Risk of re-Conviction X Risk of re-Imprisonment model. (RoC*RoI) (Bakker, O’Malley, & Riley, 1998). The RoC*RoI measure was developed for the New Zealand Department of Corrections to assist in the accurate prediction of an offender’s risk of conviction and likelihood of reimprisonment. The measure is based on static predictors (factors unchangeable by individual effort) from criminal history information. In developing the measure Bakker, O’Malley, and Riley (1999) used the following predictor variables:
Personal characteristics
Jail and time at large
Seriousness of offending
Offence type
The complete criminal histories of more than 133,000 offenders (those convicted of an imprison able offence in 1983, 1988, and 1989) were used to develop RoC*RoI. Available information on these offenders included their complete criminal history prior to 1983, 1988, and 1989, and for any further offending over the next five years. Logistic regression was used by Bakker et al. (1999) to determine the relationship between the predictor variables and future offending, with the size of the sample allowing random allocation to either the development or validation samples. The key strength of RoC*RoI is that it can effectively manage an enormous amount of factual information about an offender. Each piece of datum is weighed up and balanced against other pieces of factual information in an objective way to produce a statistical probability of reoffending (score range is 0.0 to 1.0, representing 0 risk to 100% risk of serious recidivism). As this is computer generated human error in calculating the score is eliminated.
The RoC*RoI actuarial measure is in fact a combination of two risk models. RoC equals Risk of re-Conviction, while RoI equals the Risk of re-Imprisonment. These two risk models derive from exploiting the mathematical relationship between basic social and demographic variables, criminal history variables and future offending. The RoC*RoI measure, therefore, is an expression of the likelihood that a person will be both reconvicted in the future and be sentenced to a term of imprisonment for that offence. As a combined measure, it is quite possible that any individual may have a very high chance of re-offending (say 90%), but a very low chance of also being sent to prison for that offence (say 10%). In such a circumstance, the actual chance of someone being both reconvicted for an offence, and being sent to prison for that offence would be only 9 percent. Conversely, it is possible for a person to have a very low chance of reoffending, but a very high chance of receiving a prison term if they do. Again, the combined value expressed by the RoC*RoI measure would result in a low probability of being reconvicted and sent to prison. The Corrections Department has adopted RoC*RoI as its primary recidivism measure, rather than just risk of conviction alone, because this gives some indication of serious re-offending. A number of confusing results have been reported with the use of RoC*RoI with child sex offenders and youth offenders. Many child sex offenders have very low RoC*RoI scores. This reflects the fact that often this is a specialist form of offending, which occurs at a very low frequency with long gaps between offences. Sexual offending against children may also go undetected for long periods due to the nature of the offences and their effects on victims. The RoC*RoI model was developed as a measure designed to predict future general criminal offending. Sex offending against children is not necessarily highly correlated with other forms of criminal behaviour.
As has already been noted, the RoC*RoI measure relies upon previous recorded offences in developing estimates of future risk. There are cases of very young offenders who come into the criminal justice system, who show no official record of offending in the adults courts, but who may have extensive offending histories which have previously been dealt with in the juvenile court. In these cases, the RoC*RoI measure can only be calculated on the criminal history data that are available, and this does not include their often extensive Youth Court criminal histories.
The Roc*RoI model has been found to be very accurate. Bakker et al. (1999) report that comparing the predicted outcome to an optimal fitted model (45-degree “ideal” trend line) produced plotted data that were mathematically close to the ideal outcome line. The model did have some slight instability in which the data path moved under the 45-degree trend line at the upper end of the graph, with this believed to be due to small numbers in the validation sample with very high scores (.80 and over). Further analysis on the overall predictive accuracy of the RoC*RoI measure was carried out using Receiver Operating Characteristic (ROC) analysis with an Area Under of the Curve (AUC) of .76 found. This is interpreted as the instrument being able to discriminate 76% of the area under the curve plotted from the true false positive rate against the false positive rate for serious reoffending (SE = .0072) (Bakker et al., 1998).
ROC analysis is based on Signal Detection Theory (Swets, 1996). Blackwell in the 1950s used Thurstone’s (1920s) theory involving two overlapping (bell-shaped) distributions to perform a “yes-no” detection task (cited in Swets, 1996). It is the relationship between the detection of the threshold (sensitivity) and non-detection (specificity) in which the rate of detection versus no detection is greater than 50/50. In statistical theory, the two overlapping distributions are a null and alternative hypothesis. ROC analysis shows for a given score the discriminative acuity how the true-positive rates (sensitivity) varies with the false-positive error (specificity or false positive fraction which is subtracted from 1.0 for a series of possible score cut-off scores). Discrimination between the two distributions is reflected in a numeric value indicating the area under the curve. The AUC being defined as a measure of the locus of an ROC curve on its graph. The AUC figure measures dozens of empirical ROC’s that are fitted well by a linear function, with varying slope (changes in score detection), thus allowing the use of several decision criteria simultaneously instead of the adoption of single cut-off scores. Area Under the Curve varies between 0.5 and 1.0 with 1 reflecting perfect discrimination or no false positive error, and .50 indicating chance discrimination. An AUC = .80 is an overall figure of an instruments ability to discriminate 80% of the area under a curve plotted from the sensitivity against the specificity for an identified behaviour.
The use of ROC analysis in the area of risk assessment has become the method of choice over the last ten years (Mossman, 1994; Rice, 1997; Quinsey et al, 1998). This has been because of ROC not being as dependant on the base rate of interest, in this case violent recidivism, as are correlation-based methods and indexes derived from 2 X 2 contingency tables (such as with false positive and false negative tables based on a single cut-off). Behaviours with base rates of under 50% reduce the size of correlations and the base rate for violence is usually lower than 50%. Another advantage is that ROC's allow the comparison of various predictive measures with a single optimal threshold (AUC) produced to allow the relative accuracy of a measure to be compared.