A note on bounds for the causal infectiousness effect in vaccine trials

In vaccine trials, the vaccination of one person might prevent the infection of another. This dependency makes it difficult to estimate the effect of a vaccine on infection. To deal with this issue, causal inference along with a principal stratification framework has been discussed. Unfortunately, however, no standard method has been established for estimating the causal infectiousness effect (CIE). Recently, in a setting of two persons per household, it has been reported that the crude estimator becomes the upper bound of the CIE under two plausible assumptions. Here, we present the lower bound for the CIE by strengthening one of these two assumptions.