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 (EM) 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 and is therefore computationally undemanding. Subsequently, the specificity of the screening test can be estimated jointly with the cumulative incidence function via a grid search algorithm.
A simulation study showed that our estimator in general outperforms the estimator that assumes the screening test is perfect, that is, the bias tends to zero for large sample size and its mean squared error is lower. The specificity of the screening test is estimated consistently as well, however, the data in screening and surveillance studies only provide limited information on the sensitivity so that this parameters can only be estimated accurately in large samples with a high number of observed events.
We applied the algorithm to follow-up data from women treated for cervical precancer (recurrent CIN2+), where the corrected cumulative risk after 4.5 years was higher than the uncorrected cumulative risk (18.4% vs 13.6%). With our EM algorithm, the cumulative incidence of precancerous disease can now be estimated more accurately in these settings.