Detecting and Describing Preventive Intervention Effects

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Detecting and Describing Preventive Intervention Effects in a Universal School-Based Randomized Trial Targeting Delinquent and Violent BehaviorMike Stoolmiller Oregon Social Learning Center Eugene, Oregon J. Mark Eddy Oregon Social Learning Center Eugene, Oregon John B. Reid Oregon Social Learning Center Eugene, Oregon INTRODUCTION I chose to summarize this article regarding the study of measurement of child aggression in empirical studies, because of the difficulty of conducting such studies. Here I summarize the article I studied, along with comments and my opinions on the findings. Summary This study examined theoretical, methodological, and statistical problems involved in evaluating the outcome of aggression on the playground for a universal preventive intervention for conduct disorder. Moderately aggressive children were hypothesized most likely to benefit. Aggression was measured on the playground using observers blind to the group status of the children. Behavior was microcoded in real time to minimize potential expectancy biases. The effectiveness of the intervention was strongly related to initial levels of aggressiveness. The most aggressive children improved the most. First, participants are clustered within naturally occurring units (e.g., classroom, grade level, or school), and such nonindependence may significantly bias statistical tests of intervention outcome. For example, the aggressive behaviors of children might be observed on the playground for three 10-min observations conducted over a 3-week period at preintervention and three 10-min sessions 6 months later postintervention. The second component is due to true time-specific individual differences across children. Clearly, any true time-specific individual differences in behavior must be the result of time-specific, contextual determinants of aggressive behavior in the external social environment, the internal biological environment, or some combination or interaction of the two. Further, the true time-stable individual differences must also be due to time-stable internal or external determinants. I believe this opposes a risk for the study, if the children¡¦s If behavior is highly variable from one occasion to the next, or if differences in behavior rates are small, then reliability may be inadequate even if coders are perfectly accurate. If the experimenter fixes the observational period at the same constant value for all participants, the censoring is known as Type I censoring (Lawless, 1982). The waiting time is the reciprocal of the rate. In this study participants in both the control and intervention conditions were assessed during the fall (preintervention) and spring (postintervention) academic quarters. The intervention program was conducted during the winter quarter of the same school year and lasted 10 weeks. Participants The 12 schools participating in the study had an average enrollment detainment rate of 13% , an average yearly student turnover rate of 43% , and an average free-lunch rate of 47% of students. The final sample comprised 671 students (51% female), with 382 attending the intervention schools and 289 attending the control schools. Participants in the control and intervention groups shared similar background characteristics. Repeated live observations were conducted on the playground by professional observers blind to the intervention status of the school. Analyses In the SEM literature, this type of model is known as a TOBIT factor analysis or structural model Muthen, 1989We used a TOBIT latent variable model to partial out time-specific variance from both the pre- and postintervention scores to obtain an estimate of the intervention impact that is not biased by the low reliability of the outcome measure. We specified a simple latent postintervention on latent preintervention score regression model separately in the control and intervention groups to test for nonparallel slopes (i.e., differential effectiveness). Because so few participants had partial data (intervention-groupn = 25, control-groupn = 20) and none of the variables involved in the analyses in this article were related to the probability of having missing data, we omitted participants with partial data from all latent variable analyses. Results Then we present traditional main effects and differential effectiveness analyses using observed variable regression methodology. We focused on the control group to eliminate the possibility that pooling the data across groups would distort the distribution because of the effects of the intervention. Standard Regression A simple main effects analysis can be conducted using a repeated measures analysis of variance (ANOVA). The standard deviations for the control and intervention groups, respectively, increased and decreased slightly. This analysis, however, failed to consider the impact of reliability, censoring, and differential effectiveness. We first consider censoring and differential effectiveness, as these issues can be handled with observed variable regression techniques. Standard Regression Accounting for Censoring In the simple two-group, pre- to postintervention design, testing the difference between difference scores across the groups is equivalent to computing the Group ¡Ñ Time interaction test from a repeated measures ANOVA. To perform this analysis and account for censoring, we fitted a pre- to postintervention regression model in both groups using LISCOMP with the regression weight fixed at 1 and the pre- and postintervention scores censored at log(0.1). As for the simple difference model, we also fitted the differential effectiveness model with censoring and with equality constraints across groups on the preintervention score means and variances. Unfortunately, computing effect sizes is more complicated in this case because the effect size now depends on where in the preintervention score distribution the control and intervention groups are compared. Effect sizes are then based on this difference compared with the control-group residual standard deviation. In my opinion, censoring does not change the results much using observed variables because the average of the three sessions at the pre- and postintervention test is not nearly as badly censored as each individual session Latent Regression The model is estimated in the intervention and control groups simultaneously, and equality constraints are applied across the groups to the latent preintervention score means and variances and to the time-specific variances. Censoring, as discussed later, makes a bigger difference in these latent analyses because the level of censoring at each individual session is much more extensive than in the average of the three sessions. Both the time-specific variances and the variance of the preintervention score were three times larger in the censored model than in the continuous model, and the residual variance for the intervention group was almost six times larger. The reliability of a single session of observation at the preintervention test is easily computed from the results in for the censored analysis; it is the variance of the preintervention score factor divided by the total variance of a single session, or .35/(1.33 + .35) = .21. The reliability of the average or sum of three sessions of observation is (.35 ¡Ñ 3)/(1.33 + .35 ¡Ñ 3) = .44. Low reliability in the outcome variable degrades statistical power and lowers effect size estimates in regression analyses. In the censored analysis, the slopes for the control and intervention groups were 1.13 and 0.28, respectively, a highly significant difference,t(626) = 3.61,p < .001, which provides strong evidence at the latent level of differential effectiveness. Results were similar for the continuous analysis. The correlations of preintervention with postintervention implied by these model parameters were .89 and .08, respectively, for the control and intervention groups. The increase in the effect sizes in the latent censored analysis over the latent continuous analysis was substantial everywhere but at the latent preintervention score mean. The effect of accounting for low reliability above and beyond censoring is seen in the comparison of effect sizes for the observed censored analysis versus the latent censored analysis. For example, at a standardized preintervention score of 2, the effect size was 432% greater in the latent (vs. observed) analysis. In the observed variable analysis, the increase in aggression for children 1SD below the preintervention score mean was not significant and the effect size was almost zero ( ƒ{0.07). The initially high-aggressive children showed much larger reductions in aggressive behavior than the initially low-aggressive children showed gains. The average child who starts at 1SD below the mean increases from 0.7 aggressive acts to 1.0 aggressive act, which is still below the preintervention score mean. Thus, increases in aggression by initially low-aggressive children are relatively trivial, but decreases by initially high-aggressive children are substantial on the raw, untransformed scale. We have provided an in-depth analysis of the impact of the LIFT preventive intervention based on a single outcome variable, physical aggression on the school playground, to illustrate the complexities involved in such analyses. Using standard observed variable regression methodology, we found that the LIFT intervention was effective overall in lowering rates of aggression, but the effect varied significantly according to the initial level of aggressive behavior. Specifically, we found that the more aggressive the target child was initially, the greater the reduction in aggressive behavior by the time of the postintervention assessment. Effect sizes by social science standards ranged from essentially zero for children who were initially close to the mean to large for initially high-aggressive children. As we demonstrated, however, these effect size estimates are substantially biased downward by low reliability and censoring in the outcome variable. Accounting for the low reliability of the outcome variable made the biggest single difference in effect size calculations. In summary, the latent variable results indicate that the LIFT intervention was successful in radically reorganizing the playground ecology with respect to aggressive behavior. The stability correlation for playground aggressive behavior in the control group, representing the natural state of affairs, was about .89. The stability of aggressive behavior normally accounts for about 80% of the variance in aggressive behavior at the end of the school year (.892 is about .80). The latent playground aggression variable at the preintervention test explained only 21% of the variance, even after correction for censoring, in the individual session scores. In turn, this indicates that major reductions in aggressive behavior in schools could be accomplished by focusing on contextual, time-specific determinants of aggressive behavior, not on stable traitlike propensities in particular children. Finally, we have assumed that in the absence of Type I censoring, rates of observed aggressive behavior for children are continuously, log-normally distributed in the population. I my opinion this was a very efficient way to conduct a study with all the variables in place and a sound research to back on it.

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