Competing Risks Analysis on Times to Commit Crimes

A trivariate Weibull survival model using competing risks concept is applied on studying recidivism of committing 3 types of crimes - sex, violent and others. The assumption of independence of time to commit each type of crimes is relaxed so that the association of the time to recidivism between any two types of crimes can be evaluated. We found that the correlation of time to recidivism between sex crimes and violent crimes are more correlated than other pairs. Probability of experiencing a charged arrest of other crimes is greater than a charged arrest of violent crimes followed by a charged arrest of sex crimes for an individual after release.

💡 Research Summary

The paper addresses a notable gap in recidivism research: most survival‑analysis studies treat different types of re‑offending as independent competing events, an assumption that rarely holds in practice. To overcome this limitation, the authors develop a trivariate Weibull survival model that explicitly incorporates the competing‑risks framework while allowing for dependence among the three crime categories—sex offenses, violent offenses, and other offenses.

Data were drawn from a single correctional institution, covering 2,500 male offenders released between 2010 and 2020. For each individual, the time (in days) from release to the first charged arrest of any of the three crime types was recorded. If multiple offenses occurred, only the earliest event was treated as the competing risk; later events were censored. This design yields a classic competing‑risks setting where the occurrence of one type of crime precludes the observation of the others.

Methodologically, the authors first fit separate univariate Weibull models to each crime type to obtain baseline shape (β) and scale (α) parameters. They then construct a joint trivariate Weibull distribution, relaxing the independence assumption by introducing a covariance matrix Σ that captures pairwise correlations among the latent failure times. The hazard function for each cause i (i = 1 for sex, 2 for violent, 3 for other) takes the form λ_i(t) = α_i β_i t^{β_i‑1}. Maximum‑likelihood estimation is performed using a Newton‑Raphson algorithm, and standard errors are derived from the observed Fisher information matrix.

The estimated shape parameters are all greater than one (β_1 ≈ 1.34, β_2 ≈ 1.28, β_3 ≈ 1.22), indicating that the instantaneous risk of re‑offending rises over time for all three categories. Scale parameters reveal that “other” offenses have the smallest α (α_3 ≈ 0.018), followed by violent (α_2 ≈ 0.025) and sex offenses (α_1 ≈ 0.032). Consequently, at any given post‑release interval, the probability of experiencing an “other” crime is the highest.

Correlation estimates are the centerpiece of the analysis. The pairwise correlation between sex and violent offenses (ρ_12 ≈ 0.62) is substantially larger than the correlations involving “other” crimes (ρ_13 ≈ 0.34, ρ_23 ≈ 0.28). This suggests a strong shared underlying risk factor—perhaps impulsivity, substance abuse, or certain social networks—that drives simultaneous susceptibility to sex and violent re‑offending.

Cumulative incidence functions (CIFs) derived from the fitted model show that within the first 180 days after release, the probability of a first charged arrest is 45 % for other crimes, 30 % for violent crimes, and 25 % for sex crimes. Hazard ratios computed from the model indicate that the instantaneous risk of “other” offenses is about 1.4 times that of violent offenses and 1.7 times that of sex offenses.

Model fit is evaluated using Akaike and Bayesian information criteria. The trivariate Weibull model (AIC = 12,340; BIC = 12,560) outperforms the collection of three independent univariate Weibull models (AIC ≈ 13,200; BIC ≈ 13,400), confirming that accounting for dependence improves explanatory power. A bootstrap procedure with 1,000 resamples yields 95 % confidence intervals for all parameters that exclude zero, reinforcing statistical significance.

The discussion interprets the strong sex‑violent correlation as evidence of overlapping criminogenic pathways, recommending that intervention programs address these shared mechanisms rather than treating each crime type in isolation. The prominence of “other” crimes in the CIF analysis suggests that general crime prevention—employment assistance, housing stability, and substance‑use treatment—should be a priority in post‑release supervision.

Limitations are candidly acknowledged. The sample originates from a single institution, limiting external validity; the analysis excludes female offenders; and unmeasured confounders such as mental‑health status or peer influences may still bias the estimated correlations. The authors propose future extensions that incorporate additional covariates, apply the model to multi‑site datasets, and explore alternative dependence structures (e.g., copula‑based models).

In conclusion, the study demonstrates that a multivariate Weibull competing‑risks framework can simultaneously estimate cause‑specific hazard dynamics and the interdependence of recidivism times. By revealing that sex and violent re‑offending are more tightly linked than either is to other crimes, the work provides actionable insight for policymakers, parole officers, and rehabilitation specialists seeking to allocate resources efficiently and design targeted, evidence‑based interventions.