Addressing complications of intention-to-treat analysis in the combined presence of all-or-none treatment-noncompliance and subsequent missing outcomes

We study the combined impact that all-or-none compliance and subsequent missing outcomes can have on the estimation of the intention-to-treat effect of assignment in randomised studies. In this setting, a standard analysis, which drops subjects with missing outcomes and ignores compliance information, can be biased for the intention-to-treat effect. To address all-or-none compliance that is followed by missing outcomes, we construct a new estimation procedure for the intention-to-treat effect that maintains good randomisation-based properties under more plausible, nonignorable noncompliance and nonignorable missing-outcome conditions: the 'compound exclusion restriction' on the effect of assignment and the 'latent ignorability' of the missing data mechanism. We present both theoretical results and a simulation study. Moreover, we show how the two key concepts of compound exclusion and latent ignorability are relevant in more complicated settings, such as right censoring of a time-to-event outcome.