On dose-response modeling for evaluation of drugs combinations

Abstract

We introduce a framework of dose-response modeling for the evaluation of drug combinations. We focus on adaptive techniques in dose-finding studies when several endpoints can be observed simultaneously on each subject. This framework may fit well for clinical trials and we discuss its algorithmization. The generalized bivariate probit model is discussed in particular. Necessary conditions for plausible behavior of drug combinations are given from the theoretical stochastic perspective.

Keywords:

• dose response
• modeling
• adaptive techniques
• drug combinations
• bivariate probit

Subject classification codes:

• Primary 62J12
• Secondary 62J20

Acknowledgments

We acknowledge the support of the Editors and the informative and insightful suggestions of the Referees. Milan Stehlík acknowledges ANID Chile COVBIO0003. We acknowledge “personal communication” to Madeline Bauer, especially for giving an original idea to use tessellations and the Nelder Mead method. This applies to every place we mention [6] and [7].

Notes

1 E.g. $z_i=\frac{x_i-\min (x)}{\max (x)-\min (x)}.$

Additional information

Funding

Jozef Kiseľák was supported by the Slovak Research and Development Agency under Contract no. APVV-21-0369 and by the grant VEGA MŠ SR 1/0526/20.