Preliminary Estimates of Homicide Offenders' Recidivism: WA Data Analysis

1. The recidivism of homicide offenders: preliminary estimates from the WA recidivism data-base Rod Broadhurst and Ross Maller with Brigitte Bouhours, Russell Brewer and Max Maller

2. Measuring recidivism • We observe `true' recidivism if the observation is uncensored, otherwise we know only that the potential to do so exceeds the censoring value (i.e. cut-off date).  • We use the Kaplan--Meier Estimator (KME) for data display and for nonparametric analysis. Typically, in recidivism analysis, the KME levels off at a value less than 1, revealing the possible presence of long-term survivors who will not recidivate (visible in “censored” data, when the KME levels off). • The question of `sufficient follow-up’ is highly relevant.  Aims • estimate the proportion of long-term survivors; • test confidence that there really are long-term survivors in the population; • test whether proportions of long-term survivors (if present) differ between subgroups of interest; • test whether the failure rates of `susceptibles' differ between subgroups of interest; and   • measure the time or ‘speed’ to fail for those who do.

3. Data Definition • All individuals whose career includes at least onehomicide offence, such as murder, manslaughter (type 1): attempt, conspiracy and/or accessory to murder (type 2); and dangerous driving causing death (type 3). • a grave offence includes: robbery, blackmail and extortion, assault, sexual assault, abduction and other offences against the person, burglary, arson and child pornography. • Outcomes: 1. re-occurrence of homicide offence (homologous re-offending) 2. occurrence of a grave offence (serious and violent) and 3. occurrence of any offence (after arrest for homicide). • ‘Static’ variables are available for each event such as age, sex, aboriginality, prior (signal) offence, offence type (up to three) and arrest outcome (type of intervention). Occupation, length of prison or CBO, employment and bail status, as well as locality are also available.

4. Re-arrest of homicide offenders in WA 1984-2005*                          N Any Grave Homicide Male Non-Indigenous 764  284 101 11Male Indigenous 122 102 76 2Female Non-Indigenous 166 31 11 2Female Indigenous  36 21 15 0 All 1088 438 203 15 *Note - rearrest for at least any offence following arrest for the signal offence by the cut off date 31.12.2005;

5. Attrition/undercounting of offending • Offender deaths (natural) See: Ferrante, Anna, NiniLoh, and Max Maller 2009, ‘Assessing the impact of time spent in custody and mortality on the estimation of recidivism’, Current Issues in Criminal Justice 21(2): 273-87. • Offender movement not captured: interstate or extra-jurisdiction re-offending not recorded • Age and cohort effects over 20 + year follow-up • Arrest/re-arrest (apprehensions) less accurate than conviction

6. Methods • John W. Boag, 1949, ‘Maximum Likelihood Estimates of the Proportion of Patients Cured by Cancer Therapy’, Journal of the Royal Statistical Society. Series B (Methodological) , Vol. 11 (1), pp. 15-53 • Maltz, M. D. and McCleary, R. 1977, The mathematics of behavioural change: recidivism and construct validity, Evaluation Quarterly, 1, 421-438. • Lattimore, Pamela, Christy Visher, and Richard Linster 1995, ‘Predicting rearrest for violence among serious youthful offenders, Journal of Research in Crime and Delinquency 32(1): 54-85.  • Maller, Ross and Xian Zhou 1996, Survival Analysis with Long-Term Survivors, Wiley, Chichester. • Christoffersen, MogenNygaard, Brian Francis and Keith Soothill2002, ‘An upbringing of violence? Identifying the likelihood of violent crime among the 1966 birth cohort in Denmark’,Journal of Forensic Psychiatry and Psychology 14(2): 367-81. • Bierens Herman and Jose Carvalho 2007 ‘Semi-nonparametric competing risk analysis of recidivism’, Journal of Applied Econometrics 22: 971-93. • Liu, Yuan Y, Min Yang, Malcolm Ramsay, Xiao Li, and Jeremy Coid, 201, ‘A comparison of logistic regression, classification and neural networks models in predicting violent re-offending,’Journal of Quantitative Criminology 27: 547-73.

7. Recent References Baay, Pieter, MariekeLiem& Paul Nieuwbeerta 2012, ‘“Ex-imprisoned homicide offenders: Once bitten, twice shy?” The effect of the length of imprisonment on recidivism for homicide offenders’, Homicide Studies 16: 259-79. (Cox’s R N=612) Berk, Richard, Lawrence Sherman, Geoffrey Barnes, Ellen Kurtz, & Lindsay Ahlman 2009, ‘Forecasting murder within a population of probationers and parolees: A high states application of statistical learning’,Journal of the Royal Statistical Society 172: 191-211. (random forests algorithm) Hill, Andreas, NielsHabermann, Dietrich Klusmann, Wolfgang Berner, & Peers Briken 2008, ‘Criminal recidivism in sexual homicide perpetrators’, International Journal of Offender Therapy and Comparative Criminology 52(1): 5-20. (N=166; Cox’s R) Vries, Anne and MariekeLiem 2007, ‘Recidivism of juvenile homicide offenders’,Behavioral Science and the Law 29: 483-98. (Cox’s R; N=137) Roberts, Albert, Kristen Zgoba, and ChahidShahidullah 2007, ‘Recidivism among four types of homicide offenders: An exploratory analysis of 336 homicide offenders in New Jersey’, Aggression and Violent Behavior12: 493-507. (N=336, Cox’s R) Soothill, Keith, Brian Francis, Elizabeth Ackerley, and Rachel Fligelstone 2002, ‘Murder and serious sexual assault: What criminal histories can reveal about future serious offending’, Police Research Series, Paper 144, Home Office, London. (N= 569 – odds ratio; conditional logistic regression/ control group)

9. Model fitting • In this study, the time to re-offend data are fitted by a Weibull mixture distribution (model) of the form • p[1 − exp{−(λt)α}], t ≥ 0. • p = proportion of susceptibles • 1-p = proportion of non-recidivists • l= rate of recidivism • = shape of distribution • test of significance -2 log likelihood ratio (chi-square)

10. MA 0.92 (.85, .97) FA 0.72 (.53, .87) MNA 0.45 (.41; .49) FNA 0.22 (.16, .23) All 0.45 (.40, .50)

11. MA   0.79 (.69,.87)FA 0.61 (.40,.83)MA 0.19 (.15, .24) FN 0.08 (.04,.14)

12. Priors 1  Type 1 0.32 (.44; .21)Priors 1  Type 2  0.30 (.38; .23)Priors 2  Type 1  0.62 (.70; .54)  Priors 2  Type 2  0.61  (.72; .52)

13. Age 1 Priors 1  0.44  (.55; .35)Age 1 Priors 2  0.15  (.24; .09)Age 2 Priors 1   0.62 (.74; .06) Age 2 Priors 2   0.43 (.55 ; .33)

14. MA   0.79 (.69;.87)FA 0.61 (.40;.83)MA 0.19 (.15;.24) FN 0.08 (.04;.14)

15. Age 1 0.25 (.19; .32) Age 2 0.08 (.04; .14)

16. No Priors 0.08 (.17; .14) Priors 0.33 (.25; .42)

17. Type 1 0.21 (.17; .22) Type 2 0.14 (.07; .26) Type 3 0.15 (.10; .23)

18. Questions welcome – contact roderic.broadhurst@anu.edu.au or ross.maller@anu.edu.au