Power calculation for mosquito bioassays: Quantifying variability in the WHO tube bioassay and developing sample size guidance for the PBO synergism assay using a Shiny application

Background
\nThe WHO tube bioassay is a method for exposing mosquitos to determine susceptibility to insecticides, with mortality to discriminating doses <98% indicating possible resistance and <90% confirming resistance. This bioassay is also used for synergism testing to assess if susceptibility is restored by pre-exposure to the synergist piperonyl butoxide.
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\nMethods
\nHere we perform testing with pyrethroid-susceptible and pyrethroid-resistant An. gambiae to quantify the variability of the WHO tube bioassay and identify its sources. These estimates of within and between day variability are then used to evaluate the power of the bioassay to detect a mortality difference between pyrethroid-only and pyrethroid-PBO.
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\nResults
\nWe show that approximately two-thirds of variation occurs between days, with the pyrethroid-susceptible strain twice as variable as the pyrethroid-resistant strain. The total number of mosquitoes in the tube and their bodyweight contributes to approximately 10% of this variability. Changes in temperature and humidity, within a climate-controlled insectary, didn’t impact mortality. Using a simulation-based framework, we show that the current synergism guidelines, using a 4x4 design, can reliably detect a difference between 90% and 100% mortality (>90% power). However, as the mortality of either group gets closer to 50%, a 10% difference between groups is more difficult to reliably detect. In the worst-case scenario where the mortality of either group is 50%, the mortality difference must be >22.5% to be detected with 80% power. We provide an R shiny application to assess power for other comparisons.
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\nConclusions
\nOur findings indicate that detecting synergism with the WHO tube assay is more difficult than assumed by the current WHO guidelines. Additionally, we demonstrate the value of using a Shiny application to make the outputs of simulation-based power analysis readily available to end-users, allowing them to determine the number of tubes needed to detect a given mortality difference.