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Components of the Indirect Effect in Vaccine Trials: Identification of Contagion and Infectiousness Effects

VanderWeele, Tyler J.; Tchetgen Tchetgen, Eric J.; Halloran, M. Elizabeth


Unfortunately, due to a data entry error, the numbers reported in the illustration were incorrect. On page 757, first column, beginning with line 18 under “Illustration,” the estimates reported ought to have been:

…an overall estimate of the indirect effect of 0.26 (95% CI = 0.20 − 0.32), an estimate of the contagion effect of 0.45 (0.40 − 0.51) and an estimate of the infectiousness effect of 0.57 (0.47 − 0.69). The indirect effect on the risk-ratio scale decomposes into the product of the contagion and infectiousness effects: 0.26=0.45×0.57. On the vaccine-efficacy scale, we would have an overall indirect effect of 1-0.26=74%, a contagion effect of 1-0.45=55%, an infectiousness effect of 1-0.57=43%, and vaccine-efficacy component due to the infectiousness effect of (0.45)(43%)=19% (essentially taking into account the fact that the infectiousness effect will operate only if the contagion effect has not). We can then decompose the indirect effect on the vaccine efficacy scale into the sum of the contagion effect and the component due to infectiousness: 74%=55%+19%….

The authors thank Yasutaka Chiba for catching this error.

Epidemiology. 23(6):940, November 2012.

doi: 10.1097/EDE.0b013e31825fb7a0
Infectious Disease

Vaccination of one person may prevent the infection of another either because the vaccine prevents the first from being infected and from infecting the second, or because, even if the first person is infected, the vaccine may render the infection less infectious. We might refer to the first of these mechanisms as a contagion effect and the second as an infectiousness effect. In the simple setting of a randomized vaccine trial with households of size two, we use counterfactual theory under interference to provide formal definitions of a contagion effect and an unconditional infectiousness effect. Using ideas analogous to mediation analysis, we show that the indirect effect (the effect of one person's vaccine on another's outcome) can be decomposed into a contagion effect and an unconditional infectiousness effect on the risk difference, risk ratio, odds ratio, and vaccine efficacy scales. We provide identification assumptions for such contagion and unconditional infectiousness effects and describe a simple statistical technique to estimate these effects when they are identified. We also give a sensitivity analysis technique to assess how inferences would change under violations of the identification assumptions. The concepts and results of this paper are illustrated with hypothetical vaccine trial data.

From the Departments of Epidemiology and Biostatistics, Harvard School of Public Health, Boston, MA.

Submitted 6 December 2011; accepted 15 May 2012.

National Institutes of Health grants ES017876, HD060696, AI085073, and AI032042. The other authors have nothing to declare.

Correspondence: Tyler J. VanderWeele, Harvard School of Public Health, Departments of Epidemiology and Biostatistics, 677 Huntington Ave, Boston, MA 02115. E-mail:

© 2012 Lippincott Williams & Wilkins, Inc.