Optimal test procedures for multiple hypotheses controlling the familywise expected loss.

Area of Science:

• Statistical methodology
• Decision theory
• Hypothesis testing

Background:

• Traditional methods for multiple hypothesis testing often use restrictive Type I error rate controls.
• The standard familywise error rate may not adequately address scenarios with differential costs of incorrect decisions.

Purpose of the Study:

• To develop a decision-theoretic framework for multiple hypothesis testing that accounts for varying losses from incorrect decisions.
• To introduce the concept of controlling familywise expected loss as an alternative to conventional error rates.
• To find optimal decision rules with bounded expected loss under diverse parameter configurations.

Main Methods:

• Utilizing a decision-theoretic approach to define loss functions for hypothesis testing.
• Calculating the expectation of loss functions with respect to the data's sampling distribution.
• Searching for decision rules that optimize criteria within a class of rules with bounded expected loss.

Main Results:

• Demonstrated that controlling familywise expected loss is a viable alternative to controlling familywise error rate.
• Developed a method to incorporate unequal loss values for different types of incorrect decisions.
• Identified optimal decision rules under specified optimality criteria and loss functions.

Conclusions:

• The proposed decision-theoretic approach offers a more flexible and context-aware method for multiple hypothesis testing.
• Controlling familywise expected loss is particularly useful in applications where the consequences of Type I and Type II errors differ significantly.
• The methodology can be applied to practical problems, such as evaluating new medicinal treatments across patient subgroups.