Feasibility of Reducing Animal Numbers in Radiation Countermeasure Experiments from Historic Levels when using Sample Size Calculations

Abstract

Historically, animal numbers have most often been in the hundreds for experiments designed to estimate the dose reduction factor (DRF) of a radiation countermeasure treatment compared to a control treatment. Before 2010, researchers had to rely on previous experience, both from others and their own, to determine the number of animals needed for a DRF experiment. In 2010, a formal sample size formula was developed by Kodell et al. This theoretical work showed that sample sizes for realistic, yet hypothetical, DRF experiments could be less than a hundred animals and still have sufficient power to detect clinically meaningful DRF values. However, researchers have been slow to use the formula for their DRF experiments, whether from ignorance to its existence or hesitancy to depart from "tried and true" sample sizes. Here, we adapt the sample size formula to better fit usual DRF experiments, and, importantly, we provide real experimental evidence from two independent DRF experiments that sample sizes smaller than what have typically been used can still statistically detect clinically meaningful DRF values. In addition, we update a literature review of DRF experiments which can be used to inform future DRF experiments, provide answers to questions that researchers have asked when considering sample size calculations rather than solely relying on previous experience, whether their own or others', and, in the supplementary material, provide R code implementing the formula, along with several exercises to familiarize the user with the adapted formula.

FIG. 1.

Assumed parameters for a prospective DRF experiment. Radiation doses to be administered to control (Ctrl, orange) and countermeasure-treated (Trt, green) animals are indicated. Also indicated are the assumed LD₅₀ for control, the slope on expected % mortality in both Ctrl and Trt groups, and the desired DRF to detect. The LD₅₀ for countermeasure-treated animals is the product of the DRF and LD₅₀ for control animals. Note, in keeping with a planned probit regression analysis, radiation doses are mapped onto the log₁₀ scale and % morality onto the probit scale.

FIG. 2.

From the retrospective study, power (solid) for detecting a DRF of 1.10 and hypothesis-rejection rates (dashed), plotted by treatment × radiation dose subgroup sample size.

FIG. 3.

From the prospective study, power (solid) for detecting a DRF of 1.10 and hypothesis-rejection rates (dashed), plotted by treatment × radiation dose subgroup sample size.

FIG. 4.

Power curves plotted by detectable DRF for the different dose designs in Table 1. Power was computed assuming 72 animals distributed equally among the doses for both control and countermeasure treated animals; all other assumed parameters (ii, v and vi) were as for the retrospective study. The 6-dose design is the original dose design used in the retrospective study.