Date of Award


Degree Name

Doctor of Philosophy



First Advisor

Dr. Michael R. Stoline

Second Advisor

Dr. Daniel Mihalko

Third Advisor

Dr. Robert Buck

Fourth Advisor

Dr. Steven F. Francom


This research evaluated and compared three methods for the detection of qualitative treatment-by-center interaction proposed by Azzalini and Cox, Gail and Simon and Ciminera et al., through the analysis of simulated data for multicenter studies of two and three centers with two treatments. The effect of unequal sample size and the presence of an overall treatment effect on characteristics of the methods were examined.

The approach, underlying assumptions and theory of the three methods differ. For this study, they were adapted to establish a common basis for evaluation, thus allowing a meaningful comparison of the methods. For the test presented by Azzalini and Cox, this included deriving an approximate method and an exact method to allow for unequal sample sizes.

These methods were also compared to a common, ad-hoc method of identifying qualitative interaction, i.e. assessing the signs of the treatment effects by center. Two tests of overall interaction: the ANOVA test of interaction and the H statistic proposed by Gail and Simon were also examined.

Each method was further evaluated in a two-stage testing system, serving as a preliminary test to determine if the treatment-by-center interaction term should be included in the final analysis model.

The results indicate that the test for qualitative interaction proposed by Gail and Simon is the recommended method for detecting qualitative interaction. The error rates for patterns not exhibiting qualitative interaction are consistently lowest for this method. The second recommended choice would be the exactmethod of Azzalini and Cox.

This study did not provide a good evaluation of two-stage testing, except for the cases with equal sample sizes. For those cases, two-stage testing with one ofthe recommended methods was preferable to using a final analysis model without the interaction term.

This study was not designed to evaluate the effect that unequal sample size and inclusion of the treatment-by-center interaction term in the final model would have on the power of the test of overall treatment difference. However, the results show that in simulations with a high degree of imbalance, a study designed to have 80% power may have only 52%.


Fifth Advisor: Dr. D. Dal Kratzer

Access Setting

Dissertation-Open Access