When some individuals are screen-detected before the beginning of the study, but otherwise would have been diagnosed symptomatically during the study, this results in different case-ascertainment probabilities among screened and unscreened participants, referred to here as lead-time-biased case-ascertainment (LTBCA). In fact, this issue can arise even in risk-factor studies nested within a randomized screening trial; even though the screening intervention is randomly allocated to trial arms, there is no randomization to potential risk-factors and uptake of screening can differ by risk-factor strata. Under the assumptions that neither screening nor the risk factor affects underlying incidence and no other forms of bias operate, we simulate and compare the underlying cumulative incidence and that observed in the study due to LTBCA. The example used will be constructed from the randomized Prostate, Lung, Colorectal, and Ovarian cancer screening trial. The derived mathematical model is applied to simulating two nested studies to evaluate the potential for screening bias in observational lung cancer studies. Because of differential screening under plausible assumptions about preclinical incidence and duration, the simulations presented here show that LTBCA due to chest x-ray screening can significantly increase the estimated risk of lung cancer due to smoking by 1% and 50%. Traditional adjustment methods cannot account for this bias, as the influence screening has on observational study estimates involves events outside of the study observation window (enrollment and follow-up) that change eligibility for potential participants, thus biasing case ascertainment.