[Frontiers in Bioscience E2, 279-292, January 1, 2010]

Applying Emax model and bivariate thin plate splines to assess drug interactions

Maiying Kong1 , J. Jack Lee2

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

TABLE OF CONTENTS

1. Abstract
2. Introduction
2. Introduction
3. Statistical methods
3.1. Estimating dose-effect curves
3.2. Predicting additive effects
3.3. Assessing drug interactions using bivariate thin plate splines
4. Case studies
4.1. Case study 1: cancer cells grown in a medium with 2.3 .μM folic acid (low FA experiment)
4.2. Case study 2: cancer cells grown in a medium with 78 μM folic acid (high FA experiment)
5. Summary and perspective
6. Acknowledgement
References

1. ABSTRACT

We review the semiparametric approach previously proposed by Kong and Lee and extend it to a case in which the dose-effect curves follow the Emax model instead of the median effect equation. When the maximum effects for the investigated drugs are different, we provide a procedure to obtain the additive effect based on the Loewe additivity model. Then, we apply a bivariate thin plate spline approach to estimate the effect beyond additivity along with its 95% point-wise confidence interval as well as its 95% simultaneous confidence interval for any combination dose. Thus, synergy, additivity, and antagonism can be identified. The advantages of the method are that it provides an overall assessment of the combination effect on the entire two-dimensional dose space spanned by the experimental doses, and it enables us to identify complex patterns of drug interaction in combination studies. In addition, this approach is robust to outliers. To illustrate this procedure, we analyzed data from two case studies.