The additivity assumption is that the relative effect of interventions on the CBCL-Total can be considered the sum of the relative effects on the CBCL-Internalising and CBCL-Externalising on the SMD scale. McFarlane et al.¹¹⁵ (under 5 years and 6–18 years), and Kot¹¹² report all of CBCL-Internalising, CBCL-Externalising, and CBCL-Total, which makes it possible to explore whether or not the results of these studies are consistent with the additivity assumption. We estimated two separate models: model 1 (M1): SMD for CBCL-Total is independent of the SMD for CBCL-Internalising and CBCL-Externalising; model 2 (M2): SMD for CBCL-Total is the sum of the SMD for CBCL-Internalising and the SMD for CBCL-Externalising.

The posterior mean residual deviance for M1 was 17.9 compared with 15.3 for model M2, compared with 18 data points. This suggests that both models fit adequately, with a better fit under the additive assumption. The Deviance Information Criterion¹⁸⁶ was 35.8 for model M1 compared with 30.2 for model M2, again suggesting that the additive model is the most parsimonious.

The results from the McFarlane et al.¹¹⁵ (< 5 years and 6–18 years) and Kot¹¹² studies are therefore consistent with the additivity assumption