IMR Press / FBE / Volume 2 / Issue 1 / DOI: 10.2741/E90

Frontiers in Bioscience-Elite (FBE) is published by IMR Press from Volume 13 Issue 2 (2021). Previous articles were published by another publisher on a subscription basis, and they are hosted by IMR Press on as a courtesy and upon agreement with Frontiers in Bioscience.


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

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

*Author to whom correspondence should be addressed.


Front. Biosci. (Elite Ed) 2010, 2(1), 279–292;
Published: 1 January 2010

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.

Bivariate splines
Combination therapy
Emax model
the Loewe additivity model
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