Medical Decision Making via Simultaneous Confidence Intervals Based on Selection Procedures

Abstract

Just in medical decision making a major problem is to compare several treatments with regard to their efficiency. One intends to separate good from bad treatments. But since in real situations the mechanism of the influence of a treatment is full of complexities every final decision is made under uncertainty. We have to accept the fact that decisions may be wrong. To control the error being made if a wrong statement is given one has to design a clinical trial according to statistical requirements. In the preceding situation the classical approach to decision making suggests to make inference for all pairwise comparisons of treatments via simultaneous confidence intervals or tests. This method however is at best indirect since the comparisons between only good or only bad treatments are included in the resulting statements. So they do not contribute to the solution of the task stated above. Rather it would be better to turn one’s attention to simultaneous inference between all treatments and the unknown best. In this paper we intend to give an introduction to statistical methods for latter inference taking into account newest developments in this area. Finally medical applications are presented.