Fully nonparametric estimation of the marginal survival function based on case-control clustered data

David M. Zucker, Malka Gorfine

Research output: Contribution to journalArticlepeer-review


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.

Original languageAmerican English
Pages (from-to)5415-5453
Number of pages39
JournalElectronic Journal of Statistics
Issue number2
StatePublished - 2019

Bibliographical note

Funding Information:
The authors would like to thank Dr. Stanford for her generosity in sharing the prostate cancer dataset that was used for illustrating the method. Malka Gorfine gratefully acknowledges support from the U.S.-Israel Binational Science Foundation in carrying out this work.

Publisher Copyright:
© 2019, Institute of Mathematical Statistics. All rights reserved.


  • Case-control
  • Family study
  • Local linear
  • Multivariate survival data
  • Nonparametric estimator


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