  A common type of zero-inflated data has certain true values incorrectly
replaced by zeros due to data recording conventions (rare outcomes assumed to
be absent) or details of data recording equipment (e.g. artificial zeros in
gene expression data).
  Existing methods for zero-inflated data either fit the observed data
likelihood via parametric mixture models that explicitly represent excess
zeros, or aim to replace excess zeros by imputed values. If the goal of the
analysis relies on knowing true data realizations, a particular challenge with
zero-inflated data is identifiability, since it is difficult to correctly
determine which observed zeros are real and which are inflated.
  This paper views zero-inflated data as a general type of missing data
problem, where the observability indicator for a potentially censored variable
is itself unobserved whenever a zero is recorded. We show that, without
additional assumptions, target parameters involving a zero-inflated variable
are not identified. However, if a proxy of the missingness indicator is
observed, a modification of the effect restoration approach of Kuroki and Pearl
allows identification and estimation, given the proxy-indicator relationship is
known.
  If this relationship is unknown, our approach yields a partial identification
strategy for sensitivity analysis. Specifically, we show that only certain
proxy-indicator relationships are compatible with the observed data
distribution. We give an analytic bound for this relationship in cases with a
categorical outcome, which is sharp in certain models. For more complex cases,
sharp numerical bounds may be computed using methods in Duarte et al.[2023].
  We illustrate our method via simulation studies and a data application on
central line-associated bloodstream infections (CLABSIs).
