Longitudinal structural mixed models for the analysis of surgical trials with noncompliance

Patient noncompliance complicates the analysis of many randomized trials seeking to evaluate the effect of surgical intervention as compared with a nonsurgical treatment. If selection for treatment depends on intermediate patient characteristics or outcomes, then 'as-treated' analyses may be biased for the estimation of causal effects. Therefore, the selection mechanism for treatment and/or compliance should be carefully considered when conducting analysis of surgical trials. We compare the performance of alternative methods when endogenous processes lead to patient crossover. We adopt an underlying longitudinal structural mixed model that is a natural example of a structural nested model. Likelihood-based methods are not typically used in this context; however, we show that standard linear mixed models will be valid under selection mechanisms that depend only on past covariate and outcome history. If there are underlying patient characteristics that influence selection, then likelihood methods can be extended via maximization of the joint likelihood of exposure and outcomes. Semi-parametric causal estimation methods such as marginal structural models, g-estimation, and instrumental variable approaches can also be valid, and we both review and evaluate their implementation in this setting. The assumptions required for valid estimation vary across approaches; thus, the choice of methods for analysis should be driven by which outcome and selection assumptions are plausible.