NelsonAalenFitter¶

class
lifelines.fitters.nelson_aalen_fitter.
NelsonAalenFitter
(alpha=0.05, nelson_aalen_smoothing=True, **kwargs)¶ Bases:
lifelines.fitters.UnivariateFitter
Class for fitting the NelsonAalen estimate for the cumulative hazard.
NelsonAalenFitter(alpha=0.05, nelson_aalen_smoothing=True)
Parameters:  alpha (float, optional (default=0.05)) – The alpha value associated with the confidence intervals.
 nelson_aalen_smoothing (bool, optional) – If the event times are naturally discrete (like discrete years, minutes, etc.) then it is advisable to turn this parameter to False. See [1], pg.84.
Notes
[1] Aalen, O., Borgan, O., Gjessing, H., 2008. Survival and Event History Analysis

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

confidence_interval_
¶ The lower and upper confidence intervals for the cumulative hazard
Type: DataFrame

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

event_table
¶ A summary of the life table
Type: DataFrame

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.

cumulative_density_at_times
(times, label=None)¶

cumulative_hazard_at_times
(times, label=None)¶

divide
(other) → pandas.core.frame.DataFrame¶ Divide self’s survival function from another model’s survival function.
Parameters: other (same object as self)

fit
(durations, event_observed=None, timeline=None, entry=None, label=None, alpha=None, ci_labels=None, weights=None)¶ Parameters:  durations (an array, or pd.Series, of length n) – duration subject was observed for
 timeline (iterable) – return the best estimate at the values in timelines (positively increasing)
 event_observed (an array, or pd.Series, of length n) – True if the the death was observed, False if the event was lost (rightcensored). 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 lefttruncated observations, i.e the birth event was not observed. If None, defaults to all 0 (all birth events observed.)
 label (string) – a string to name the column of the estimate.
 alpha (float) – the alpha value in the confidence intervals. Overrides the initializing alpha for this call to fit only.
 ci_labels (iterable) – add custom column names to the generated confidence intervals as a length2 list: [<lowerbound name>, <upperbound name>]. Default: <label>_lower_<1alpha/2>
 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: Return type: self, with new properties like
cumulative_hazard_
.

hazard_at_times
(times, label=None)¶

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)¶ Plots a pretty figure of the model
Matplotlib plot arguments can be passed in inside the kwargs, plus
Parameters: show_censors (bool) – place markers at censorship events. Default: False
censor_styles (dict) – If show_censors, this dictionary will be passed into the plot call.
ci_alpha (float) – the transparency level of the confidence interval. Default: 0.3
ci_force_lines (bool) – force the confidence intervals to be line plots (versus default shaded areas). Default: False
ci_show (bool) – show confidence intervals. Default: True
ci_legend (bool) – if ci_force_lines is True, this is a boolean flag to add the lines’ labels to the legend. Default: False
at_risk_counts (bool) – show group sizes at time points. See function
add_at_risk_counts
for details. Default: Falseloc (slice) – specify a timebased subsection of the curves to plot, ex:
>>> model.plot(loc=slice(0.,10.))
will plot the time values between t=0. and t=10.
iloc (slice) – specify a locationbased subsection of the curves to plot, ex:
>>> model.plot(iloc=slice(0,10))
will plot the first 10 time points.
Returns: a pyplot axis object
Return type: ax

plot_cumulative_density
(**kwargs)¶

plot_cumulative_hazard
(**kwargs)¶

plot_density
(**kwargs)¶

plot_hazard
(bandwidth=None, **kwargs)¶

plot_survival_function
(**kwargs)¶

predict
(times: Union[Iterable[float], float], interpolate=False) → pandas.core.series.Series¶ Predict the fitter 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.

smoothed_hazard_
(bandwidth)¶ Parameters: bandwidth (float) – the bandwith used in the Epanechnikov kernel. Returns: a DataFrame of the smoothed hazard Return type: DataFrame

smoothed_hazard_confidence_intervals_
(bandwidth, hazard_=None)¶ Parameters:  bandwidth (float) – the bandwidth to use in the Epanechnikov kernel. > 0
 hazard_ (numpy array) – a computed (n,) numpy array of estimated hazard rates. If none, uses
smoothed_hazard_

subtract
(other) → pandas.core.frame.DataFrame¶ Subtract self’s survival function from another model’s survival function.
Parameters: other (same object as self)

survival_function_at_times
(times, label=None)¶