When evaluating the bene"t of detecting cancer by screening we try to answer the question, &what would a screen detected subject's outcome have been if his/her cancer had progressed to clinical detection'. By &outcome' we mean survival time, cancer size and stage, lead time e!ects and more. Because only an unethical study can answer it directly, researchers have attempted to answer the question indirectly using data from randomized cancer screening studies (subjects randomized to study (screened) or control (not screened)). Inferences are made by "rst selecting the cancer cohort (those subjects who are found to have cancer), then comparing subjects having screen detected cancers to subjects having clinically detected cancers. However, there are two di$culties with this approach: (i) because screening (intends to) detect cancers early, at the trial's end the study group contains more cancer cases than the control group and so the cancer cohort has some unidenti"ed control subjects missing (that is, subjects having cancer during the screening period that have not yet been clinically detected); (ii) because screen detected cancers (may) di!er from clinically detected cancers, the comparison group should include only a (non-identi"ed) subset of the cancer cohort's control subjects (that is, only those control subjects having cancers that would have been screen detected). Statistical literature acknowledges these di$culties and attempts to solve them separately, but without success; those methods do not yield meaningful causal inferences and admit substantial bias. Recently, Angrist, Imbens and Rubin and Imbens and Rubin provide a framework for instrumental variable methods that we interpret as allowing us to make causal inferences with incompletely identi"ed comparison groups. We apply their framework to evaluating cancer screening trials and "nd that we may simultaneously accommodate both di$culties while giving a meaningful answer to the question posed above. Using data from a breast cancer screening trial we demonstrate the general method with a variety of outcome measures and extensions.