Nonparametric survival analysis of infectious disease data.

This paper develops nonparametric methods based on contact intervals for the analysis of infectious disease data. 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. The hazard function of the contact interval distribution equals the hazard of infectious contact from i to j, so it provides a summary of the evolution of infectiousness over time. When who-infects-whom is observed, the Nelson-Aalen estimator produces an unbiased estimate of the cumulative hazard function of the contact interval distribution. When who-infects-whom is not observed, we use an EM algorithm to average the Nelson-Aalen estimates from all possible combinations of who-infected-whom consistent with the observed data. This converges to a nonparametric maximum likelihood estimate of the 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.