BENK: The Beran Estimator with Neural Kernels for Estimating the Heterogeneous Treatment Effect

Abstract

A method for estimating the conditional average treatment effect under the 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 neural kernels. The conditional average treatment effect is estimated by using the survival functions as outcomes of the control and treatment neural networks, which consist 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. BENK does not require a large dataset for training due to its special way for training networks by means of pairs of examples from the control and treatment groups. The proposed method extends a set of models that estimate the conditional average treatment effect. Various numerical simulation experiments illustrate BENK and compare it with the well-known T-learner, S-learner and X-learner for several types of control and treatment outcome functions based on the Cox models, the random survival forest and the Beran estimator with Gaussian kernels. The code of the proposed algorithms implementing BENK is publicly available.

Keywords

• treatment effect
• survival analysis
• Nadaraya–Watson regression
• Beran estimator
• neural network
• meta-learner