Health-related factors predict return to custody in a large cohort of ex-prisoners: new approaches to predicting re-incarceration

For the final reduced multivariate Cox proportional hazards model presented in Table 3 of the main text, we assessed the proportional hazards assumption via the Schoenfeld residuals. We examined plots of the residuals for each variable against time to check for a non-­‐zero slope, which indicates that the proportional hazards assumption is violated (Hosmer et al. 1999). We then performed statistical tests of this assumption via a generalised linear regression of the residuals against time. A global test of proportional hazards for the reduced model provided some evidence that this assumption was violated (í µí¼’ ! (29) = 43.04, p = 0.0451), and tests for individual variables (Table S1) indicated that it was most strongly violated for Indigenous status (í µí¼’ ! (1) = 9.96, p = 0.0016) and being sedentary (í µí¼’ ! (1) = 9.07, p = 0.0026). A plot of the Schoenfeld residuals for Indigenous status vs. time (Figure S1) and sedentary vs. time (Figure S2) indicated that the HRs for both of these variables were different after approximately 500 days following release. We therefore ran a new model including a time-­‐varying HR (split at 500 days after release) for Indigenous status and sedentary. A likelihood ratio test comparing this model to the time-­‐constant version provided strong evidence against the null hypothesis of time constant HRs for these variables (p = 0.0013). Repeating the global test of proportional hazards for the new model provided no evidence against this assumption (í µí¼’ ! (31) = 28.57, p = 0.5916).