title: Nonparametric survival analysis of infectious disease data.
abstract: This paper develops nonparametric methods based on contact intervals for the analysis of infectious disease data. The contact interval from personito personjis the time between the onset of infectiousness iniand infectious contact fromitoj, 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 fromitoj, 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.
authors.affiliation: Department of Biostatistics and Emerging Pathogens Institute, University of Florida, Gainesville, Florida, USA.
authors.forename: Eben
authors.initials: E
authors.lastname: Kenah
keywords: Chain-binomial models; Contact intervals; Generation intervals; Infectious disease; Nonparametric methods; Survival analysis