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splitpopsurv

Split-population (cure / mover–stayer) survival models in R: 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 an R 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

Author

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

Installation

# install.packages("remotes")
remotes::install_github("nobifukuda/splitpopsurv")

Usage

library(splitpopsurv)

# mydata needs: time, event (0/1), group (0/1), and your covariates
fit <- fit_splitpop_weibull(
  hform = ~ x1,           # H_regression: covariates for timing
  pform = ~ x2,           # P_regression: covariates for cure probability
  data  = mydata,
  time  = "time",
  event = "event",
  group = "group",
  method = "BFGS"
)

summary(fit)   # coefficients, SEs, z-values, log-likelihood
coef(fit)      # named parameter vector

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 (especially for the cure-probability coefficients), while the corrected formula implemented here recovers the true parameters accurately. See docs/manual.html for the full derivation and the simulation results.

A companion Stata command implementing the same corrected models is also available; see the author’s contact details below.

License

MIT — see LICENSE.

References

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.

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

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
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