Incomplete factorial designs for randomized clinical trials

Recently there has been increased interest in considering factorial designs for randomized clinical trials when one wishes to study two or more treatments. Such designs may offer impressive gains in efficiency compared with a series of trials studying one treatment at a time. This is especially true when the treatments do not interact with one another. If interactions are of special interest, factorial designs provide one sensible approach for studying them, but larger sample sizes would be required because tests for interactions have lower power than those for main effects. In trials designed to test putative agents for preventing cancer, interactions may be of less interest so that fractions of higher‐order factorial designs might be appropriate. Sometimes it may not be reasonable, interesting, feasible, or ethical to study all treatment combinations required in a complete or fractional factorial design, yet one may want to preserve some of the factorial structure to increase efficiency and to aid understanding. For such situations, incomplete factorial designs are proposed. Although not all of the advantages of full factorial designs are preserved, such designs may provide reasonable compromises for certain situations.