  We introduce a self-censoring model for multivariate nonignorable nonmonotone
missing data, where the missingness process of each outcome is affected by its
own value and is associated with missingness indicators of other outcomes,
while conditionally independent of the other outcomes. The self-censoring model
complements previous graphical approaches for the analysis of multivariate
nonignorable missing data. It is identified under a completeness condition
stating that any variability in one outcome can be captured by variability in
the other outcomes among complete cases. For estimation, we propose a suite of
semiparametric estimators including doubly robust estimators that deliver valid
inferences under partial misspecification of the full-data distribution. We
evaluate the performance of the proposed estimators with simulations and apply
them to analyze a study about the effect of highly active antiretroviral
therapy on preterm delivery of HIV-positive mothers.
