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

The relative potency of one agent to another is commonly represented by the ratio of two quantal response parameters; for example, the LD_{50} of animals receiving a treatment to the LD_{50} of control animals, where LD_{50} is the dose of toxin that is lethal to 50% of animals. Though others have considered interval estimators of LD_{50}, 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.