  Inferential challenges that arise when data are censored have been
extensively studied under the classical frameworks. In this paper, we provide
an alternative generalized inferential model approach whose output is a
data-dependent plausibility function. This construction is driven by an
association between the distribution of the relative likelihood function at the
interest parameter and an unobserved auxiliary variable. The plausibility
function emerges from the distribution of a suitably calibrated random set
designed to predict that unobserved auxiliary variable. The evaluation of this
plausibility function requires a novel use of the classical Kaplan--Meier
estimator to estimate the censoring rather than the event distribution. We
prove that the proposed method provides valid inference, at least
approximately, and our real- and simulated-data examples demonstrate its
superior performance compared to existing methods.
