Randomization for the direct effect of an infectious disease intervention in a clustered study population
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Randomized trials of infectious disease interventions often focus on populations of connected or potentially interacting individuals. When the pathogen of interest is contagious (transmissible) between study subjects, infection outcomes may exhibit dependence, and it can be challenging to define and estimate the causal "direct effect" of the intervention on individuals who receive it. Two very different paradigms guide researchers in conceptualizing this effect: a randomization design-based perspective defines the direct effect as a contrast between the infection risk of a given individual under treatment versus no treatment, averaged over the conditional distribution of randomized assignments to other individuals in the cluster; a structural model-based perspective defines the direct effect as a contrast between the infection risk of a given individual under treatment versus no treatment, with exposure to infectiousness held constant. In this paper, we show that the design- and model-based definitions of the causal direct effect are incompatible under some randomization designs when the outcome is contagious. In particular, design-based average risk differences may not recover the sign of the true individualistic effect of the intervention, even in large samples. The results suggest that widely recommended randomization designs and estimators may provide misleading inferences about the direct effect of an intervention - such as a vaccine - when outcomes are contagious.
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