def cdf_plot(model, timeline=None, ax=None, **plot_kwargs):
"""
"""
from lifelines import KaplanMeierFitter
if ax is None:
ax = plt.gca()
if timeline is None:
timeline = model.timeline
COL_EMP = "empirical CDF"
if CensoringType.is_left_censoring(model):
empirical_kmf = KaplanMeierFitter().fit_left_censoring(
model.durations, model.event_observed, label=COL_EMP, timeline=timeline
)
elif CensoringType.is_right_censoring(model):
empirical_kmf = KaplanMeierFitter().fit_right_censoring(
model.durations, model.event_observed, label=COL_EMP, timeline=timeline
)
elif CensoringType.is_interval_censoring(model):
raise NotImplementedError("lifelines does not have a non-parametric interval model yet.")
empirical_kmf.plot_cumulative_density(ax=ax, **plot_kwargs)
dist = get_distribution_name_of_lifelines_model(model)
dist_object = create_scipy_stats_model_from_lifelines_model(model)
ax.plot(timeline, dist_object.cdf(timeline), label="fitted %s" % dist, **plot_kwargs)
ax.legend()
return ax
def _ll_null(self):
if hasattr(self, "_ll_null_"):
return self._ll_null_
initial_point = np.zeros(len(self._fitted_parameter_names))
model = self.__class__(breakpoints=self.breakpoints[:-1], penalizer=self.penalizer)
regressors = {param_name: ["_intercept"] for param_name in self._fitted_parameter_names}
if CensoringType.is_right_censoring(self):
df = pd.DataFrame({"T": self.durations, "E": self.event_observed, "entry": self.entry, "_intercept": 1.0})
model.fit_right_censoring(
df, "T", "E", initial_point=initial_point, entry_col="entry", regressors=regressors
)
elif CensoringType.is_interval_censoring(self):
df = pd.DataFrame(
{
"lb": self.lower_bound,
"ub": self.upper_bound,
"E": self.event_observed,
"entry": self.entry,
"_intercept": 1.0,
}
)
model.fit_interval_censoring(
df, "lb", "ub", "E", initial_point=initial_point, entry_col="entry", regressors=regressors
)
if CensoringType.is_left_censoring(self):
raise NotImplementedError()
self._ll_null_ = model.log_likelihood_
return self._ll_null_
def cdf_plot(model, timeline=None, **plot_kwargs):
from lifelines import KaplanMeierFitter
set_kwargs_ax(plot_kwargs)
ax = plot_kwargs.pop("ax")
if timeline is None:
timeline = model.timeline
COL_EMP = "empirical quantiles"
if CensoringType.is_left_censoring(model):
kmf = KaplanMeierFitter().fit_left_censoring(model.durations,
model.event_observed,
label=COL_EMP,
timeline=timeline)
elif CensoringType.is_right_censoring(model):
kmf = KaplanMeierFitter().fit_right_censoring(model.durations,
model.event_observed,
label=COL_EMP,
timeline=timeline)
elif CensoringType.is_interval_censoring(model):
raise NotImplementedError()
kmf.plot_cumulative_density(ax=ax, **plot_kwargs)
dist = get_distribution_name_of_lifelines_model(model)
dist_object = create_scipy_stats_model_from_lifelines_model(model)
ax.plot(timeline,
dist_object.cdf(timeline),
label="fitted %s" % dist,
**plot_kwargs)
ax.legend()
return ax
def _create_initial_point(self, Ts, E, *args):
if CensoringType.is_right_censoring(self):
log_data = log(Ts[0])
elif CensoringType.is_left_censoring(self):
log_data = log(Ts[1])
elif CensoringType.is_interval_censoring(self):
log_data = log(Ts[1] - Ts[0])
return np.array([log_data.mean(), log(log_data.std()), 0.1])
def _create_initial_point(self, Ts, E, *args):
if CensoringType.is_right_censoring(self):
T = Ts[0]
elif CensoringType.is_left_censoring(self):
T = Ts[1]
elif CensoringType.is_interval_censoring(self):
T = Ts[1] - Ts[0]
return np.array([np.median(T), 1.0])
def _get_initial_values(self, Ts, E, *args):
if CensoringType.is_right_censoring(self):
log_data = np.log(Ts[0])
elif CensoringType.is_left_censoring(self):
log_data = np.log(Ts[1])
elif CensoringType.is_interval_censoring(self):
log_data = np.log(Ts[1] - Ts[0])
return np.array([log_data.mean(), np.log(log_data.std()), 1.0])
def _create_initial_point(self, Ts, E, *args):
if CensoringType.is_right_censoring(self):
log_T = np.log(Ts[0])
elif CensoringType.is_left_censoring(self):
log_T = np.log(Ts[1])
elif CensoringType.is_interval_censoring(self):
log_T = np.log(Ts[1])
return np.array([np.median(log_T), 1.0])
def _create_initial_point(self, Ts, E, *args):
if CensoringType.is_right_censoring(self):
log_data = log(Ts[0])
elif CensoringType.is_left_censoring(self):
log_data = log(Ts[1])
elif CensoringType.is_interval_censoring(self):
# this fails if Ts[1] == Ts[0], so we add a some fudge factors.
log_data = log(Ts[1] - Ts[0] + 0.01)
return np.array([log_data.mean(), log(log_data.std() + 0.01), 0.1])
def cdf_plot(model, timeline=None, ax=None, **plot_kwargs):
"""
This plot compares the empirical CDF (derived by KaplanMeier) vs the model CDF.
Parameters
------------
model: lifelines univariate model
timeline: iterable
ax: matplotlib axis
"""
from lifelines import KaplanMeierFitter
from matplotlib import pyplot as plt
if ax is None:
ax = plt.gca()
if timeline is None:
timeline = model.timeline
COL_EMP = "empirical CDF"
if CensoringType.is_left_censoring(model):
empirical_kmf = KaplanMeierFitter().fit_left_censoring(
model.durations,
model.event_observed,
label=COL_EMP,
timeline=timeline,
weights=model.weights,
entry=model.entry)
elif CensoringType.is_right_censoring(model):
empirical_kmf = KaplanMeierFitter().fit_right_censoring(
model.durations,
model.event_observed,
label=COL_EMP,
timeline=timeline,
weights=model.weights,
entry=model.entry)
elif CensoringType.is_interval_censoring(model):
empirical_kmf = KaplanMeierFitter().fit_interval_censoring(
model.lower_bound,
model.upper_bound,
label=COL_EMP,
timeline=timeline,
weights=model.weights,
entry=model.entry)
empirical_kmf.plot_cumulative_density(ax=ax, **plot_kwargs)
dist = get_distribution_name_of_lifelines_model(model)
dist_object = create_scipy_stats_model_from_lifelines_model(model)
ax.plot(timeline,
dist_object.cdf(timeline),
label="fitted %s" % dist,
**plot_kwargs)
ax.legend()
return ax
def _create_initial_point(self, Ts, E, *args):
if CensoringType.is_right_censoring(self):
T = Ts[0]
elif CensoringType.is_left_censoring(self):
T = np.clip(0.0001, np.inf, Ts[1])
elif CensoringType.is_interval_censoring(self):
if E.sum() > 0:
# Ts[1] can contain infs, so ignore this data
okay_data = Ts[1] < 1e10
T = Ts[1]
T = T[okay_data]
else:
T = np.array([1.0])
return np.array([np.median(T), 1.0])
def _ll_null(self):
if hasattr(self, "_ll_null_"):
return self._ll_null_
initial_point = np.zeros(len(self._fitted_parameter_names))
regressors = {
name: ["intercept"]
for name in self._fitted_parameter_names
}
model = self.__class__()
with warnings.catch_warnings():
warnings.simplefilter("ignore")
if CensoringType.is_right_censoring(self):
df = pd.DataFrame({
"T": self.durations,
"E": self.event_observed,
"entry": self.entry,
"intercept": 1
})
model.fit_right_censoring(df,
"T",
"E",
initial_point=initial_point,
entry_col="entry",
regressors=regressors)
elif CensoringType.is_interval_censoring(self):
df = pd.DataFrame({
"lb": self.lower_bound,
"ub": self.upper_bound,
"E": self.event_observed,
"entry": self.entry,
"intercept": 1,
})
model.fit_interval_censoring(df,
"lb",
"ub",
"E",
initial_point=initial_point,
entry_col="entry",
regressors=regressors)
if CensoringType.is_left_censoring(self):
raise NotImplementedError()
self._ll_null_ = model._log_likelihood
return self._ll_null_
def cdf_plot(model, timeline=None, ax=None, **plot_kwargs):
"""
Cumulative Distribution Function
"""
from lifelines import KaplanMeierFitter
#kmf = KaplanMeierFitter()
#kmf.fit(durations = churn_data['tenure'], event_observed = churn_data['Churn - Yes'] )
if ax is None:
ax = plt.gca()
if timeline is None:
timeline = model.timeline
CDL_EMP = "empirical CDF"
if CensoringType.is_left_censoring(model):
emp_kmf = KaplanMeierFitter().fit_left_censoring(model.durations,
model.event_observed,
label=CDL_EMP,
timeline=timeline,
weights=model.weights,
entry=model.entry)
if CensoringType.is_right_censoring(model):
emp_kmf = KaplanMeierFitter().fit_right_censoring(
model.durations,
model.event_observed,
label=CDL_EMP,
timeline=timeline,
weights=model.weights,
entry=model.entry)
if CensoringType.is_interval_censoring(model):
emp_kmf = KaplanMeierFitter().fit_interval_censoring(
model.lower_bound,
model.upper_bound,
label=CDL_EMP,
timeline=timeline,
weights=model.weights,
entry=model.entry)
def qq_plot(model, ax=None, **plot_kwargs):
"""
Produces a quantile-quantile plot of the empirical CDF against
the fitted parametric CDF. Large deviances away from the line y=x
can invalidate a model (though we expect some natural deviance in the tails).
Parameters
-----------
model: obj
A fitted lifelines univariate parametric model, like ``WeibullFitter``
plot_kwargs:
kwargs for the plot.
Returns
--------
ax:
The axes which was used.
Examples
---------
>>> from lifelines import *
>>> from lifelines.plotting import qq_plot
>>> from lifelines.datasets import load_rossi
>>> df = load_rossi()
>>> wf = WeibullFitter().fit(df['week'], df['arrest'])
>>> qq_plot(wf)
"""
from lifelines.utils import qth_survival_times
from lifelines import KaplanMeierFitter
if ax is None:
ax = plt.gca()
dist = get_distribution_name_of_lifelines_model(model)
dist_object = create_scipy_stats_model_from_lifelines_model(model)
COL_EMP = "empirical quantiles"
COL_THEO = "fitted %s quantiles" % dist
if CensoringType.is_left_censoring(model):
kmf = KaplanMeierFitter().fit_left_censoring(model.durations, model.event_observed, label=COL_EMP)
elif CensoringType.is_right_censoring(model):
kmf = KaplanMeierFitter().fit_right_censoring(model.durations, model.event_observed, label=COL_EMP)
elif CensoringType.is_interval_censoring(model):
raise NotImplementedError("lifelines does not have a non-parametric interval model yet.")
q = np.unique(kmf.cumulative_density_.values[:, 0])
# this is equivalent to the old code `qth_survival_times(q, kmf.cumulative_density, cdf=True)`
quantiles = qth_survival_times(1 - q, kmf.survival_function_)
quantiles[COL_THEO] = dist_object.ppf(q)
quantiles = quantiles.replace([-np.inf, 0, np.inf], np.nan).dropna()
max_, min_ = quantiles[COL_EMP].max(), quantiles[COL_EMP].min()
quantiles.plot.scatter(COL_THEO, COL_EMP, c="none", edgecolor="k", lw=0.5, ax=ax)
ax.plot([min_, max_], [min_, max_], c="k", ls=":", lw=1.0)
ax.set_ylim(min_, max_)
ax.set_xlim(min_, max_)
return ax
def qq_plot(model, ax=None, **plot_kwargs):
"""
Produces a quantile-quantile plot of the empirical CDF against
the fitted parametric CDF. Large deviances away from the line y=x
can invalidate a model (though we expect some natural deviance in the tails).
Parameters
-----------
model: obj
A fitted lifelines univariate parametric model, like ``WeibullFitter``
plot_kwargs:
kwargs for the plot.
Returns
--------
ax:
The axes which was used.
Examples
---------
.. code:: python
from lifelines import *
from lifelines.plotting import qq_plot
from lifelines.datasets import load_rossi
df = load_rossi()
wf = WeibullFitter().fit(df['week'], df['arrest'])
qq_plot(wf)
Notes
------
The interval censoring case uses the mean between the upper and lower bounds.
"""
from lifelines.utils import qth_survival_times
from lifelines import KaplanMeierFitter
if ax is None:
ax = plt.gca()
dist = get_distribution_name_of_lifelines_model(model)
dist_object = create_scipy_stats_model_from_lifelines_model(model)
COL_EMP = "empirical quantiles"
COL_THEO = "fitted %s quantiles" % dist
if CensoringType.is_left_censoring(model):
kmf = KaplanMeierFitter().fit_left_censoring(
model.durations, model.event_observed, label=COL_EMP, weights=model.weights, entry=model.entry
)
sf, cdf = kmf.survival_function_[COL_EMP], kmf.cumulative_density_[COL_EMP]
elif CensoringType.is_right_censoring(model):
kmf = KaplanMeierFitter().fit_right_censoring(
model.durations, model.event_observed, label=COL_EMP, weights=model.weights, entry=model.entry
)
sf, cdf = kmf.survival_function_[COL_EMP], kmf.cumulative_density_[COL_EMP]
elif CensoringType.is_interval_censoring(model):
kmf = KaplanMeierFitter().fit_interval_censoring(
model.lower_bound, model.upper_bound, label=COL_EMP, weights=model.weights, entry=model.entry
)
sf, cdf = kmf.survival_function_.mean(1), kmf.cumulative_density_[COL_EMP + "_lower"]
q = np.unique(cdf.values)
quantiles = qth_survival_times(1 - q, sf)
quantiles[COL_THEO] = dist_object.ppf(q)
quantiles = quantiles.replace([-np.inf, 0, np.inf], np.nan).dropna()
max_, min_ = quantiles[COL_EMP].max(), quantiles[COL_EMP].min()
quantiles.plot.scatter(COL_THEO, COL_EMP, c="none", edgecolor="k", lw=0.5, ax=ax)
ax.plot([min_, max_], [min_, max_], c="k", ls=":", lw=1.0)
ax.set_ylim(min_, max_)
ax.set_xlim(min_, max_)
return ax
def survival_probability_calibration(model: RegressionFitter,
training_df: pd.DataFrame,
t0: float,
ax=None):
r"""
Smoothed calibration curves for time-to-event models. This is analogous to
calibration curves for classification models, extended to handle survival probabilities
and censoring. Produces a matplotlib figure and some metrics.
We want to calibrate our model's prediction of :math:`P(T < \text{t0})` against the observed frequencies.
Parameters
-------------
model:
a fitted lifelines regression model to be evaluated
training_df: DataFrame
the DataFrame used to train the model
t0: float
the time to evaluate the probability of event occurring prior at.
Returns
----------
ax:
mpl axes
ICI:
mean absolute difference between predicted and observed
E50:
median absolute difference between predicted and observed
https://onlinelibrary.wiley.com/doi/full/10.1002/sim.8570
"""
def ccl(p):
return np.log(-np.log(1 - p))
if ax is None:
ax = plt.gca()
T = model.duration_col
E = model.event_col
predictions_at_t0 = np.clip(
1 -
model.predict_survival_function(training_df, times=[t0]).T.squeeze(),
1e-10, 1 - 1e-10)
# create new dataset with the predictions
prediction_df = pd.DataFrame({
"ccl_at_%d" % t0: ccl(predictions_at_t0),
"constant": 1,
T: model.durations,
E: model.event_observed
})
# fit new dataset to flexible spline model
# this new model connects prediction probabilities and actual survival. It should be very flexible, almost to the point of overfitting. It's goal is just to smooth out the data!
knots = 3
regressors = {
"beta_": ["ccl_at_%d" % t0],
"gamma0_": ["constant"],
"gamma1_": ["constant"],
"gamma2_": ["constant"]
}
# this model is from examples/royson_crowther_clements_splines.py
crc = CRCSplineFitter(knots, penalizer=0)
if CensoringType.is_right_censoring(model):
crc.fit_right_censoring(prediction_df, T, E, regressors=regressors)
elif CensoringType.is_left_censoring(model):
crc.fit_left_censoring(prediction_df, T, E, regressors=regressors)
elif CensoringType.is_interval_censoring(model):
crc.fit_interval_censoring(prediction_df, T, E, regressors=regressors)
# predict new model at values 0 to 1, but remember to ccl it!
x = np.linspace(np.clip(predictions_at_t0.min() - 0.01, 0, 1),
np.clip(predictions_at_t0.max() + 0.01, 0, 1), 100)
y = 1 - crc.predict_survival_function(pd.DataFrame({
"ccl_at_%d" % t0: ccl(x),
"constant": 1
}),
times=[t0]).T.squeeze()
# plot our results
ax.set_title(
"Smoothed calibration curve of \npredicted vs observed probabilities of t ≤ %d mortality"
% t0)
color = "tab:red"
ax.plot(x, y, label="smoothed calibration curve", color=color)
ax.set_xlabel("Predicted probability of \nt ≤ %d mortality" % t0)
ax.set_ylabel("Observed probability of \nt ≤ %d mortality" % t0,
color=color)
ax.tick_params(axis="y", labelcolor=color)
# plot x=y line
ax.plot(x, x, c="k", ls="--")
ax.legend()
# plot histogram of our original predictions
color = "tab:blue"
twin_ax = ax.twinx()
twin_ax.set_ylabel("Count of \npredicted probabilities",
color=color) # we already handled the x-label with ax1
twin_ax.tick_params(axis="y", labelcolor=color)
twin_ax.hist(predictions_at_t0, alpha=0.3, bins="sqrt", color=color)
plt.tight_layout()
deltas = ((1 - crc.predict_survival_function(
prediction_df, times=[t0])).T.squeeze() - predictions_at_t0).abs()
ICI = deltas.mean()
E50 = np.percentile(deltas, 50)
print("ICI = ", ICI)
print("E50 = ", E50)
return ax, ICI, E50
def print_summary(self, decimals=2, **kwargs):
"""
Print summary statistics describing the fit, the coefficients, and the error bounds.
Parameters
-----------
decimals: int, optional (default=2)
specify the number of decimal places to show
alpha: float or iterable
specify confidence intervals to show
kwargs:
print additional metadata in the output (useful to provide model names, dataset names, etc.) when comparing
multiple outputs.
"""
# Print information about data first
justify = string_justify(18)
print(self)
if self.event_col:
print("{} = '{}'".format(justify("event col"), self.event_col))
if self.weights_col:
print("{} = '{}'".format(justify("weights col"), self.weights_col))
if self.penalizer > 0:
print("{} = {}".format(justify("penalizer"), self.penalizer))
if self.robust:
print("{} = {}".format(justify("robust variance"), True))
print("{} = {}".format(justify("number of subjects"),
self._n_examples))
print("{} = {}".format(justify("number of events"),
self.event_observed.sum()))
print("{} = {:.{prec}f}".format(justify("log-likelihood"),
self._log_likelihood,
prec=decimals))
print("{} = {}".format(justify("time fit was run"),
self._time_fit_was_called))
for k, v in kwargs.items():
print("{} = {}\n".format(justify(k), v))
print(end="\n")
print("---")
df = self.summary
print(
df.to_string(
float_format=format_floats(decimals),
formatters={
"p": format_p_value(decimals),
"exp(coef)": format_exp_floats(decimals)
},
))
print("---")
if CensoringType.is_right_censoring(self):
print("Concordance = {:.{prec}f}".format(self.score_,
prec=decimals))
with np.errstate(invalid="ignore", divide="ignore"):
sr = self.log_likelihood_ratio_test()
print(
"Log-likelihood ratio test = {:.{prec}f} on {} df, -log2(p)={:.{prec}f}"
.format(sr.test_statistic,
sr.degrees_freedom,
-np.log2(sr.p_value),
prec=decimals))
