SplineFitter

class lifelines.fitters.spline_fitter.SplineFitter(knot_locations: ndarray, *args, **kwargs)

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 proportional-hazards and proportional-odds 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