Non-Parametric Survival Analysis of Infectious Disease Data

Abstract

SummaryThe paper develops non-parametric 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 expectation–maximization algorithm to average the Nelson–Aalen estimates from all possible combinations of who infected whom consistent with the observed data. This converges to a non-parametric maximum likelihood estimate of the cumulative hazard function that we call the marginal Nelson–Aalen estimate. We study the behaviour of these methods in simulations and use them to analyse household surveillance data from the 2009 influenza A(H1N1) pandemic.