Interval estimators of relative potency in toxicology and radiation countermeasure studies: comparing methods and experimental designs

ABSTRACT

The relative potency of one agent to another is commonly represented by the ratio of two quantal response parameters; for example, the LD₅₀ of animals receiving a treatment to the LD₅₀ of control animals, where LD₅₀ is the dose of toxin that is lethal to 50% of animals. Though others have considered interval estimators of LD₅₀, here, we extend Bayesian, bootstrap, likelihood ratio, Fieller’s and Wald’s methods to estimate intervals for relative potency in a parallel-line assay context. In addition to comparing their coverage probabilities, we also consider their power in two types of dose designs: one assigning treatment and control the same doses vs. one choosing doses for treatment and control to achieve same lethality targets. We explore these methods in realistic contexts of relative potency of radiation countermeasures. For larger experiments (e.g., ≥100 animals), the methods return similar results regardless of the interval estimation method or experiment design. For smaller experiments (e.g., < 60 animals), Wald’s method stands out among the others, producing intervals that hold closely to nominal levels and providing more power than the other methods in statistically efficient designs. Using this simple statistical method within a statistically efficient design, researchers can reduce animal numbers.

KEYWORDS:

• Power
• sample size
• parallel-line assay
• dose reduction factor
• 3Rs

Acknowledgments

We are very grateful to Ralph L. Kodell for his insight into and feedback on this work. The content is solely the responsibility of the authors and does not necessarily represent the official views of the NIH.

Supplementary material

Supplemental data for this article can be accessed here.

Notes

1. We abbreviate both credible intervals and confidence intervals with CI. Though these differ in interpretation of θ, analysts use them in the same way to make statistical inference on θ.

2. We accidently coded the last increment of 3.5 as 3.55. Hence, we report on 3.55 instead of 3.5.

3. This number (200) of simulations keeps the Monte Carlo error for power estimates at less than √[(½×½)/200] ≈ .035.

Additional information

Funding

This work was partially supported by the following grants: (i) UL1TR000039 through the National Center for Advancing Translational Sciences of the National Institutes of Health (NIH), (ii) P20 GM109005 through the National Institute of General Medical Sciences of the NIH, (iii) R21 CA184756 through the National Cancer Institute of the NIH, and (iv) U19 AI67798 through the National Institute of Allergy and Infectious Diseases of the NIH.