  In medical studies, the collected covariates usually contain underlying
outliers. For clustered /longitudinal data with censored observations, the
traditional Gehan-type estimator is robust to outliers existing in response but
sensitive to outliers in the covariate domain, and it also ignores the
within-cluster correlations. To take account of within-cluster correlations,
varying cluster sizes, and outliers in covariates, we propose weighted
Gehan-type estimating functions for parameter estimation in the accelerated
failure time model for clustered data. We provide the asymptotic properties of
the resulting estimators and carry out simulation studies to evaluate the
performance of the proposed method under a variety of realistic settings. The
simulation results demonstrate that the proposed method is robust to the
outliers existing in the covariate domain and lead to much more efficient
estimators when a strong within-cluster correlation exists. Finally, the
proposed method is applied to a medical dataset and more reliable and
convincing results are hence obtained.
