Fig 3. Example results from optimization of procedural parameters.

The procedure outlined in Fig 2 was evaluated by Monte Carlo simulation (350–1000 simulations for each set of values). The parameters modeled were: (1) the starting dose (D₀), ranging from 1/27^th to 27x AID₅₀; the number of animals challenged at each dose during the dose ranging (group size: N_C); the target standard error on the estimate of AID₅₀ (σ_T); the maximum number of exposures (E_MAX) of any single animal; and the order of the kinetics of infection (m). Shown in red are the suggested values of these parameters, i.e., those that resulted in the fewest animals, the fewest rounds, and the most accurate estimate of AID₅₀. Where not graphed, parameter values were held constant, as follows: N_C = 8, σ_T = 0.5, D₀ = 1/3, m = 1, E_MAX = unlimited. (A) The number of animals required is not strongly dependent upon the group size, except in cases where the starting estimate of D₀ is greater than 1 AID₅₀. Thus, in the case where D₀ is low, the number of rounds required decreases with increasing group size, to a point. (B) The number of animals required increases when D₀ goes above 1, but the number of rounds (shown for phase 1) is not strongly impacted by D₀. (C) The number of animals required decreases as the target standard error (σ_T) on the final estimate of AID₅₀ decreases (i.e., more precision requires more data). (D) Decreasing E_MAX increases the number of animals required, particularly at low D₀. If D₀ is close to 1, then a limit of three exposures performs equally to no limit. (E) When E_MAX is limited, then the number of animals required increases when D₀ is far from AID₅₀ in either direction. (F) Example outcomes on parameters when using a infection kinetics with nonlinear order (m = 3 or m = 0.5). The pattern of results is largely similar to first-order kinetics, with similar optima. Bar and whisker plots show the median, interquartile range, and full range excluding outliers.