Contact intervals, survival analysis of epidemic data, and estimation of R_0
Abstract
We argue that the time from the onset of infectiousness to infectious contact, which we call the contact interval, is a better basis for inference in epidemic data than generation or serial intervals. Since an infectious person might recover before making infectious contact or make infectious contact with previously infected persons, infectious contact intervals can be right-censored and survival analysis is the natural approach to estimation. We derive likelihoods for completely-observed stochastic ``Susceptible-Exposed-Infectious-Removed'' (SEIR) models in close-contact groups and generalize these to network-based, mass-action, and two-level models. In a series of simulations, we evaluate the performance of these methods and show that assumptions about the underlying contact process play a crucial role in estimating contact interval distribution parameters and R_0. Methods based on generation and serial intervals are incomplete-data methods without corresponding complete-data methods, and they rely on strong assumptions that are not always explicit. Methods based on contact intervals allow clearer expression of assumptions, greater flexibility in the choice of an underlying transmission model, and the application of methods from survival analysis to infectious disease epidemiology. In an appendix, we show that these methods reproduce and generalize standard discrete-time likelihoods when the contact interval distribution is discrete.Keywords
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