A Family-based Graphical Approach for Testing Hierarchically Ordered Families of Hypotheses

12/01/2018
by   Zhiying Qiu, et al.
New Jersey Institute of Technology
0

In applications of clinical trials, tested hypotheses are often grouped as multiple hierarchically ordered families. To test such structured hypotheses, various gatekeeping strategies have been developed in the literature, such as series gatekeeping, parallel gatekeeping, tree-structured gatekeeping strategies, etc. However, these gatekeeping strategies are often either non-intuitive or less flexible when addressing increasingly complex logical relationships among families of hypotheses. In order to overcome the issue, in this paper, we develop a new family-based graphical approach, which can easily derive and visualize different gatekeeping strategies. In the proposed approach, a directed and weighted graph is used to represent the generated gatekeeping strategy where each node corresponds to a family of hypotheses and two simple updating rules are used for updating the critical value of each family and the transition coefficient between any two families. Theoretically, we show that the proposed graphical approach strongly controls the overall familywise error rate at a pre-specified level. Through some case studies and a real clinical example, we demonstrate simplicity and flexibility of the proposed approach.

READ FULL TEXT

page 1

page 2

page 3

page 4

04/03/2020

Graphical approaches for the control of generalised error rates

When simultaneously testing multiple hypotheses, the usual approach in t...
12/01/2018

A New Approach for Large Scale Multiple Testing with Application to FDR Control for Graphically Structured Hypotheses

In many large scale multiple testing applications, the hypotheses often ...
08/23/2020

False discovery rate envelope for functional test statistics

False discovery rate (FDR) is a common way to control the number of fals...
02/25/2022

Familial Inference

Statistical hypotheses are translations of scientific hypotheses into st...
07/01/2023

A Direct Approach to Simultaneous Tests of Superiority and Noninferiority with Multiple Endpoints

In clinical trials it is often desirable to test for superiority and non...
04/15/2023

Gini-stable Lorenz curves and their relation to the generalised Pareto distribution

We study an iterative discrete information production process (IPP) wher...

Please sign up or login with your details

Forgot password? Click here to reset