For cost-effectiveness and efficiency, many new cohorts are being assembled from patients in routine screening based on electronic health records. We develop risk models that address some of the features of screening data. First, patients can enter screening with pre-existing asymptomatic disease (left-censoring). Second, disease can only be diagnosed at the time of irregular screening visits (interval-censoring). Third, screening tests can misclassify the disease status which leave in question the exact time intervals in which disease onset occurred. Estimates of the misclassification matrix of screening test results for disease status are often available from FDA submissions in which trials used gold standards that are not available in routine screening (e.g., colposcopic biopsies for negative screening tests for cervical cancer). We propose a model for estimating absolute risks in screening data using the estimated misclassification. While our methods assume conditional independence of the timing of the next screening visit and disease onset given past/current screening results and covariates, our simulation studies demonstrate robustness of the methods to this assumption.