# Self-reporting and screening: Data with current-status and censored observations

## TL;DR

This paper develops new methods for estimating failure-time distributions from survival data that include uncensored, right-censored, and left-censored observations, with applications in medical screening and patient patience analysis.

## Contribution

It introduces a novel approach combining parametric and nonparametric techniques for distribution estimation from mixed censored data types.

## Key findings

- The proposed estimators perform well in simulated scenarios.
- Application to emergency department data illustrates practical utility.
- Method handles complex censoring patterns effectively.

## Abstract

We consider survival data that combine three types of observations: uncensored, right-censored, and left-censored. Such data arises from screening a medical condition, in situations where self-detection arises naturally. Our goal is to estimate the failure-time distribution, based on these three observation types. We propose a novel methodology for distribution estimation using both parametric and nonparametric techniques. We then evaluate the performance of these estimators via simulated data. Finally, as a case study, we estimate the patience of patients who arrive at an emergency department and wait for treatment. Three categories of patients are observed: those who leave the system and announce it, and thus their patience time is observed; those who get service and thus their patience time is right-censored by the waiting time; and those who leave the system without announcing it. For the third category, the patients' absence is revealed only when they are called to service, which is after they have already left; formally, their patience time is left-censored. Other applications of our proposed methodology are discussed.