An important concept in epidemiology is attributable risk, defined as the difference in risk between an exposed and an unexposed group. For example, in an intervention trial, the attributable risk is the difference in risk between a group that receives an intervention and another that does not. A fundamental assumption in estimating the attributable risk associated with the intervention is that disease outcomes are independent. When estimating population risks associated with treatment regimens designed to affect exposure to infectious pathogens, however, there may be bias due to the fact that infectious pathogens can be transmitted from host to host causing a potential statistical dependency in disease status among participants.
By incorporating these dependencies among individuals in a transmission model, we show how the bias of attributable risk estimates could be quantified to adjust effect estimates reported from intervention trials.
Analysis of the model suggests that this bias in attributable risk estimates is a function of transmission from person to person, either directly or indirectly via the environment.
To estimate this bias, we used a mathematical model of community- and household-level disease transmission to explicitly incorporate the dependency among participants. We illustrate the method using a plausible model of infectious diarrheal disease.