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Stat Med. 2017 Sep 20;36(21):3412-3421. doi: 10.1002/sim.7373. Epub 2017 Jun 20.

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

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Department of Epidemiology and Biostatistics, Amsterdam Public Health Research Institute, VU University Medical Center, Amsterdam, The Netherlands.
Radboud Institute for Health Sciences, Radboud University Medical Center, Nijmegen, The Netherlands.


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.


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

[Indexed for MEDLINE]

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