Sequential testing of multiple hypotheses, simultaneous confidence estimation, and multichannel change-point detection

University Of Texas At Dallas, Richardson TX

Investigators

Abstract

The project focuses on the development of new theory and methodology of sequential multiple comparisons. It aims to develop cost-minimizing methods and supporting theory for conducting multiple statistical inferences sequentially. This includes testing multiple hypotheses, constructing sequences of simultaneous confidence sets, detecting changes in multiple channels, and making other sequential statistical decisions involving multiple parameters or multiple measurements. This study extends the recently obtained step-up and step-down procedures for multiple comparisons to sequential designs. It searches for optimal stopping rules that minimize the expected cost of the experiment while controlling for the false positive and false negative rates. The new methodology combines flexibility and cost-optimization of sequential procedures with the ability of modern statistical methods for multiple comparisons to control the familywise error rate and power. Proposed sequences of simultaneous confidence sets generalize the idea of repeated confidence intervals to the case of multiple parameters and achieve the desired overall confidence level. The new multiple hypothesis testing methodology is used for the derivation of sequential change-point detection algorithms sensitive to a change in any one or several parameters. Deliverables of the project include a sound statistical methodology for designing multiple comparison experiments at the minimum expected cost. One of the main applications is in sequential clinical trials that are conducted to answer multiple questions, for example, about the efficacy and safety of the tested treatment. Cost-optimization of such medical studies ultimately results in the reduced cost of health care. The new change-point detection procedures allow simultaneous tracking of changes in multiple parameters, which is used for the timely discovery of epidemic and pre-epidemic patterns and bioterrorist attacks. Controlling for the rate of false alarms, proposed change-point detection schemes are aimed to minimize the expected detection delay ensuring prompt reaction to unexpected changes. Their application sheds light to a number of global questions. Is the economy (welfare, climate, environment) changing? In what way and what direction is it changing? When did the change begin? Does the change continue, or has the process stabilized? Proposed sequential statistical tools address these and other important questions that involve multiple statistical comparisons.