A two-stage experimental design for dilution assays

Jake M. Ferguson, Tanya A. Miura, Craig R. Miller

Research output: Contribution to journalArticlepeer-review


Dilution assays to determine solute concentration have found wide use in biomedical research. Many dilution assays return imprecise concentration estimates because they are only done to orders of magnitude. Previous statistical work has focused on how to design efficient experiments that can return more precise estimates, however this work has not considered the practical difficulties of implementing these designs in the laboratory. We developed a two-stage experiment with a first stage that obtains an order of magnitude estimate and a second stage that concentrates effort on the most informative dilution to increase estimator precision. We show using simulations and an empirical example that the best two-stage experimental designs yield estimates that are remarkably more accurate than standard methods with equivalent effort. This work demonstrates how to utilize previous advances in experimental design in a manner consistent with current laboratory practice. We expect that multi-stage designs will prove to be useful for obtaining precise estimates with minimal experimental effort.

Original languageEnglish
Pages (from-to)1009-1016
Number of pages8
Issue number3
StatePublished - Sep 1 2019

Bibliographical note

Funding Information:
This work was supported by the Center for Modeling Complex Interactions through NIH Award #P20GM104420. The authors would like to thank Dr. Bhim Thapa for technical assistance. As well as three anonymous reviewers whose comments greatly improved the quality of this manuscript.

Publisher Copyright:
© 2019 International Biometric Society


  • efficient experimental design
  • fisher information
  • generalized linear model
  • parameter estimation
  • single-hit poisson model

ASJC Scopus subject areas

  • Statistics and Probability
  • Biochemistry, Genetics and Molecular Biology (all)
  • Immunology and Microbiology (all)
  • Agricultural and Biological Sciences (all)
  • Applied Mathematics


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