The Systolic Hypertension in the Elderly Program (SHEP), a randomized, double-masked, placebo-controlled trial of 4736 persons, was designed to assess the efficacy of antihypertensive drug treatment to reduce the risk of fatal and nonfatal strokes among people age 60 and over with isolated systolic hypertension. The statistical method used in interim monitoring of results was conditional power (or stochastic curtailment). The findings did not become conclusive until near the completion of the trial, and therefore SHEP was continued to its scheduled closing date. The trial demonstrated a 36% reduction in the incidence of stroke in the active treatment group (P = .0003). In addition to evaluating overall efficacy of treatment, the monitoring process considered such other issues as nonstroke outcomes, lag time between first report of stroke and final confirmation of stroke diagnosis, consistency of results across subgroups, and completeness of follow-up. The purpose of this article is to review these factors with primary emphasis on the statistical aspects.