The Effects of Sanction Intensity on Criminal Conduct - JDAI Helpdesk

(IRR = 1.41, p ≤ .107). SES did not predict frequency <strong>of</strong> recidivism, but increasing status
was significantly associated with non-<strong>of</strong>fending.
Figure 2.3 shows the Kaplan-Meier survival estimates for the treatment and
control groups. <strong>The</strong> Kaplan-Meier survival estimate is the probability <strong>of</strong> not <strong>of</strong>fending
on a daily basis. <strong>The</strong> most striking feature <strong>of</strong> the graph is that the probability <strong>of</strong> failure is
very low for all low-risk <strong>of</strong>fenders. Figure 2.3 is a visual representation <strong>of</strong> the figures
reported above: approximately 21 per cent <strong>of</strong> the sample had failed after two years. <strong>The</strong>
survivor functions for the treatment and control groups look extremely similar. This is
confirmed by the log-rank test for equality <strong>of</strong> survivor functions, which indicates that the
probability <strong>of</strong> survival in the two groups is identical (χ 2 (1 d.f.) = .00, p ≤ .996).
We extend this basic comparison by modeling time to first failure with controls
for additional covariates using Cox proportional hazards regression. 20
Table 2.4 presents
the results <strong>of</strong> the regression model in terms <strong>of</strong> hazard ratios (HR). <strong>The</strong> hazard is the risk
<strong>of</strong> failure over time, and thus is equivalent to the incidence rate ratio. <strong>The</strong> model
confirms that there is no difference in hazards between the treatment and control groups
(HR = 1.03, p ≤ .777). As we saw in the results for prevalence and frequency outcomes,
other factors appear to have a greater influence on the risk <strong>of</strong> failure regardless <strong>of</strong>
treatment assignment. Being in the West probation region is associated with a 36 per
cent lower risk <strong>of</strong> failure over time than being in the Northeast, as we would expect from
the result <strong>of</strong> our logistic model (HR = .64, p ≤ .001). Older and higher SES <strong>of</strong>fenders
were also at a significantly lower risk <strong>of</strong> failure over time.
As we have seen, Cox regression does not require us to make assumptions about
the shape <strong>of</strong> the hazard or survivor functions. However, it is possible to graph the
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