The 2 x 2 factorial design: its application to a randomized trial of aspirin and carotene in U.S. physicians.

The 2 x 2 factorial design calls for randomizing each participant to treatment A or B to address one question and further assignment at random within each group to treatment C or D to examine a second issue, permitting the simultaneous test of two different hypotheses. This design can increase the efficiency of large-scale clinical trials. The Physicians' Health Study, a randomized trial of aspirin and beta-carotene among U.S. physicians, illustrates some features and potential problems in the design and analysis of a factorial trial. The most common concern, interaction between treatments, is generally an advantage rather than a limitation of this design. Although such interactions are relatively uncommon, this design provides a means to measure an effect which otherwise might not be apparent. If the interaction is sufficiently severe, however, then loss of power is possible.