Multiple Comparisons with Control Under Stochastic Ordering: Controlling FDR

Abstract

Multiple comparisons of the effects of several treatments with a control (MCC) has been a central problem in medicine and other areas. Nearly all of existing papers are devoted to comparing means of the effects. To study medical problems more deeply, one needs more information than mean relationship from the given data. It can be expected to get more useful and deeper conclusion by comparing the probability distributions, i.e., by comparison under stochastic orders. This paper presents a likelihood ratio testing procedure to compare effects under stochastic order for MCC problems, controlling the false discovery rate (FDR). Setting a test controlling FDR under stochastic order faces several non trivial problems. These problems are analyzed and solved in this paper. To facilitate the test more easily, the asymptotic p values for the test are used and their distributions are derived. It is shown that controllability of FDR for this comparison procedure can be guaranteed. A real data example is used to illustrate how to apply this testing procedure and what the test can tell. Simulation results show that this testing procedure works quite well, better than some other tests.

Keywords:

• False discovery rate
• Likelihood ratio
• Multiple comparisons with a control
• Simple stochastic order

Mathematical Subject Classification:

• 62J15; 62G30