Predictive inference, causal reasoning, and model assessment in nonparametric Bayesian analysis: a case study

Structural mean models for compliance analysis in randomized clinical trials and the impact of errors on measures of exposure

Partial compliance with assigned treatment regimes is common in drug trials and calls for a causal analysis of the effect of treatment actually received. As such observed exposure is no longer randomized, selection bias must be carefully accounted for. The framework of potential outcomes allows this by defining a subject-specific treatment-free reference outcome, which may be latent and is modelled in relation to the observed (treated) data. Causal parameters enter these structural models explicitly. In this paper we review recent progress in randomization-based inference for structural mean modelling, from the additive linear model to the structural generalized linear models. An arsenal of tools currently available for standard association regression has steadily been developed in the structural setting, providing many parallel features to help randomization-based inference. We argue that measurement error on exposure is an important practical complication that has, however, not yet been addressed. We show how standard additive linear structural mean models are robust against unbiased measurement error and how efficient, asymptotically unbiased inference can be drawn when the degree of measurement error bias is known. The impact of measurement error is illustrated in a blood pressure example and finite sample properties are verified by simulation. We end with a plea for more and careful use of this methodology and point to directions for further development.