Determination of an adequate sample size for a clinical trial has traditionally involved the specification of type I (false positive) and type II (false negative) error rates, and a difference that one wishes to detect. Because newer therapy has generally been more invasive or more toxic, it is conventional for the type I error to be 0.05 in order that new therapy not be accepted as superior unless its advantages are definitively established. Recently, many new trials have been directed toward showing that a more conservative treatment is equivalent in efficacy to a standard intensive therapy. In this paper, we provide formulas which prescribe the sample size necessary to meet certain criteria specified by the investigator for this alternative type of clinical trial. In addition, the percent increase in total sample size is described when more patients are allocated to one treatment than the other.