A method for estimating the conditional average treatment effect under
condition of censored time-to-event data called BENK (the Beran Estimator with
Neural Kernels) is proposed. The main idea behind the method is to apply the
Beran estimator for estimating the survival functions of controls and
treatments. Instead of typical kernel functions in the Beran estimator, it is
proposed to implement kernels in the form of neural networks of a specific form
called the neural kernels. The conditional average treatment effect is
estimated by using the survival functions as outcomes of the control and
treatment neural networks which consists of a set of neural kernels with shared
parameters. The neural kernels are more flexible and can accurately model a
complex location structure of feature vectors. Various numerical simulation
experiments illustrate BENK and compare it with the well-known T-learner,
S-learner and X-learner for several types of the control and treatment outcome
functions based on the Cox models, the random survival forest and the
Nadaraya-Watson regression with Gaussian kernels. The code of proposed
algorithms implementing BENK is available in https://github.com/Stasychbr/BENK