# An improved fully nonparametric estimator of the marginal survival function based on case-control clustered data

## TL;DR

This paper introduces a new nonparametric estimator for the marginal survival function in case-control family studies, accounting for within-family correlations and right-censored data, with proven asymptotic properties and demonstrated effectiveness through simulations and real data application.

## Contribution

It proposes a novel local linear nonparametric estimator for the marginal survival function in family-based case-control studies, addressing within-family correlation and censoring.

## Key findings

- Estimator performs well in simulations
- Asymptotic properties are established
- Method applied successfully to prostate cancer data

## Abstract

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