The problem of drug screening is to select from a large number of drugs those having some particular desirable biological effect. A sample of laboratory animals are treated with the drug and some measure of the effect on each animal is obtained. These experimental results lead to the decision to 'accept' or 'reject' the drug. The drug screening is intended to be but a first step in the search for new therapeutic agents. Presumably, a drug accepted by the screen will be carefully scrutinized and subjected to many further tests before being considered for use in a controlled clinical trial. A rejected drug is dropped from further consideration. Since acceptance or rejection depends on results in a sample, two possibilities of error are involved: the screen can reject an effective drug (false negative) and can accept an ineffective drug (false positive). The problem of designing a screen is to determine an 'optimal' plan which takes into account these two possibilities of error. Two main approaches have been taken in the statistical consideration of drug screening. One is the fixed probability level approach where the two possibilities of error are arbitrarily fixed and screening plans meeting these conditions are examined. This is the approach used by the Cancer Chemotherapy National Service Center (at the National Cancer Institute, Bethesda, Maryland) in the screening of anti-mouse tumour drugs and the approach used in this research. Second is the decision theory approach where costs are assigned for each of the two possible wrong decisions and for experimentation and screening plans minimizing an over-all cost function are examined. This decision theory approach has recently been