  A case-control family study is a study where individuals with a disease of
interest (case probands) and individuals without the disease (control probands)
are randomly sampled from a well-defined population. Possibly right-censored
age at onset and disease status are observed for both probands and their
relatives. Correlation among the outcomes within a family is induced by factors
such as inherited genetic susceptibility, shared environment, and common
behavior patterns. For this setting, we present a nonparametric estimator of
the marginal survival function, based on local linear estimation of conditional
survival functions. Asymptotic theory for the estimator is provided, and
simulation results are presented showing that the method performs well. The
method is illustrated on data from a prostate cancer study.
  Keywords: case-control; family study; multivariate survival; nonparametric
estimator; local linear
