Self-reporting and screening: Data with right-censored, left-censored, and complete observations

Jonathan Yefenof, Yair Goldberg, Jennifer Wiler, Avishai Mandelbaum, Ya'acov Ritov

Research output: Contribution to journalArticlepeer-review


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 semiparametric 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 this 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.

Original languageEnglish
Pages (from-to)3561-3578
Number of pages18
JournalStatistics in Medicine
Issue number18
StatePublished - 15 Aug 2022
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2022 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.


  • current status data
  • left censoring
  • nonparametric estimation
  • right censoring
  • survival analysis

ASJC Scopus subject areas

  • Epidemiology
  • Statistics and Probability


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