2 48 CHAPTER 2 occurring in the group of offenders scoring high on dynamic risk scores, controlling for their static and initial dynamic (in case of Research Question 3b) scores. Thus, it represents the difference in recidivism of presumed LR versus HR men with a history of sexual offenses, above and beyond the effect of their static risk level for Research Question 2, and both static risk level and initial dynamic risk level for Research Question 3b, independent of follow up time. Because the distribution of log hazard ratio is nearly normal, the log transformation is applied for the meta-analytic integration. The formula for hazard rate is: 36 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 occurring in the group of offenders scoring high on dynamic risk scores, controlling for their static and initial dynamic (in case of Research Question 3b) scores. Thus, it represents the difference in recidivism of presumed LR versus HR men with a history of sexual offenses, above and beyond the effect of their static risk level for Research Question 2, and both static risk level and initial dynamic risk level for Research Question 3b, independent of follow up time. Because the distribution of log hazard ratio is nearly normal, the log transformation is applied for the meta-analytic integration. The formula for hazard rate is: () = *+ ,+ = *+/ *+ ,+/ ,+ where Oi is the observed number of recidivists in group i, Ei is the expected number of non-recidivists in group i, and Hi is the overall hazard rate for the ith group. A confidence interval for hazard ratios is computed by first transforming to the log scale, which more accurately approximates a normal distribution, calculating the limits, and subsequently transforming back to the original scale. The calculation is made using the formula: ( ()) ± 1−∝/28 -.,+!"9 where -.,+!" =:1/ / +1/ ( 2.3.5.3 Meta-analytic integration For the meta-analytic integration of the effect sizes of the included studies, both fixed and random effects model are used. These two meta-analytic models produce identical results when variability across the included studies is low. With increasing variability across studies, random-effect models give relatively more weight to smaller studies, resulting in confidence intervals that exceed those of fixed-effect models (Helmus et al., 2013). For this reason, we used fixed-effect models to construct a combined confidence interval when effect sizes were relatively homogeneous across included studies. However, if effect sizes across studies were heterogeneous, a random-effect model was used. Cochran’s Q was used to test for heterogeneity. In addition, the I2 statistic was used to describe the variability in effect sizes that could not be explained by chance. where Oi is the observed number of recidivists in group i, Ei is the expected number of non-recidivists in group i, and Hi is the overall hazard rate for the it interval for hazard ratios is computed by first transforming to the log scale, which more accurately approximates a normal distribution, calculating the limits, and subsequently transforming back to the original scale. The calculation is made using the formula: / / i i, i i it ( ) ± 1−∝/28 I where 36 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 occurring in the group of offenders scoring high on dynamic risk scores, controlling for their static and initial dynamic (in case of Research Question 3b) scores. Thus, it represents the difference in recidivism of presumed LR versus HR men with a history of sexual offenses, above and beyond the effect of their static risk level for Research Question 2, and both static risk level and initial dynamic risk level for Research Question 3b, independent of follow up time. Because the distribution of log hazard ratio is nearly normal, the log transformation is applied for the meta-analytic integration. The formula for hazard rate is: () = *+ ,+ = *+/ *+ ,+/ ,+ where Oi is the observed number of recidivists in group i, Ei is the expected number of non-recidivists in group i, and Hi is the overall hazard rate for the ith group. A confidence interval for hazard ratios is computed by first transforming to the log scale, which more accurately approximates a normal distribution, calculating the limits, and subsequently transforming back to the original scale. The calculation is made using the formula: ( ()) ± 1−∝/28 -.,+!"9 where -.,+!" =:1/ / +1/ ( 2.3.5.3 Meta-analytic integration For the meta-analytic integration of the effect sizes of the included studies, both fixed and random effects model are used. These two meta-analytic models produce identical results when variability across the included studies is low. With increasing variability across studies, random-effect models give relatively more weight to smaller studies, resulting in confidence intervals that exceed those of fixed-effect models (Helmus et al., 2013). For this reason, we used fixed-effect models to construct a combined confidence interval when effect sizes were relatively homogeneous across included studies. However, if effect sizes across studies were heterogeneous, a random-effect model was used. Cochran’s Q was used to test for heterogeneity. In addition, the I2 statistic was used to describe the variability in effect sizes that could not be explained by chance. 2.3.5.3 Meta-analytic integration For the meta-analytic integration of the effect sizes of the included studies, both fixed and random effects models are used. These two meta-analytic models produce identical results when variability across the included studies is low. With increasing variability across studies, random-effect models give relatively more weight to smaller studies, resulting in confidence intervals that exceed those of fixed-effect models (Helmus et al., 2013). For this reason, we used fixed-effect models to construct a combined confidence interval when effect sizes were relatively homogeneous across included studies. However, if effect sizes across studies were heterogeneous, a random-effect model was used. Cochran’s Q was used to test for heterogeneity. In addition, the I2 statistic was used to describe the variability in effect sizes that could not be explained by chance. Because the findings of meta-analyses can be strongly influenced by outlying effect sizes and large sample sizes, we removed outliers following Hanson and Bussière (1998) and Hanson and Morton-Bourgon (2009). A study was classified as an outlier if the overall Q was significant and the effect size of that particular study was the most extreme value and accounted for more than 50% of the variability (effect sizes will be presented both with and without outliers). Following Helmus, Babchishin, and Hanson
RkJQdWJsaXNoZXIy MjY0ODMw