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Updated: Feb 14, 2026

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Optimal designs for active controlled dose-finding trials with efficacy-toxicity outcomes.

K Schorning1, H Dette1, K Kettelhake1

  • 1Fakultät für Mathematik, Ruhr-Universität Bochum, 44780 Bochum, GermanyKirsten.Schorning@rub.deholger.dette@rub.deKatrin.Kettelhake@rub.de.

Biometrika
|February 13, 2018
PubMed
Summary

This study presents optimal designs for active controlled dose-finding trials using nonlinear regression models for bivariate outcomes. The findings offer insights into dose selection and outcome correlation for improved trial efficiency.

Keywords:
Admissible designEquivalence theoremParticle swarm optimizationTchebycheff system

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Area of Science:

  • Biostatistics
  • Clinical Trial Design
  • Pharmacometrics

Background:

  • Estimating drug efficacy and toxicity is crucial in clinical trials.
  • Dose-finding trials require efficient designs to balance patient safety and therapeutic benefit.
  • Bivariate continuous outcomes in dose-finding studies present unique analytical challenges.

Purpose of the Study:

  • To derive optimal designs for active controlled dose-finding trials with bivariate continuous outcomes.
  • To establish upper bounds on the number of doses and identify conditions for including boundary points in optimal designs.
  • To analytically describe minimally supported optimal designs and their independence from outcome correlation.

Main Methods:

  • Application of nonlinear regression models to describe bivariate continuous outcomes.
  • Derivation of optimal design criteria for efficacy and toxicity estimation.
  • Analysis of design space boundaries and correlation effects.

Main Results:

  • Optimal designs were derived for estimating efficacy and toxicity in active controlled dose-finding trials.
  • Upper bounds for the number of doses were determined, with conditions for boundary point inclusion.
  • Minimally supported optimal designs were analytically described and found to be independent of outcome correlation.

Conclusions:

  • The derived optimal designs enhance the efficiency of dose-finding trials with bivariate outcomes.
  • Understanding dose-response relationships and correlation is key for robust trial design.
  • The findings provide a theoretical framework for designing trials that efficiently estimate efficacy and toxicity.