compmed: A new command for estimating causal mediation effects with non-adherence to treatment allocation

In clinical trials, a standard intention-to-treat analysis will unbiasedly estimate the causal effect of treatment offer, though ignores the impact of participant non- adherence. To account for this, one can estimate a complier-average causal effect (CACE), the average causal effect of treatment receipt in the principal strata of participants who would comply with their randomisation allocation. Evaluating how interventions lead to changes in the outcome (the mechanism) is also key for the development of more effective interventions. A mediation analysis aims to decompose a total treatment effect into an indirect effect, one that operates via changing the mediator, and a direct effect. To identify mediation effects with non- adherence, it has been shown that the CACE can be decomposed into a direct effect, the Complier-Average Natural Direct Effect (CANDE), and a mediated effect, the Complier-Average Causal Mediated Effect (CACME). These can be estimated with linear Structural Equation Models (SEMs) with Instrumental Variables. However, obtaining estimates of the CACME and CANDE in Stata requires (1) correct fitting of the SEM in Stata and (2) correct identification of the pathways that correspond to the CACME and CANDE. To address these challenges, we introduce a new command, compmed, which allows users to perform the relevant SEM fitting for estimating the CACME and CANDE using a single, more intuitive, and user-friendly interface. Compmed requires the user to specify only the continuous outcome, continuous mediator, treatment receipt, and randomisation variables. Estimates, standard errors, and 95% confidence intervals are reported for all effects.