Estimation of the multivariate survival function under random censorship

Estimation of the survival function P[T > t] under random censorship has
been well-studied in the univariate case. Here T is usually a time to an
event such as death of an individual or failure of an item. In the
multivariate case, one may be interested in the survival times of pairs of
individuals (e.g. example, twins or married couples), or times to
different events involving the same individual (e.g. onset of cancer in
different organs or times to response of successive treatments).

In the univariate case, the product-limit estimator is the estimator of
choice since it satisfies numerous nice properties. The problem of
estimating the survival function in the multivariate case is much more
challenging. I will describe a number of approaches to this problem.