Factorial and reciprocal control designs.

The basic principles of factorial designs are briefly reviewed and estimating equations for a 2(3) factorial design are presented in order to show how easily the basic idea of the 2 x 2 factorial design generalizes to higher dimensions. Fractional factorial designs are explained and advocated for situations in which the number of experimental groups might otherwise become unmanageably large or costly. Actual examples of use in medical settings are presented for both a 2(3) full factorial and a half-fractional 2(4) design. A new class of designs called reciprocal control designs is proposed for certain disease screening studies. An example is provided by a study designed to screen for lung, colorectal, and prostate cancers.