  The accelerated failure time (AFT) model is widely used to analyze
relationships between variables in the presence of censored observations.
However, this model relies on some assumptions such as the error distribution,
which can lead to biased or inefficient estimates if these assumptions are
violated. In order to overcome this challenge, we propose a novel approach that
incorporates a semiparametric skew-normal scale mixture distribution for the
error term in the AFT model. By allowing for more flexibility and robustness,
this approach reduces the risk of misspecification and improves the accuracy of
parameter estimation. We investigate the identifiability and consistency of the
proposed model and develop a practical estimation algorithm. To evaluate the
performance of our approach, we conduct extensive simulation studies and real
data analyses. The results demonstrate the effectiveness of our method in
providing robust and accurate estimates in various scenarios.
