Sequential testing in psychodiagnostics using minimax decision theory

The purpose of this paper is to derive optimal rules for sequential testing problems in psychodiagnostics. In sequential psychodiagnostic testing, each time after a patient has been exposed to a new form of treatment, a decision must be made whether to declare this new treatment effective, ineffective, or to continue testing and exposing the new treatment to another patient suffering from the same mental health problem. The framework of minimax decision theory is proposed for solving such sequential testing problems; that is, optimal rules are obtained by minimizing the maximum expected losses associated with all possible decision rules at each stage of testing. The main advantage of this approach is that costs of testing can be explicitly taken into account. The paper concludes with a simulation study, in which the minimax strategy is compared with other procedures that exist for similar classification decision problems in the literature.