  Existing survival analysis techniques heavily rely on strong modelling
assumptions and are, therefore, prone to model misspecification errors. In this
paper, we develop an inferential method based on ideas from conformal
prediction, which can wrap around any survival prediction algorithm to produce
calibrated, covariate-dependent lower predictive bounds on survival times. In
the Type I right-censoring setting, when the censoring times are completely
exogenous, the lower predictive bounds have guaranteed coverage in finite
samples without any assumptions other than that of operating on independent and
identically distributed data points. Under a more general conditionally
independent censoring assumption, the bounds satisfy a doubly robust property
which states the following: marginal coverage is approximately guaranteed if
either the censoring mechanism or the conditional survival function is
estimated well. Further, we demonstrate that the lower predictive bounds remain
valid and informative for other types of censoring. The validity and efficiency
of our procedure are demonstrated on synthetic data and real COVID-19 data from
the UK Biobank.
