LogLogisticAFTFitter¶
- class lifelines.fitters.log_logistic_aft_fitter.LogLogisticAFTFitter(alpha=0.05, penalizer=0.0, l1_ratio=0.0, fit_intercept=True, model_ancillary=False)¶
This class implements a Log-Logistic AFT model. The model has parameterized form, with \(\alpha(x) = \exp\left(a_0 + a_1x_1 + ... + a_n x_n \right)\), and optionally, \(\beta(y) = \exp\left(b_0 + b_1 y_1 + ... + b_m y_m \right)\),
The cumulative hazard rate is
\[H(t; x , y) = \log\left(1 + \left(\frac{t}{\alpha(x)}\right)^{\beta(y)}\right)\]The \(\alpha\) (scale) parameter has an interpretation as being equal to the median lifetime. The \(\beta\) parameter influences the shape of the hazard.
After calling the
.fit
method, you have access to properties like:params_
,print_summary()
. A summary of the fit is available with the methodprint_summary()
.- Parameters:
alpha (float, optional (default=0.05)) – the level in the confidence intervals.
fit_intercept (boolean, optional (default=True)) – Allow lifelines to add an intercept column of 1s to df, and ancillary if applicable.
penalizer (float or array, optional (default=0.0)) – the penalizer coefficient to the size of the coefficients. See l1_ratio. Must be equal to or greater than 0. Alternatively, penalizer is an array equal in size to the number of parameters, with penalty coefficients for specific variables. For example, penalizer=0.01 * np.ones(p) is the same as penalizer=0.01
- l1_ratio: float, optional (default=0.0)
how much of the penalizer should be attributed to an l1 penalty (otherwise an l2 penalty). The penalty function looks like
penalizer * l1_ratio * ||w||_1 + 0.5 * penalizer * (1 - l1_ratio) * ||w||^2_2
- model_ancillary: optional (default=False)
set the model instance to always model the ancillary parameter with the supplied Dataframe. This is useful for grid-search optimization.
- params_¶
The estimated coefficients
- Type:
DataFrame
- confidence_intervals_¶
The lower and upper confidence intervals for the coefficients
- Type:
DataFrame
- durations¶
The event_observed variable provided
- Type:
Series
- event_observed¶
The event_observed variable provided
- Type:
Series
- weights¶
The event_observed variable provided
- Type:
Series
- variance_matrix_¶
The variance matrix of the coefficients
- Type:
DataFrame
- standard_errors_¶
the standard errors of the estimates
- Type:
Series
- score_¶
the concordance index of the model.
- Type:
float
- predict_expectation(df, ancillary=None) Series ¶
Predict the expectation of lifetimes, \(E[T | x]\).
- Parameters:
X (DataFrame) – a (n,d) DataFrame. If a DataFrame, columns can be in any order. If a numpy array, columns must be in the same order as the training data.
ancillary_X (DataFrame, optional) – a (n,d) DataFrame. If a DataFrame, columns can be in any order. If a numpy array, columns must be in the same order as the training data.
- Returns:
percentiles – the median lifetimes for the individuals. If the survival curve of an individual does not cross 0.5, then the result is infinity.
- Return type:
DataFrame
See also
predict_median
- predict_percentile(df, ancillary=None, p=0.5, conditional_after=None) Series ¶
Returns the median lifetimes for the individuals, by default. If the survival curve of an individual does not cross
p
, then the result is infinity. http://stats.stackexchange.com/questions/102986/percentile-loss-functions- Parameters:
X (DataFrame) – a (n,d) DataFrame. If a DataFrame, columns can be in any order. If a numpy array, columns must be in the same order as the training data.
ancillary_X (DataFrame, optional) – a (n,d) DataFrame. If a DataFrame, columns can be in any order. If a numpy array, columns must be in the same order as the training data.
p (float, optional (default=0.5)) – the percentile, must be between 0 and 1.
- Returns:
percentiles
- Return type:
DataFrame
See also
predict_median