Complier-Average Causal Effect (CACE) Analysis with Nonnormal Variables: Problems and Remedies

Introduction: This study investigates the pitfalls of employing the Complier-Average Causal Effect (CACE; Little & Yau, 1998) analysis with non-normal data. CACE analysis is based upon Rubin's causal inference which incorporates engagement status in the overall analysis of intervention effects. CACE retains the strengths of random assignment at the individual level and also allows the estimation of a control subgroup that strongly resembles those families who engaged in an intervention. CACE analysis has a direct implication for an intervention design where families with few problems often opt out of the service, while those at higher risk tend to engage in the intervention. However, as shown below, CACE analysis does not function properly with non-normal data. Based upon present findings, we will conduct a simulation study to examine how CACE is impacted by data with various degrees of non-normality.  

 

Methods:The sample consisted of 998 adolescents (47.2% females) and their families from a longitudinal randomized control trial of the Family Check-Up (FCU) which is a family-centered large scale intervention. Teacher reports of bullying perpetration were assessed from age 11 to 13 and they were all highly skewed (i.e., skewness ranges from 1.5 ~ 2.0). Families in the intervention condition who elected to receive the FCU were coded as engagers (n = 115), and who did not choose to receive the FCU were coded as non-engagers (n = 385). In the control condition, engagement status was coded as missing data. Covariates such as gender, ethnicity, and family conflict were included in the CACE model in order to improve prediction of engagement status for the control condition.

 

Results: Two CACE models were run. The first used the raw scores of bullying behaviors. This model yielded a high entropy of .91 and there was a significant FCU intervention effect on the growth of bullying behaviors (B = -0.91, SE = 0.15, p < .001) indicating that bullying behaviors among youth in the intervention group reduced over time. However, significant disproportionate class sizes were observed between engagers in the treatment condition (n = 115; 74.2%) and in the control condition (n= 40; 25.8%). The other CACE model used the log transformed bullying variables. This model had an entropy of .68. The class size of the estimated engagers in the control condition slightly increased (n = 51; 30.7%). A significant intervention effect was observed but the direction of the effect was reversed (B = 0.05, SE= 0.02, p< .01).

 

Conclusions: We will summarize the simulation results and discussion how the CACE analysis is affected by nonnormal variables. The problems behind the problems and suggestions of remedies will be discussed.