Min Lin
The Ohio State University
Title
Survival Analysis on Contact Networks
Abstract
Event times on a contact network are strongly dependent: when one individual changes state, both the hazards and the relevant risk sets for other individuals may change. I will begin with simple examples illustrating why estimation based only on the observed transmission tree can be misleading.
The main probabilistic idea is to represent an SEIR epidemic, for each realization of the underlying randomness, as a static weighted directed graph. Infection times then become shortest-path distances from the index case. This representation yields a useful node-removal property: conditional on a node not yet being infected by time t, the information available up to time t can be characterized using the graph with that node deleted. This property leads to pairwise martingales and the corresponding likelihood. In the homogeneous exponential case, the same construction recovers the classical mass-action process.
I will finish with nonparametric estimation. After aggregating the dependent pairwise data into independent empirical units, the estimator can be written as an explicit functional of empirical processes, so functional delta methods give uniform weak convergence to a Gaussian limit. Because the natural function space is a nonseparable Banach space, measurability requires some additional care.
