Multivariate CACE analysis with an application to Arthritis Health Journal Study

Treatment noncompliance is a common issue in randomized controlled trials that may plague the randomization settings and bias the treatment effect estimation. The complier-average causal effect (CACE) model has become popular in estimating the method effectiveness under noncompliance. Performing multiple univariate CACE analysis separately fails to capture the potential correlations among multivariate outcomes, which will lead to biased estimates and significant loss of power in detecting actual treatment effect. Motivated by the Arthritis Health Journal Study, we propose a multivariate CACE model to better account for the correlations among outcomes. In our simulation study, the global likelihood ratio test is conducted to evaluate the treatment effect which fails to control the type I error for moderate sample sizes. So, we further perform a parametric bootstrap test to address this issue. Our simulation results suggest that the Multivariate CACE model outperforms multiple Univariate CACE models in the precision of estimation and statistical power in the case of correlated multivariate outcomes.