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.

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.