An EM algorithm for nonparametric estimation of the cumulative incidence function from repeated imperfect test results

Birgit I. Witte, Johannes Berkhof, Marianne A. Jonker

Research output: Contribution to journalArticleAcademicpeer-review

2 Citations (Scopus)


In screening and surveillance studies, event times are interval censored. Besides, screening tests are imperfect so that the interval at which an event takes place may be uncertain. We describe an expectation–maximization algorithm to find the nonparametric maximum likelihood estimator of the cumulative incidence function of an event based on screening test data. Our algorithm has a closed-form solution for the combined expectation and maximization step and is computationally undemanding. A simulation study indicated that the bias of the estimator tends to zero for large sample size, and its mean squared error is in general lower than the mean squared error of the estimator that assumes the screening test is perfect. We apply the algorithm to follow-up data from women treated for cervical precancer.

Original languageEnglish
Pages (from-to)3412-3421
Number of pages10
JournalStatistics in medicine
Issue number21
Publication statusPublished - 20 Sept 2017


  • EM algorithm
  • cervical post-treatment surveillance
  • interval censoring
  • nonparametric maximum likelihood estimation
  • screening test

Cite this