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The study of treatment effects is often complicated by noncompliance andmissing data. In the one-sided noncompliance setting where of interest are thecomplier and noncomplier average causal effects (CACE and NACE), we addressoutcome missingness of the \textit{latent missing at random} type (LMAR, alsoknown as \textit{latent ignorability}). That is, conditional on covariates andtreatment assigned, the missingness may depend on compliance type. Within theinstrumental variable (IV) approach to noncompliance, methods have beenproposed for handling LMAR outcome that additionally invoke an exclusionrestriction type assumption on missingness, but no solution has been proposedfor when a non-IV approach is used. This paper focuses on effect identificationin the presence of LMAR outcome, with a view to flexibly accommodate differentprincipal identification approaches. We show that under treatment assignmentignorability and LMAR only, effect nonidentifiability boils down to a set oftwo connected mixture equations involving unidentified stratum-specificresponse probabilities and outcome means. This clarifies that (except for aspecial case) effect identification generally requires two additionalassumptions: a \textit{specific missingness mechanism} assumption and a\textit{principal identification} assumption. This provides a template foridentifying effects based on separate choices of these assumptions. We considera range of specific missingness assumptions, including those that have appearedin the literature and some new ones. Incidentally, we find an issue in theexisting assumptions, and propose a modification of the assumptions to avoidthe issue. Results under different assumptions are illustrated using data fromthe Baltimore Experience Corps Trial.

Identification of complier and noncomplier average causal effects in the  presence of latent missing-at-random (LMAR) outcomes: a unifying view and  choices of assumptions