A Latent-factor MCACE Model for Multidimensional Outcomes and Treatment Noncompliance with Application to a Longitudinal Trial of Arthritis Health Journal.

Real-world randomized controlled trials (RCTs) evaluating multifaceted interventions often employ multiple study outcomes to measure treatment effects on a small set of underlying constructs. Motivated by a longitudinal RCT evaluating a behavioural intervention, the Arthritis Health Journal (AHJ), we propose a latent-factor multivariate complier average causal effects (MCACE) model for multidimensional longitudinal outcomes with principal strata of compliance types for parsimonious estimation of intervention effects in RCTs with treatment noncompliance. Within each compliance type, a factor regression model relates multiple outcomes to latent constructs, which follow hierarchical regression models. Under the model, high dimensional outcomes are reduced to low dimensional latent factors. This dimension reduction leads to a parsimonious and efficient test of overall CACEs on multiple outcomes, mitigating the multiple testing issues associated with multidimensional outcomes and weak instrumental variable problems associated with low compliance rates. Simulation studies demonstrate that the latent-factor MCACE model outperforms univariate CACE analysis in terms of both statistical power and Type I error control. The application to the AHJ study selects two underlying factors (self-efficacy and interaction with health care providers). Significant and beneficial treatment effects are detected on both factors. Overall, our analysis directly answers the main scientific questions posed by the RCT and yields novel findings not discovered previously.