SplineFitter¶

class
lifelines.fitters.spline_fitter.
SplineFitter
(knot_locations: numpy.array, *args, **kwargs)¶ Bases:
lifelines.fitters.KnownModelParametricUnivariateFitter
,lifelines.fitters.mixins.SplineFitterMixin
Model the cumulative hazard using \(N\) cubic splines. This offers great flexibility and smoothness of the cumulative hazard.
\[H(t) = \exp{\left( \phi_0 + \phi_1\log{t} + \sum_{j=2}^N \phi_j v_j(\log{t})\right)}\]where \(v_j\) are our cubic basis functions at predetermined knots. See references for exact definition.
Parameters: knot_locations (list, np.array) – The locations of the cubic breakpoints. Must be length two or more. Typically, the first knot is the minimum observed death, the last knot is the maximum observed death, and the knots in between are the centiles of observed data (ex: if one additional knot, choose the 50th percentile, the median. If two additional knots, choose the 33rd and 66th percentiles). References
Royston, P., & Parmar, M. K. B. (2002). Flexible parametric proportionalhazards and proportionalodds models for censored survival data, with application to prognostic modelling and estimation of treatment effects. Statistics in Medicine, 21(15), 2175–2197. doi:10.1002/sim.1203
Examples
from lifelines import SplineFitter from lifelines.datasets import load_waltons waltons = load_waltons() T, E = waltons['T'], waltons['E'] knots = np.percentile(T.loc[E.astype(bool)], [0, 50, 100]) sf = SplineFitter(knots) sf.fit(T, E) sf.plot() print(sf.knots)

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

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

density_
¶ The estimated density function (PDF) (with custom timeline if provided)
Type: DataFrame

variance_matrix_
¶ The variance matrix of the coefficients
Type: DataFrame

median_survival_time_
¶ The median time to event
Type: float

lambda_
¶ The fitted parameter in the model
Type: float

rho_
¶ The fitted parameter in the model
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

knot_locations
¶ The locations of the breakpoints.
Type: array

n_knots
¶ Count of breakpoints
Type: int

AIC_
¶

basis
(x: numpy.array, knot: float, min_knot: float, max_knot: float)¶

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 self’s survival function from another model’s survival function.
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_

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.

params_
¶

percentile
(p: float) → float¶ 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 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.

print_summary
(decimals=2, style=None, columns=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}
 columns – only display a subset of
summary
columns. Default all.  kwargs – print additional metadata in the output (useful to provide model names, dataset names, etc.) when comparing multiple outputs.

static
relu
(x: numpy.array)¶

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

summary
¶ Summary statistics describing the fit.
See also

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.
