AbstractThe basic principles of factorial designs are briefly reviewed and estimating equations for a 23factorial design are presented in order to show how easily the basic idea of the 2 × 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 23full factorial and a half‐fractional 24design. A new class of designs calledreciprocal control designsis proposed for certain disease screening studies. An example is provided by a study designed to screen for lung, colorectal, and prostate cance