JDS Journal of Data Science 1683-86021680-743X1680-743X School of Statistics, Renmin University of China JDS1239 10.6339/26-JDS1239 Data Science in Action Predictive Modeling of Short-Term Recidivism: A Mixture Cure Rate Approach with Diverse Link Functions YooChaeyeonchaeyeon.yoo@uconn.edu1∗ DeyDipak K.1 University of Connecticut, Storrs, USA Corresponding author. Email: chaeyeon.yoo@uconn.edu. 2026297202600121 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.

9420252762026 2026 The Author(s). Published by the School of Statistics and the Center for Applied Statistics, Renmin University of China.2026 Open access article under the CC BY license.

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.

 accelerated failure time Bayesian inference generalized logistic distribution time-to-event 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 R ˆ 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