Valid and approximately valid confidence intervals for current status data

We introduce a new approach for creating pointwise confidence intervals for the distribution of event times for current status data. Existing methods are based on asymptotics. Our approach is based on binomial properties and motivates confidence intervals that are very simple to apply and are valid that is guarantee nominal coverage. Although these confidence intervals are necessarily conservative for small sample sizes, asymptotically their coverage rate approaches the nominal one. This binomial approach also motivates approximately valid confidence intervals, and simulations show that these approximate intervals generally have coverage rates closer to the nominal level with shorter length than existing intervals, such as the confidence interval based on the likelihood ratio test. Unlike previous asymptotic methods that require different asymptotic distributions for continuous or grid‐based assessment, the binomial approach can be applied to either type of assessment distribution.