Counting Process Models for Infectious Disease Data: Distinguishing Exposure to Infection from Susceptibility

Differences in infection rates among types of individuals within a population can arise from differences in amount of exposure to infection or from differences in susceptibility to infection. We derive models for infection rates that incorporate contact rates between individuals and variables affecting susceptibility to infection. We emphasize the distinction between controlling for exposure opportunity (expected exposure) and actual exposure. We present a marked counting process model for the combined contact and infection transmission processes. When the contact process is not observable, we develop thinned counting process models that reduce to a proportional hazards model. We show that the different commonly used parameters for evaluating covariate effects, such as vaccine efficacy, form a hierarchy depending on the amount of information available about the components of the transmission system.