predictions_50 = median_survival_times(unconditioned_sf)
print(predictions_50)
fig, ax = plt.subplots(nrows=1, ncols=1, figsize=(8, 4))
for f in unconditioned_sf:
ax.plot(unconditioned_sf[f], alpha=.5, label=f)
#ax.legend()
fig, ax = plt.subplots(nrows=1, ncols=1, figsize=(8, 4))
for i, f in enumerate(reversed(unconditioned_sf.columns)):
#print( i )
if i < num_d:
print(i, f)
ax.plot(unconditioned_sf[f], alpha=1, label=f)
else:
ax.plot(unconditioned_sf[f], alpha=0.1, label=f, c='grey')
