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

• Published in: Statistics in medicine Vol. 36; no. 21; pp. 3412 - 3421
• Main Authors: Witte, Birgit I., Berkhof, Johannes, Jonker, Marianne A.
• Format: Journal Article
• Language: English
• Published: England Wiley Subscription Services, Inc 20.09.2017
• Subjects: Algorithms; Bias; Cervical cancer; cervical post‐treatment surveillance; Computer Simulation; Early Diagnosis; EM algorithm; Female; Humans; Incidence; interval censoring; Likelihood Functions; Medical statistics; Medical tests; nonparametric maximum likelihood estimation; Nonparametric statistics; Population Surveillance; screening test; Sensitivity and Specificity; Statistics, Nonparametric; Uterine Cervical Neoplasms - pathology; Uterine Cervical Neoplasms - therapy; cervical post-treatment surveillance; nonparametric maximum likelihood estimation; interval censoring; screening test; EM algorithm
• ISSN: 0277-6715; 1097-0258; 1097-0258
• DOI: 10.1002/sim.7373

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. Copyright © 2017 John Wiley & Sons, Ltd.