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, making this paper the first to present for this data setting a fully nonparametric estimator with proven consistency. Simulation results are presented showing that the method performs well. The method is illustrated on data from a prostate cancer study.
"Fully nonparametric estimation of the marginal survival function based on case-control clustered data." Electron. J. Statist. 13 (2) 5415 - 5453, 2019. https://doi.org/10.1214/19-EJS1651