Weibull Mixture cure model implementation

[AMDelo]

Hello, currently we can use the univariate model for mixture cure, but it would be helpful if a regression model for Weibull mixture cure is implemented.

[CamDavidsonPilon]

I think that's possible with some additional code:

# -*- coding: utf-8 -*-
from lifelines.fitters import ParametricRegressionFitter
import autograd.numpy as np
from autograd.scipy.special import expit
import matplotlib.pyplot as plt
from scipy.stats import weibull_min


class CureModel(ParametricRegressionFitter):
    """
    This is a Weibull survival model with a cure component.

    """

    _fitted_parameter_names = ["lambda_", "beta_", "rho_"]

    def _cumulative_hazard(self, params, T, Xs):
        c = expit(np.dot(Xs["beta_"], params["beta_"]))
        lambda_ = np.exp(np.dot(Xs["lambda_"], params["lambda_"]))
        rho_ = np.exp(np.dot(Xs["rho_"], params["rho_"]))

        survival = np.exp(-((T / lambda_) ** rho_))
        return -np.log((1 - c) * 1.0 + c * survival)


from lifelines.datasets import load_rossi

swf = CureModel(penalizer=0.00001)

rossi = load_rossi()

covariates = {
    "lambda_": rossi.columns.difference(["week", "arrest"]),
    "rho_": ["1"],
    "beta_": rossi.columns.difference(["week", "arrest"]),
}

swf.fit(rossi, "week", event_col="arrest", regressors=covariates)  # TODO: name
swf.print_summary(4)
# swf.plot()
# plt.show()

[AMDelo]

Thank you for your reply. It seems the code throws an error, and the problem could be in the "rho" assignment in the covariates dictionary. The error: KeyError: "None of [Index(['1'], dtype='object')] are in the [columns]"

Update: found the issue, the ["1"] should be outside of a list. Thank you!

[AMDelo]

Do you have any reference on how to interpret the lambda and beta coefficients for the parameters, as well as the rho coefficient?

[josarago]

is this possible with a generalized gamma regression fitter?

[robchadil]

2nd this. Possible to implement with GG?

[josarago]

would this implementation be correct when using conditional_after to predict the cdf?

def predict_cumulative_density(self, df, times=None, conditional_after=None):
       return self.predict_survival_function(df, times=times, conditional_after=conditional_after).apply(lambda x: (1 - x))

[josarago]

Actually I think it's correct