Practical Design Approaches for Assessing Parallelism in Dose Response Modelling

  • Timothy E. O’Brien
  • Jack Silcox
Part of the ICSA Book Series in Statistics book series (ICSABSS)


Scientific researchers in biomedicine, pharmaceutical science and toxicology often face situations in which binary logistic regression model fits are used to compare two drugs or substances, often by means of comparisons of median doses or concentrations (EC50 or LD50). Applications are given in works spanning early bioassay findings of Finney (1971, 1978) to more recent results in Rich (2013) and Gupta and Vale (2017). Furthermore, Wheeler et al. (2006) underscores the caution that instead of examining for overlap in separate EC50 confidence intervals, testing is best based on estimation and confidence intervals associated with the relative potency parameter. Notably, before fitting such curves and testing for differing potencies, an important requirement is that these dose response curves be parallel. As such, various works have introduced meaningful means to assess parallelism in logistic regression settings, including Gottschalk and Dunn (2005), Jonkman and Sidak (2009), Novick et al. (2012), Yang and Zhang (2012), Yang et al. (2012), Fleetwood et al. (2015) and Sidak and Jonkman (2016).


Dose response Geometric design Lack of fit Logistic regression Mechanism of action Median lethal concentration Model misspecification Parallelism Robust optimal design Uniform design 


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Timothy E. O’Brien
    • 1
    • 2
  • Jack Silcox
    • 1
    • 3
  1. 1.Department of Mathematics and StatisticsLoyola University ChicagoChicagoUSA
  2. 2.Institute of Environmental Sustainability, Loyola University ChicagoChicagoUSA
  3. 3.University of Utah, Cognitive and Neural Science PhD ProgramSalt Lake CityUSA

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