2 47 PREDICTIVE PROPERTIES DYNAMIC INSTRUMENTS 2.3.5 STATISTICAL ANALYSES 2.3.5.1 Calculation of effect sizes For studies reporting the predictive properties of several dynamic risk assessment instruments within the same sample, the weighted mean of the effect sizes of all included instruments was computed. For studies reporting different effect sizes for the incremental validity of one dynamic risk assessment instrument over several static instruments within the same sample, the weighted mean of the effect sizes on that particular dynamic risk assessment instrument was computed. For studies reporting the predictive validity of both pre- and posttreatment scores, the weighted mean of the effect size of both assessments was computed. Transformations of the effect sizes of individual studies and the meta-analytic integration was conducted using Comprehensive Meta-Analysis (CMA; Version 2; Borenstein et al., 2005). 2.3.5.2 Effect size metric outcome For Research Questions 1 and 3a, regarding the predictive properties of dynamic risk assessment instruments and the predictive validity of regular change scores, we used the standardized mean difference, Cohen’s d, as effect size metric outcome. It was computed as follows (Hasselblad & Hedges, 1995): 35 2.3.5.1 Calculation of effect sizes For studies reporting the predictive properties of several dynamic risk assessment instruments within the same sample, the weighted mean of the effect sizes of all included instruments was computed. For studies reporting different effect sizes for the incremental validity of one dynamic risk assessment instrument over several static instruments within the same sample, the weighted mean of the effect sizes on that particular dynamic risk assessment instrument was computed. For studies reporting the predictive validity of both pre- and posttreatment scores, the weighted mean of the effect size of both assessments was computed. Transformations of the effect sizes of individual studies and the metaanalytic integration was conducted using Comprehensive Meta-Analysis (CMA; Version 2; Borenstein et al., 2005). 2.3.5.2 Effect size metric outcome For Research Questions 1 and 3a, regarding the predictive properties of dynamic risk assessment instruments and the predictive validity of regular change scores, we used the standardized mean difference, Cohen’s d, as effect size metric outcome. It was computed as follows (Hasselblad & Hedges, 1995): = ! − " #$$%&' where M1 is the mean score of the group recidivist, M2 is the mean score of the group nonrecidivists, and SDpooled is the pooledwithin SD of both groups, computed as follows: #$$%&' =( ( ! −1) ! " +( " −1) " " ! + " −2 If not all information necessary for these calculations was available, Cohen’s d was calculated using the receiver operating characteristic area (AUC), correlation coefficient, or the LogOddsRatio (see Appendix A in the online supplemental materials for the formulas used to convert these effect sizes into Cohen’s d). For Research Question 2 and 3b, regarding the incremental validity of scores on dynamic risk assessment instruments over scores on static risk assessment instruments and the predictive validity of change scores corrected for static and initial dynamic scores, where M1 is the mean score of the group recidivist, M2 is the mean score of the group non-recidivists, and SDpooled is the pooledwithin SD of both groups, computed as follows: 35 2.3.5 Statistical analyses 2.3.5.1 Calculation of effect sizes For studies reporting the predictive properties of several dynamic risk assessment instruments within the same sample, the weighted mean of the effect sizes of all included instruments was computed. For studies reporting different effect sizes for the incremental validity of one dynamic risk assessment instrument over several static instruments within the same sample, the weighted mean of the effect sizes on that particular dynamic risk assessment instrument was computed. For studies reporting the predictive validity of both pre- and posttreatment scores, the weighted mean of the effect size of both assessments was computed. Transformations of the effect sizes of individual studies and the metaanalytic integration was conducted using Comprehensive Meta-Analysis (CMA; Version 2; Borenstein et al., 2005). 2.3.5.2 Effect size metric outcome For Research Questions 1 and 3a, regarding the predictive properties of dynamic risk assessment instruments and the predictive validity of regular change scores, we used the standardized mean difference, Cohen’s d, as effect size metric outcome. It was computed as follows (Hasselblad & Hedges, 1995): = ! − " #$$%&' where M1 is the mean score of the group recidivist, M2 is the mean score of the group nonrecidivists, and SDpooled is the pooledwithin SD of both groups, computed as follows: #$$%&' =( ( ! −1) ! " +( " −1) " " ! + " −2 If not all information necessary for these calculations was available, Cohen’s d was calculated using the receiver operating characteristic area (AUC), correlation coefficient, or the LogOddsRatio (see Appendix A in the online supplemental materials for the formulas used to convert these effect sizes into Cohen’s d). For Research Question 2 and 3b, regarding the incremental validity of scores on dynamic risk assessment instruments over scores on static risk assessment instruments and the predictive validity of change scores corrected for static and initial dynamic scores, If not all information necessary for these calculations was available, Cohen’s d was calculated using the receiver operating characteristic area (AUC), correlation coefficient, or the LogOddsRatio (see Appendix A in the online supplemental materials for the formulas used to convert these effects sizes into Cohen’s d). For Research Question 2 and 3b, regarding the incremental validity of scores on dynamic risk assessment instruments over scores on static risk assessment instruments and the predictive validity of change scores corrected for static and initial dynamic scores, we used the Cox estimate of the hazard ratio as effect size measure, and included static risk scores and for Research Question 3b also initial dynamic scores as a covariate. The hazard ratio reflects the chance of recidivism occurring in the group of offenders scoring low on dynamic risk scores divided by the chance of recidivism
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