MixtureCureFitter¶

class
lifelines.fitters.mixture_cure_fitter.
MixtureCureFitter
(base_fitter, *args, **kwargs)¶ Bases:
lifelines.fitters.ParametricUnivariateFitter
This class implements a Mixture Cure Model for univariate data with a configurable distribution for the noncure portion. The model survival function has parameterized form:
\[S(t) = c + \left(1  c\right)S_b(t), \;\; 1 > c > 0\]where \(S_b(t)\) is a parametric survival function describing the noncure portion of the population, and \(c\) is the cured fraction of the population.
After calling the
.fit
method, you have access to properties like:cumulative_hazard_
,survival_function_
,lambda_
andrho_
. A summary of the fit is available with the methodprint_summary()
. The parameters for both the cure portion of the model and from the base_fitter are available. The cure fraction is calledcured_fraction_
, and parameters from the base_fitter will be available with their own appropriate names.Parameters:  base_fitter (ParametricUnivariateFitter, required) – an instance of a fitter that describes the noncure portion of the population.
 alpha (float, optional (default=0.05)) – the level in the confidence intervals.
Important
The base_fitter instance is used to describe the noncure portion of the population, but is not actually fit to the data. Some internal properties are modified, and it should not be used for any other purpose after passing it to the constructor of this class.
Examples
from lifelines import MixtureCureFitter, ExponentialFitter fitter = MixtureCureFitter(base_fitter=ExponentialFitter()) fitter.fit(T, event_observed=observed) print(fitter.cured_fraction_) print(fitter.lambda_) # This is available because it is a parameter of the ExponentialFitter

cumulative_hazard_
¶ The estimated cumulative hazard (with custom timeline if provided)
Type: DataFrame

cured_fraction_
¶ The fitted parameter \(c\) in the model
Type: float

hazard_
¶ The estimated hazard (with custom timeline if provided)
Type: DataFrame

survival_function_
¶ The estimated survival function (with custom timeline if provided)
Type: DataFrame

cumulative_density_
¶ The estimated cumulative density function (with custom timeline if provided)
Type: DataFrame

variance_matrix_
¶ The variance matrix of the coefficients
Type: numpy array

median_survival_time_
¶ The median time to event
Type: float

durations
¶ The durations provided
Type: array

event_observed
¶ The event_observed variable provided
Type: array

timeline
¶ The time line to use for plotting and indexing
Type: array

entry
¶ The entry array provided, or None
Type: array or None

AIC_
¶

conditional_time_to_event_
¶ Return a DataFrame, with index equal to survival_function_, that estimates the median duration remaining until the death event, given survival up until time t. For example, if an individual exists until age 1, their expected life remaining given they lived to time 1 might be 9 years.

confidence_interval_
¶ The confidence interval of the cumulative hazard. This is an alias for
confidence_interval_cumulative_hazard_
.

confidence_interval_cumulative_density_
¶ The lower and upper confidence intervals for the cumulative density

confidence_interval_cumulative_hazard_
¶ The confidence interval of the cumulative hazard. This is an alias for
confidence_interval_
.

confidence_interval_density_
¶ The confidence interval of the hazard.

confidence_interval_hazard_
¶ The confidence interval of the hazard.

confidence_interval_survival_function_
¶ The lower and upper confidence intervals for the survival function

cumulative_density_at_times
(times, label=None) → pandas.core.series.Series¶ Return a Pandas series of the predicted cumulative density function (1survival function) at specific times.
Parameters:  times (iterable or float) – values to return the survival function at.
 label (string, optional) – Rename the series returned. Useful for plotting.

cumulative_hazard_at_times
(times, label=None) → pandas.core.series.Series¶ Return a Pandas series of the predicted cumulative hazard value at specific times.
Parameters:  times (iterable or float) – values to return the cumulative hazard at.
 label (string, optional) – Rename the series returned. Useful for plotting.

density_at_times
(times, label=None) → pandas.core.series.Series¶ Return a Pandas series of the predicted probability density function, dCDF/dt, at specific times.
Parameters:  times (iterable or float) – values to return the survival function at.
 label (string, optional) – Rename the series returned. Useful for plotting.

divide
(other) → pandas.core.frame.DataFrame¶ Divide the {0} of two {1} objects.
Parameters: other (same object as self)

event_table
¶

fit
(durations, event_observed=None, timeline=None, label=None, alpha=None, ci_labels=None, show_progress=False, entry=None, weights=None, initial_point=None) → self¶ Parameters:  durations (an array, or pd.Series) – length n, duration subject was observed for
 event_observed (numpy array or pd.Series, optional) – length n, True if the the death was observed, False if the event was lost (rightcensored). Defaults all True if event_observed==None
 timeline (list, optional) – return the estimate at the values in timeline (positively increasing)
 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 (list, optional) – add custom column names to the generated confidence intervals as a length2 list: [<lowerbound name>, <upperbound name>]. Default: <label>_lower_<alpha>
 show_progress (bool, optional) – since this is an iterative fitting algorithm, switching this to True will display some iteration details.
 entry (an array, or pd.Series, of length n) – relative time when a subject entered the study. This is useful for lefttruncated (not leftcensored) observations. If None, all members of the population entered study when they were “born”: time zero.
 weights (an array, or pd.Series, of length n) – integer weights per observation
 initial_point ((d,) numpy array, optional) – initialize the starting point of the iterative algorithm. Default is the zero vector.
Returns: self with new properties like
cumulative_hazard_
,survival_function_
Return type: self

fit_interval_censoring
(lower_bound, upper_bound, event_observed=None, timeline=None, label=None, alpha=None, ci_labels=None, show_progress=False, entry=None, weights=None, initial_point=None) → self¶ Fit the model to an interval censored dataset.
Parameters:  lower_bound (an array, or pd.Series) – length n, the start of the period the subject experienced the event in.
 upper_bound (an array, or pd.Series) – length n, the end of the period the subject experienced the event in. If the value is equal to the corresponding value in lower_bound, then the individual’s event was observed (not censored).
 event_observed (numpy array or pd.Series, optional) – length n, if left optional, infer from
lower_bound
andupper_cound
(if lower_bound==upper_bound then event observed, if lower_bound < upper_bound, then event censored)  timeline (list, optional) – return the estimate at the values in timeline (positively increasing)
 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 (list, optional) – add custom column names to the generated confidence intervals as a length2 list: [<lowerbound name>, <upperbound name>]. Default: <label>_lower_<alpha>
 show_progress (bool, optional) – since this is an iterative fitting algorithm, switching this to True will display some iteration details.
 entry (an array, or pd.Series, of length n) – relative time when a subject entered the study. This is useful for lefttruncated (not leftcensored) observations. If None, all members of the population entered study when they were “born”: time zero.
 weights (an array, or pd.Series, of length n) – integer weights per observation
 initial_point ((d,) numpy array, optional) – initialize the starting point of the iterative algorithm. Default is the zero vector.
Returns: self with new properties like
cumulative_hazard_
,survival_function_
Return type: self

fit_left_censoring
(durations, event_observed=None, timeline=None, label=None, alpha=None, ci_labels=None, show_progress=False, entry=None, weights=None, initial_point=None) → self¶ Fit the model to a leftcensored dataset
Parameters:  durations (an array, or pd.Series) – length n, duration subject was observed for
 event_observed (numpy array or pd.Series, optional) – length n, True if the the death was observed, False if the event was lost (rightcensored). Defaults all True if event_observed==None
 timeline (list, optional) – return the estimate at the values in timeline (positively increasing)
 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 (list, optional) – add custom column names to the generated confidence intervals as a length2 list: [<lowerbound name>, <upperbound name>]. Default: <label>_lower_<alpha>
 show_progress (bool, optional) – since this is an iterative fitting algorithm, switching this to True will display some iteration details.
 entry (an array, or pd.Series, of length n) – relative time when a subject entered the study. This is useful for lefttruncated (not leftcensored) observations. If None, all members of the population entered study when they were “born”: time zero.
 weights (an array, or pd.Series, of length n) – integer weights per observation
 initial_point ((d,) numpy array, optional) – initialize the starting point of the iterative algorithm. Default is the zero vector.
Returns: Return type: self with new properties like
cumulative_hazard_
,survival_function_

fit_right_censoring
(*args, **kwargs)¶ Alias for
fit
See also
fit

hazard_at_times
(times, label=None) → pandas.core.series.Series¶ Return a Pandas series of the predicted hazard at specific times.
Parameters:  times (iterable or float) – values to return the hazard at.
 label (string, optional) – Rename the series returned. Useful for plotting.

median_survival_time_
Return the unique time point, t, such that S(t) = 0.5. This is the “halflife” of the population, and a robust summary statistic for the population, if it exists.

percentile
(p)¶ Return the unique time point, t, such that S(t) = p.
Parameters: p (float)

plot
(**kwargs)¶ Produce a prettyplot of the estimate.

plot_cumulative_density
(**kwargs)¶

plot_cumulative_hazard
(**kwargs)¶

plot_density
(**kwargs)¶

plot_hazard
(**kwargs)¶

plot_survival_function
(**kwargs)¶

predict
(times: Union[Iterable[float], float], interpolate=False) → pandas.core.series.Series¶ Predict the {0} at certain point in time. Uses a linear interpolation if points in time are not in the index.
Parameters:  times (scalar, or array) – a scalar or an array of times to predict the value of {0} at.
 interpolate (bool, optional (default=False)) – for methods that produce a stepwise solution (KaplanMeier, NelsonAalen, etc), turning this to True will use an linear interpolation method to provide a more “smooth” answer.

print_summary
(decimals=2, style=None, **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
 style (string) – {html, ascii, latex}
 kwargs – print additional metadata in the output (useful to provide model names, dataset names, etc.) when comparing multiple outputs.

subtract
(other) → pandas.core.frame.DataFrame¶ Subtract the {0} of two {1} objects.
Parameters: other (same object as self)

summary
¶ Summary statistics describing the fit.
See also
print_summary

survival_function_at_times
(times, label=None) → pandas.core.series.Series¶ Return a Pandas series of the predicted survival value at specific times.
Parameters:  times (iterable or float) – values to return the survival function at.
 label (string, optional) – Rename the series returned. Useful for plotting.