  This paper develops nonparametric methods for the survival analysis of
epidemic data based on contact intervals. The contact interval from person i to
person j is the time between the onset of infectiousness in i and infectious
contact from i to j, where we define infectious contact as a contact sufficient
to infect a susceptible individual. We show that the Nelson-Aalen estimator
produces an unbiased estimate of the contact interval cumulative hazard
function when who-infects-whom is observed. When who-infects-whom is not
observed, we average the Nelson-Aalen estimates from all transmission networks
consistent with the observed data using an EM algorithm. This converges to a
nonparametric MLE of the contact interval cumulative hazard function that we
call the marginal Nelson-Aalen estimate. We study the behavior of these methods
in simulations and use them to analyze household surveillance data from the
2009 influenza A(H1N1) pandemic. In an appendix, we show that these methods
extend chain-binomial models to continuous time.
