[Frontiers in Bioscience E2, 582-601, January 1, 2010]

Emax model and interaction index for assessing drug interaction in combination studies

J. Jack Lee,1 Heather Y. Lin,1 Diane D. Liu,1, Maiying Kong2

1Department of Biostatistics, The University of Texas M. D. Anderson Cancer Center, Unit 1411, 1515 Holcombe Boulevard, Houston, Texas 77030, U.S.A., 2Department of Bioinformatics and Biostatistics, School of Public Health and Information Sciences, University of Louisville, Louisville, Kentucky 40292, U.S.A.

TABLE OF CONTENTS

1. Abstract
2. Introduction
3. Statistical methods
3.1. Data sets
3.2. Emax model
3.3. Interaction index under the Emax model
3.4. Confidence interval for the interaction index
3.5. Data analysis plan
4. Exploratory data analysis
5. Data preprocessing: outlier rejection and data standardization
5.1. Outlier rejection
5.2. Data standardization
6. Results
6.1. Results for the low folic acid experiment
6.2. Results for the high folic acid experiment
7. Summary
8. Discussion and Perspective
9. Acknowledgement
10. References

1. ABSTRACT

Applying the Emax model in a Lowe additivity model context, we analyze data from a combination study of trimetrexate (TMQ) and AG2034 (AG) in media of low and high concentrations of folic acid (FA). The Emax model provides a sufficient fit to the data. TMQ is more potent than AG in both low and high FA media. At low TMQ:AG ratios, when a smaller amount of the more potent drug (TMQ) is added to a larger amount of the less potent drug (AG), synergy results. When the TMQ:AG ratio reaches 0.4 or larger in low FA medium, or when the TMQ:AG ratio reaches 1 or larger in high FA medium, synergy is weakened and drug interaction becomes additive. In general, synergistic effect in a dilution series is stronger at higher doses that produce stronger effects (closer to 1-Emax) than at lower dose levels that produce weaker effects (closer to 1). The two drugs are more potent in the low compared to the high FA medium. Drug synergy, however, is stronger in the high FA medium.