An intermediate endpoint is a biologic event or marker that is a precursor to a given health outcome. Examples of potential intermediate endpoints include serum cholesterol for coronary heart disease, endogenous steroid hormones for breast cancer, and CD4 count for acquired immunodeficiency syndrome. When one is studying a potential intermediate endpoint in the context of an intervention trial, five types of questions may be investigated: 1) Does the intervention affect the intermediate endpoint? 2) Is the intermediate endpoint associated with prognostic or risk factors? 3) Is the intermediate endpoint associated with the main outcome? 4) Is the intervention effect on the main outcome mediated by the intermediate endpoint? 5) Are the prognostic or risk factor effects mediated by the intermediate endpoint? In this paper, the authors show that each of these questions had different sample size requirements, and they illustrate their point with a discussion of an ancillary study of large bowel epithelial proliferation in the National Cancer Institute's Polyp Prevention Trial. The same methods may be used in an observational study, in which case questions 2, 3, and 5 are relevant. However, much larger numbers than those used in the Polyp Prevention Trial example will be required when the main outcome is rare.