LogLogisticFitter¶

class lifelines.fitters.log_logistic_fitter.LogLogisticFitter(*args, **kwargs)

This class implements a Log-Logistic model for univariate data. The model has parameterized form:

$S(t) = \left(1 + \left(\frac{t}{\alpha}\right)^{\beta}\right)^{-1}, \alpha > 0, \beta > 0,$

The $$\alpha$$ (scale) parameter has an interpretation as being equal to the median lifetime of the population. The $$\beta$$ parameter influences the shape of the hazard. See figure below:

The hazard rate is:

$h(t) = \frac{\left(\frac{\beta}{\alpha}\right)\left(\frac{t}{\alpha}\right) ^ {\beta-1}}{\left(1 + \left(\frac{t}{\alpha}\right)^{\beta}\right)}$

and the cumulative hazard is:

$H(t) = \log\left(\left(\frac{t}{\alpha}\right) ^ {\beta} + 1\right)$

After calling the .fit method, you have access to properties like: cumulative_hazard_, plot, survival_function_, alpha_ and beta_. A summary of the fit is available with the method ‘print_summary()’

Parameters:

alpha (float, optional (default=0.05)) – the level in the confidence intervals.

Examples

from lifelines import LogLogisticFitter

llf = LogLogisticFitter()
llf.fit(waltons['T'], waltons['E'])
llf.plot()
print(llf.alpha_)

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

alpha_

The fitted parameter in the model

Type:

float

beta_

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

alpha_: float
beta_: float
property median_survival_time_

Return the unique time point, t, such that S(t) = 0.5. This is the “half-life” 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)