The simplest factorial design is the 2 × 2 factorial with two levels of factor A crossed with two levels of factor B to yield four treatment combinations. A special case of the 2 × 2 factorial with a placebo and an active formulation of factor A crossed with a placebo and an active formulation of factor B. This yields the four treatment regimens:

For example, here you could have a placebo for each treatment. In one case you might have a placebo injection for A and a placebo pill for B. Such a design allows the comparison of the levels of factor A (A main effects), the comparison of the levels of factor B (B main effects), and the investigation of A × B interactions.

There are some issues to consider prior to conducting of a factorial clinical trial.

First, the treatments must be amenable to being administered in combination without changing dosage in the presence of each other treatment.

Second, it must be acceptable to not administer the individual treatments, (i.e., a placebo is ethical) or administer them at lower doses if that will be required for the combination.

Third, we must be genuinely interested in learning about treatment combinations required for the factorial design. Otherwise, some of the treatment combinations are unnecessary, yet without them, the advantages of the factorial design are diminished.

Fourth, the therapeutic questions must be chosen appropriately, e.g., treatments that use different mechanisms of action are more suitable candidates for a factorial clinical trial.