A Practical Limit to Trials Needed in One‐Person Randomized Controlled Experiments

Recently in this journal, J. Olsson and colleagues suggested the use of factorial experimental designs to guide a patient's efforts to choose among multiple interventions. These authors argue that factorial design, where every possible combination of the interventions is tried, is superior to sequential trial and errors. Factorial design is efficient in identifying the effectiveness of interventions (factor effect). Most patients care only about feeling better and not why their conditions are improving. If the goal of the patient is to get better and not to estimate the factor effect, then no control groups are needed. In this article, we show a modification in the factorial design of experiments proposed by Olsson and colleagues where a full-factorial design is planned, but experimentation is stopped when the patient's condition improves. With this modification, the number of trials is radically fewer than those needed by factorial design. For example, a patient trying out 4 different interventions with a median probability of success of .50 is expected to need 2 trials before stopping the experimentation in comparison with 32 in a full-factorial design.