Intervention dose was calculated as number of CPP sessions attended by intervention group parents, not including the booster session (range = 0–11 sessions). Mean dose was 4.3 (SD = 4.2) group sessions. Approximately one third (n = 51) of parents did not attend any parent group sessions. Among the 135 parents enrolled in the CPP, 54.8% (n = 74) attended five or fewer of the 11 group sessions. Parents who participated in the booster session (n = 44) were also more likely to have attended 6 or more parent group sessions, χ2(1, 135) = 44.1, p < .001. It was hypothesized that dose of intervention would affect parent and child outcomes. Therefore, analyses were run twice for each dependent variable, first comparing outcomes for the intervention and control conditions and again with dose added in the model to examine its effect on the dependent variables. For the second set of analyses, intervention dose was divided into three levels of control group, low dose (0 – 5 sessions), and high dose (6–11 sessions). The decision to define high dose at 6 or more sessions was based on median split of attendance among intervention parents.
Demographic and study variables were examined at baseline to determine if there were differences between parents and children in the low and high dose level groups. There were no demographic differences between these two groups. However, children in the high dose group demonstrated more baseline problem behaviors than the low dose group on aversive child behaviors, t(131) = −2.7, p < .01; and on the ECBI Intensity Scale, t(133) = −2.0, p = .05.
presents the flow of participants in the study. Thirty nine (13%) participants dropped out of the study before their 1-year follow-up. Attrition in the control condition was attributed to 17 parents (12.5%) who were lost to follow-up and one parent (0.7%) who withdrew. Attrition in the intervention condition was attributed to 11 parents (7.1%) lost to follow-up, 9 parents (5.8%) who withdrew, and 1 parent who was dropped from the study due to emotional problems that interfered with her ability to participate in group discussion. There were no differences between those who completed the study and those who did not on any of the study variables. Demographic data for the final sample is shown in .
Parent Relationship to Child, Race/Ethnicity, Educational Level, Employment and Marital Status, and Child Age and Gender by Condition
Summary of the Analytic Model
To minimize potential site effects, sites were assigned to blocks using stochastic matching (Rassler, 2002
), a method using aggregate information to create equivalent groups. The two groups were matched on race/ethnicity, household income, proportion of single-parent households, and number of children enrolled in the day care center. This method of matching is an extension of propensity matching (Rubin, 1987
), which assumes that random fluctuations will not affect the equivalence of two matched samples. In propensity matching, the values are aggregated across variables while in stochastic matching the values are aggregated across individuals. The matched groups were then randomly assigned to the intervention and control conditions. To confirm that stochastic matching had been effective, site effects were then examined using the baseline dependent variables in a random effects model. No significant site effects were found for any of the dependent variables.
This study employed an intent-to-treat model. The effectiveness of the CPP for improving parent and child outcomes up to 1-year post-intervention was analyzed using growth curve modeling with the SAS software program, PROC MIXED. The dependent variables were parenting self-efficacy, parental warmth, following through on discipline, use of corporal punishment, total commands, positive parent behavior, parent-reported child behavior problems, and aversive child behavior. In the first set of analyses, the independent variables included experimental group, Latino ethnicity, and child gender (the last two variables were included to control for baseline differences found by experimental condition). A second set of analyses then included dose level. In both sets of analyses, participants were nested within daycare centers and daycare centers were crossed with intervention condition. The model had a random component for individual and intercept, and fixed effects for time, ethnicity (dummy-coded for Latino or non-Latino), a three level linear dose effect (control group, low dose level of intervention, high dose level of intervention coded as 0, 1 and 2, respectively), and interaction effects for dose level and time. Two effect sizes, Cohen’s d and η2 are reported for each dependent variable representing the difference in means and rate of change between intervention and control groups (for the first set of analyses without dose level) or between the control and high dose level groups (for the second set of analyses which included dose level). All effects reported are from baseline to the 1-year follow-up.
Parent-child interaction videotapes for two participant dyads were incomplete. Therefore, the final sample used to analyze data from parent questionnaires (parenting self-efficacy, discipline strategies, and parent-reported child behavior problems) was 253 and to analyze parent-child interaction outcomes (positive parent behavior, total commands, aversive child behavior) was 251.
In this analysis, we chose degrees of freedom based on the number of participants and data collection intervals. However, we acknowledge that there are other approaches for calculating degrees of freedom for cluster-randomized trails. The strategy employed in this study is consistent with that recommended by Singer and Willet (2003)
and used in other similar studies (e.g., Schoenwald, Carter, Chapman, & Sheidow, 2008
). To determine whether center effects would significantly alter the analyses, we reanalyzed the data in PROC MIXED using two alternative statistical methods for estimating degrees of freedom that simultaneously adjust for center effects: Satterthwaite and Kenward-Roger approximations (Giesbrecht & Burns, 1985
; Kenward & Roger, 1997
). Both sets of analyses arrived at nearly identical results as obtained using numbers of participants and data collection intervals for calculating degrees of freedom, suggesting that the stochastic matching strategy was successful in minimizing center effects in this study.
Center Intraclass Correlations
Intraclass correlations were calculated to estimate the amount of variance explained by center effects. None of the intraclass correlations were significant. The median center variance accounted for across the dependent variables was 2.5% (range = 0% – 14.0%).
Effect of CPP on Parenting Self-Efficacy, Discipline, and Parent Behavior
Final model estimates for parenting self-efficacy, warmth, following through on discipline, corporal punishment, positive parent behavior, and total commands by condition and dose level are displayed in and . Comparing intervention and control conditions, intervention parents used less corporal punishment, F(1, 818) = 5.39, p < .05, d = −.24, η2 = .011; and fewer commands during the play session, F(1, 992) = 4.72, p < .05, d = −.32, η2 = .011; and clean-up session, F(1, 984) = 7.65, p < .01, d = −.29, η2 = .024. However, there was no effect of the intervention on parenting self-efficacy, F(1, 818) = 1.81, p = .18, d = .23, η2 = .004; following through more consistently on discipline, F(1, 818) = 1.60, p = .21, d = .08, η2 = .008; and showing greater warmth, F(1, 818) = 1.88, p = .17, d = .11, η2 = .014. At 1-year post-intervention, control parents exhibited greater improvements in positive behavior during play, F(1, 992) = 4.52, p < .05, d = −.18, η2 = .020. There were no differences in positive parent behavior during the clean-up session, F(1, 984) = .03, p = .51, d = −.06, η2 = .016.
Final Model Estimates for Parent Outcomes
Random Effects Models for Parent and Child Outcomes
Different outcomes were found when dose level was included in the analytic model. There was a linear effect for dose level on parenting self-efficacy, F(1, 818) = 3.69, p < .05, d = .37, η2 = .013, indicating that CPP had a significant effect on parenting self-efficacy for parents who attended at least half of the parent group sessions. There was also a linear dose effect on parents’ reports of following through more consistently on their discipline, F(1, 818) = 6.99, p < .01, d = .29, η2 = .044; using less corporal punishment, F (1, 818) = 7.66, p < .01, d = − .30, η2 = .022; and showing greater warmth with their children, F (1, 818) = 3.37, p <.05, d = .08, η2 = .026. Parents who attended at least half of CPP sessions also issued fewer total commands during the observed free play, F(1, 992) = 6.55, p < .01, d = − .49, η2 = .013; and clean-up session, F(1, 984) = 11.59, p < .001, d = − .38, η2 = .031. However, there were no CPP dose level effects found for positive parent behavior during the free play session, F(1, 992) = 2.16, p = .14, d = − .06, , η2 = .025; and clean-up session, F(1, 984) = .03, p = .85, d = − .00, η2 = .020.
Effect of CPP on Child Behavior Problems
Final model estimates for parent-reported child behavior problems and observed aversive child behaviors by experimental condition and dose level are presented in and . Comparing intervention to control conditions, children of parents in the intervention group exhibited fewer aversive behaviors during the play session, F(1, 992) = 7.14, p < .01, d = −.43, η2 = .012; and clean-up session, F(1, 984) = 56.94, p < .01, d = −.46, η2 = .014. However, there were no intervention effects on parent-reports of child behavior problems on the ECBI Intensity, F(1, 818) = 1.55, p = .21, d = −.17, η2 = .006; or Problem Scales, F(1, 818) = 1.16, p = .28, d = −.10, η2 = .003.
Final Model Estimates for Child Outcome
When dose level was added into the model, analyses showed significant linear effects for dose level on child behavior problems as measured by parent report and observation. Children of parents attending at least half of the group sessions had fewer behavior problems on the ECBI Intensity Scale, F(1, 818) = 3.96, p < .05, d = − .31, η2 = .013; and fewer aversive behaviors during the free play session, F(1, 992) = 16.60, p < .001, d = − .64, η2 = .038; and clean-up session, F(1, 984) = 9.32, p < .001, d = − .46, η2 = .019. No significant changes were found on ECBI Problem Scale scores by dose level, F(1, 818) = 1.55, p = .21, d = −.09, η2 = .008.