Optimal designs for health risk assessments using fractional polynomial models

Víctor Casero-Alonso, Jesús López–Fidalgo, Weng Kee Wong

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


Fractional polynomials (FP) have been shown to be more flexible than polynomial models for fitting data from an univariate regression model with a continuous outcome but design issues for FP models have lagged. We focus on FPs with a single variable and construct D-optimal designs for estimating model parameters and I-optimal designs for prediction over a user-specified region of the design space. Some analytic results are given, along with a discussion on model uncertainty. In addition, we provide an applet to facilitate users find tailor made optimal designs for their problems. As applications, we construct optimal designs for three studies that used FPs to model risk assessments of (a) testosterone levels from magnesium accumulation in certain areas of the brains in songbirds, (b) rats subject to exposure of different chemicals, and (c) hormetic effects due to small toxic exposure. In each case, we elaborate the benefits of having an optimal design in terms of cost and quality of the statistical inference.

Original languageEnglish
Pages (from-to)2695-2710
Number of pages16
JournalStochastic Environmental Research and Risk Assessment
Issue number9
Publication statusPublished - 2022 Sept

All Science Journal Classification (ASJC) codes

  • Environmental Engineering
  • Environmental Chemistry
  • Water Science and Technology
  • Safety, Risk, Reliability and Quality
  • General Environmental Science


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