Statistics and Data Science Seminar
Shi Zhao, Ph. D.
UIC, MSCS
Crossover Designs under Subject Dropouts
Abstract: Crossover experiments are used for comparing the responses to various different stimuli or treatments in areas ranging from psychology and human factor engineering to medical and agricultural applications. They are widely used in the pharmaceutical industry.
There is an extensive literature that assures us that a carefully designed crossover study will produce a wealth of information that will enable inference with high precision. This is based on the implicit, but critical, assumption that the experiment will yield all the planned observations. Yet in many situations, such as clinical trials, there is a substantial probability that some subjects will drop out of the study prior to the completion of their treatment sequence. Low, Lewis and Prescott (1999) observed that a dropout rate of between 5% and 10% is not uncommon and, in some areas, can be as high as 25%. They gave an example of a design in four periods based on a Williams Latin square where there is substantial loss of information if some observations are unavailable in period 4. Indeed, if all observations in the final period are not available, the design becomes disconnected, i.e., elementary contrasts are no longer all estimable. Majumdar, Dean and Lewis (2005) studied the maximum loss in uniformly balanced repeated measurements designs (UBRMDs) in t periods when subjects may drop out after period t-m.
We will further study UBRMDs under the subject dropouts.
(1) We will derive the "best" UBRMDs for the situation where all subjects may drop out in the final period and provide methods for constructing these designs.
(2) We will study UBRMDs under subject dropout for the model where subject effects are random and show that the Low, Lewis and Prescott (1999) result on lack of connectedness of the Williams Latin Square of order 4 is no longer valid. Compound symmetry and AR (1) covariance structures will be considered.
(3) Expected loss under various dropout probabilities will be studied.
Wednesday October 22, 2008 at 4:15 PM in SEO 612