The identification of surrogate endpoints that can replace “true” endpoints in clinical trials could provide an important advance for the evaluation of therapeutic or preventive interventions. Outcome events that are more frequent in occurrence and more proximate in time, compared with customary disease-specific mortality or incidence outcomes, could give answers that are based on smaller trials of shorter duration. However, reliance on surrogate outcomes is justifiable only if treatment comparisons that are based on a surrogate are a faithful reflection of comparisons that are based on the true endpoint. I took this perspective, almost 20 years ago ( 1 ), in defining a surrogate outcome to be “a response variable for which a test of the null hypothesis of no relationship to the treatment groups under comparison is also a valid test of the corresponding null hypothesis based on the true endpoint,” thinking that this was a minimal requirement for a short-term outcome to provide some reliable treatment effect information for the longer term outcome. However, this apparently simple requirement translates to some strong restrictions on the relationship of the treatment to the surrogate and true outcomes: Consider a treatment indicator variable x , a time to response surrogate S , and a time to response true outcome T . A dependence of T on x will imply a dependence of S on x if