Valid and Approximately Valid Confidence Intervals for Current Status Data

TL;DR

This paper proposes a simple, binomial-based framework for constructing valid and approximately valid confidence intervals for current status data, ensuring nominal coverage and improved performance over existing methods.

Contribution

It introduces a novel binomial framework for confidence intervals in current status data, providing simplicity, validity, and better coverage properties compared to prior asymptotic approaches.

Findings

Confidence intervals guarantee nominal coverage asymptotically.

Approximately valid intervals have closer coverage and shorter length.

Framework applies to both continuous and grid-based assessments.

Abstract

We introduce a new framework for creating point-wise confidence intervals for the distribution of event times for current status data. Existing methods are based on asymptotics. Our framework is based on binomial properties and motivates confidence intervals that are very simple to apply and are valid, i.e., guarantee nominal coverage. Although these confidence intervals are necessarily conservative for small sample sizes, asymptotically their coverage rate approaches the nominal one. This binomial framework 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, including the likelihood ratio-based confidence interval. Unlike previous asymptotic methods that require different asymptotic distributions for continuous or grid-based assessment, the binomial framework can be applied to either type of assessment distribution.