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Continuous diagnostic tests are often used for discriminating between healthy and diseased populations. For the clinical application of such tests, it is useful to select a cutpoint or discrimination value c that defines positive and negative test results. In general, individuals with a diagnostic test value of c or higher are classified as diseased. Several search strategies have been proposed for choosing optimal cutpoints in diagnostic tests, depending on the underlying reason for this choice. This paper introduces an R package, known as OptimalCutpoints, for selecting optimal cutpoints in diagnostic tests. It incorporates criteria that take the costs of the different diagnostic decisions into account, as well as the prevalence of the target disease and several methods based on measures of diagnostic test accuracy. Moreover, it enables optimal levels to be calculated according to levels of given (categorical) covariates. While the numerical output includes the optimal cutpoint values and associated accuracy measures with their confidence intervals, the graphical output includes the receiver operating characteristic (ROC) and predictive ROC curves. An illustration of the use of OptimalCutpoints is provided, using a real biomedical dataset.