Eben Kenah

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  Pairwise survival analysis: Contact intervals, regression, and phylogenetics
  Eben Kenah
  When integrating epidemiologic data with pathogen phylogenetics, the likelihood for the transmission model is often a branching-process likelihood based on a generation interval distribution. We show that a misspecified likelihood can lead to severely biased estimates with or without a pathogen phylogeny. Writing the likelihood as a survival likelihood with failure times in pairs---a method we call pairwise survival analysis---accounts for time spent at risk of infection. In a simple example with three infections, we show that a pairwise survival likelihood produces more accurate source attribution. In a mass-action model with negligible depletion of susceptibles, the pairwise survival likelihood depends only on information about infected individuals in the limit of a large population. However, this asymptotic likelihood has cumulative hazard terms that have no counterpart in a branching process likelihood. As an example of the flexibility of pairwise survival analysis, we describe a pairwise accelerated failure time model that can be used to estimate covariate effects on infectiousness and susceptibility. This model---modified to account for the buildup of immunity---will be used to estimate the efficacy of the Ebola vaccine based on the WHO ring vaccination trial in Guinea. This trial collected data on individuals exposed to infection who escaped as well as Ebola virus genetic sequences. Finally, we describe a pruning algorithm for calculating an approximate likelihood using both epidemiologic data and a pathogen phylogeny. Pathogen genetics can improve statistical efficiency and reduce bias, but this depends on good epidemiologic study design and a good likelihood for transmission.