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Nonparametric survival analysis of infectious disease data.

Abstract

, 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.

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