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Journal of Data Science


Predictive Modeling of Short-Term Recidivism: A Mixture Cure Rate Approach with Diverse Link Functions
Pub. online: 29 July 2026      Type: Data Science In Action      Open accessOpen Access
Received
9 April 2025
Accepted
27 June 2026
Published
29 July 2026

Abstract

Addressing short-term recidivism presents a significant challenge within the criminal justice system, necessitating robust predictive models that can accurately identify risk factors and predict outcomes. This paper introduces application of Bayesian cure rate models to predict short-term recidivism using data from individuals released from Iowa prisons in 2018. The mixture cure rate models effectively capture the recidivism risk by distinguishing between cured individuals, those unlikely to re-offend, and those susceptible to relapse. By implementing accelerated failure time models combined with logistic regression and various link functions, including logit, skewed logit, reversed power logit, and flexible generalized logit, we enhance the model’s flexibility and interpretability. Through a comparative analysis of these models, key predictors of recidivism are identified and discussed in detail.

Supplementary material

 Supplementary Material
The code supplement is available as a compressed folder. It is written in R and readily allows to replicate of the simulation results and Iowa data application. Some additional simulation results are provided within the folder.

References

 
Alper M, Durose MR, Markman J (2018). 2018 update on prisoner recidivism: A 9-year follow-up period, (2005–2014). Special Report NCJ 250975, U.S. Department of Justice, Office of Justice Programs, Bureau of Justice Statistics, Washington, DC.
 
Bazán JL, Torres-Avilés F, Suzuki AK, Louzada F (2017). Power and reversal power links for binary regressions: An application for motor insurance policyholders. Applied Stochastic Models in Business and Industry, 33(1): 22–34. https://doi.org/10.1002/asmb.2215
 
Berk R (2016). Statistical Learning from a Regression Perspective. Springer, Philadelphia, PA, 2nd edition.
 
Berkson J, Gage RP (1952). Survival curve for cancer patients following treatment. Journal of the American Statistical Association, 47(259): 501–515. https://doi.org/10.1080/01621459.1952.10501187
 
Boag JW (1949). Maximum likelihood estimates of the proportion of patients cured by cancer therapy. Journal of the Royal Statistical Society, Series B, Methodological, 11(1): 15–53. https://doi.org/10.1111/j.2517-6161.1949.tb00020.x
 
Chen MH, Dey DK, Shao QM (1999). A new skewed link model for dichotomous quantal response data. Journal of the American Statistical Association, 94(447): 909–919. https://doi.org/10.1080/01621459.1999.10473872
 
De la Cruz R, Fuentes C, Padilla O (2022). A Bayesian mixture cure rate model for estimating short-term and long-term recidivism. Entropy, 25(1): 56. https://doi.org/10.3390/e25010056
 
Dressel J, Farid H (2018). The accuracy, fairness, and limits of predicting recidivism. Science Advances, 4(1): eaao5580. https://doi.org/10.1126/sciadv.aao5580
 
Durose MR, Antenangeli L (2021). Recidivism of prisoners released in 34 states in 2012: A 5-year follow-up period, (2012–2017). Special Report NCJ 255608, U.S. Department of Justice, Office of Justice Programs, Bureau of Justice Statistics, Washington, DC.
 
Farewell VT (1977). A model for a binary variable with time-censored observations. Biometrika, 64(1): 43–46. https://doi.org/10.1093/biomet/64.1.43
 
Farewell VT (1982). The use of mixture models for the analysis of survival data with long-term survivors. Biometrics, 38(3): 1041–1046. https://doi.org/10.2307/2529885
 
Gelman A, Meng XL, Stern H (1996). Posterior predictive assessment of model fitness via realized discrepancies. Statistica Sinica, 6(4): 733–760.
 
Ghosh I, Alzaatreh A (2018). A new class of generalized logistic distribution. Communications in Statistics - Theory and Methods, 47(14): 3459–3473.
 
Gupta RD, Kundu D (2001). Exponentiated exponential family: An alternative to gamma and Weibull distributions. Biometrical Journal, 43(1): 117–130. https://doi.org/10.1002/1521-4036(200102)43:1<117::AID-BIMJ117>3.0.CO;2-R
 
Iowa Department of Corrections (2024). Iowa prison recidivism and change by cohort. Accessed: January 2024. Available at https://data.iowa.gov/Correctional-System/Iowa-Prison-Recidivism-and-Change-by-Cohort/dnzw-paxg/about_data.
 
Kim S, Chen MH, Dey DK (2008). Flexible generalized t-link models for binary response data. Biometrika, 95(3): 535–548. https://doi.org/10.1093/biomet/asm079
 
Kuk AY, Chen C (1992). A mixture model combining logistic regression with proportional hazards regression. Biometrika, 79(3): 531–541. https://doi.org/10.1093/biomet/79.3.531
 
Li CS, Taylor JMG (2002). A semi-parametric accelerated failure time cure model. Statistics in Medicine, 21(21): 3235–3247. https://doi.org/10.1002/sim.1260
 
Li D, Wang X, Dey DK (2016). A flexible cure rate model for spatially correlated survival data based on generalized extreme value distribution and Gaussian process priors. Biometrical Journal, 58(5): 1178–1197. https://doi.org/10.1002/bimj.201500040
 
Maller RA, Zhou X (1996). Survival Analysis with Long-Term Survivors. Wiley.
 
Maltz MD (1984). Recidivism. Academic Press, Florida.
 
Nagler J (1994). Scobit: An alternative estimator to logit and probit. American Journal of Political Science, 38(1): 230–255. https://doi.org/10.2307/2111343
 
Partanen J (1969). On waiting time distributions. Acta Sociologica, 12(3): 132–143. https://doi.org/10.1177/000169936901200303
 
Prasetyo RB, Kuswanto H, Iriawan N, Ulama BSS (2020). Binomial regression models with a flexible generalized logit link function. Symmetry, 12(2): 221. https://doi.org/10.3390/sym12020221
 
Robert CP, Casella G (2004). Monte Carlo Statistical Methods. Springer, New York, 2nd edition.
 
Schmidt P, Witte AD (1989). Predicting criminal recidivism using ‘split population’ survival time models. Journal of Econometrics, 40(1): 141–159. https://doi.org/10.1016/0304-4076(89)90034-1
 
Schmidt P, Witte AD (2012). Predicting Recidivism Using Survival Models. Springer Science and Business Media.
 
Scolas S, Legrand C, Oulhaj A, Ghouch A (2016). Diagnostic checks in mixture cure models with interval-censoring. Statistical Methods in Medical Research, 27(7): 2114–2131. https://doi.org/10.1177/0962280216676502
 
Spiegelhalter DJ, Best NG, Carlin, BP, Van Der Linde A (2002). Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B, Statistical Methodology, 64(4): 583–639. https://doi.org/10.1111/1467-9868.00353
 
Sy JP, Taylor JMG (2000). Estimation in a Cox proportional hazards cure model. Biometrics, 56(1): 227–236. https://doi.org/10.1111/j.0006-341X.2000.00227.x
 
Ting MH, Chu CM, Zeng G, Li D, Chng GS (2018). Predicting recidivism among youth offenders: Augmenting professional judgement with machine learning algorithms. Journal of Social Work, 18(6): 631–649. https://doi.org/10.1177/1468017317743137
 
Tollenaar N, Wartna BSJ, Van der Heijden PGM, Bogaerts S (2016). Statrec – performance, validation and preservability of a static risk prediction instrument. BMS. Bulletin de Méthodologie Sociologique, 129: 25–44. https://doi.org/10.1177/0759106315615504
 
Vehtari A, Gelman A, Gabry J (2017). Practical Bayesian model evaluation using leave-one-out cross-validation and waic. Statistics and Computing, 27(5): 1413–1432. https://doi.org/10.1007/s11222-016-9696-4
 
Vehtari A, Gelman A, Simpson D, Carpenter B, Bürkner PC (2021). Rank-normalization, folding, and localization: An improved $\hat{R}$ for assessing convergence of mcmc. Bayesian Analysis, 16(2): 667–718. https://doi.org/10.1214/20-BA1221
 
Watanabe S (2010). Asymptotic equivalence of Bayes cross-validation and widely applicable information criterion in singular learning theory. Journal of Machine Learning Research, 11: 3571–3594.
 
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. https://doi.org/10.1080/01621459.1992.10475207
 
Zhang J, Peng Y (2007). A new estimation method for the semiparametric accelerated failure time mixture cure model. Statistics in Medicine, 26(16): 3157–3171. https://doi.org/10.1002/sim.2748

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Copyright
2026 The Author(s). Published by the School of Statistics and the Center for Applied Statistics, Renmin University of China.
Open access article under the CC BY license.

Keywords
accelerated failure time Bayesian inference generalized logistic distribution time-to-event

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