A statistical model for the "N-of-1" study

The controlled clinical trial has largely replaced case-reports as the authoritative source of information concerning the efficacy of treatment. However, many situations arise in clinical practice where treatment decisions cannot be made on the basis of such studies. The definitive clinical trial may not have been performed, or the results from a particular study may not be applicable to a particular patient. Recently, "N-of-1" studies have been proposed for the experimental evaluation of therapy in a single patient. Multiple courses of active and placebo treatments are administered, and efficacy is determined by following the response measure over a period of time. The purpose of this paper is to present a statistical model appropriate for data arising from this design. The model provides for serial correlation among the response measures captured from the subject, and for heteroskedasticity across the treatment periods. ML estimation procedures are considered, and their properties are investigated. A scoring algorithm is described to iterate to the solution of the ML equations, and considerations for hypothesis testing are presented. The techniques are illustrated through an example.