splitpopsurv (Python)

Split-population (cure / mover–stayer) survival models in Python: an accelerated failure-time regression for event timing among "movers", combined with a logistic regression on the probability of belonging to the immune "stayer" population.

Five baseline timing distributions are provided — log-logistic, Weibull, log-normal, gamma, and the generalized gamma that nests the other four — following Schmidt & Witte (1989) and Yamaguchi (1992, 1998). This package is a Python translation of a set of Stata ml programs, with the log-likelihood corrected to match the published model and verified by simulation against known parameters.

📖 Full manual (theory, formulas, the likelihood correction, and a complete function reference): docs/manual.html

Companion packages implementing the same corrected models are available for R and Stata.

Author

Nobutaka Fukuda, Tohoku University — nobutaka.fukuda@tohoku.ac.jp

Installation

pip install git+https://github.com/nobifukuda/splitpopsurv-py.git

Usage

import pandas as pd
from splitpopsurv import fit_splitpop_weibull

# mydata needs: time, event (0/1), and your covariates
fit = fit_splitpop_weibull(
    data=mydata,
    time="time",
    event="event",
    h_vars=["x1"],       # H_regression: covariates for timing
    p_vars=["x2"],       # P_regression: covariates for cure probability
)

print(fit.summary())     # coefficients, SEs, z-values, log-likelihood
fit.params               # named parameter vector (numpy array)
fit.as_dataframe()        # coefficients table as a pandas DataFrame

The other four distributions use the same signature: fit_splitpop_loglogistic(), fit_splitpop_lognormal(), fit_splitpop_gamma(), fit_splitpop_ggamma().

A note on the original Stata code

All five Stata programs this package translates compute a log-likelihood term that turns out to be the marginal density where the formula requires the marginal hazard (density divided by survival) — a discrepancy from Yamaguchi's own published model. This was confirmed by fitting simulated data with known parameters: the as-translated formula gives visibly biased estimates, or fails to converge outright, while the corrected formula implemented here recovers the true parameters accurately. See docs/manual.html for the full derivation and the simulation results. This is the same correction independently verified for the R and Stata ports of this model.

Development

pip install -e ".[test]"
pytest

License

MIT — see LICENSE.

References

Prentice, R. L. (1974). A log gamma model and its maximum likelihood estimation. Biometrika, 61(3), 539–544.

Schmidt, P., & Witte, A. D. (1989). Predicting criminal recidivism using "split population" survival time models. Journal of Econometrics, 40(1), 141–159.

Yamaguchi, K. (1992). Accelerated failure-time regression models with a regression model of surviving fraction: An application to the analysis of "permanent employment" in Japan. Journal of the American Statistical Association, 87(418), 284–292.

Yamaguchi, K., & Ferguson, L. R. (1995). The stopping and spacing of childbirths and their birth-history predictors: Rational-choice theory and event-history analysis. American Sociological Review, 60(2), 272–298.

Yamaguchi, K. (1998). Mover-stayer models for analyzing event nonoccurrence and event timing with time-dependent covariates: An application to an analysis of remarriage. Sociological Methodology, 28(1), 327–361.