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

Abstract

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.

Figure 1

Model for potential outcomes over time, based on time from enrollment and treatment time. The model for population-average potential outcomes is λ₀ + λ₁ · t + [γ₀ + γ₁ · (t − s)], where t = time since enrollment (in weeks) and s = treatment time (in weeks since enrollment). The subject average outcomes add random effects b_i to the population-average model. The additional incorporation of measurement error yields the subject-specific observations. Note that surgery can occur at any time, not just at the observation times displayed here, and that s = ∞ if surgery never occurs.

Figure 2

Fitted mean models using SPORT data. The curves in the left frame are from the published SPORT analyses. The other three frames contain our intent-to-treat (ITT) estimator using dotted lines, and solid lines for (left to right) the generalized estimating equation (GEE) estimator, the linear mixed effect (LME) estimator with random intercepts and random slopes on both time and treatment, and the marginal structural model (MSM) estimator. Circles represent subjects with surgery just after enrollment, while triangles represent non-operative treatment.

Figure 3

Directed acyclic graphs (DAG) illustrating possible relationships between treatment, outcomes, and random effects. Subfigure (a) includes direct (solid) and indirect (dotted) selection, while subfigure (b) includes only direct selection.