Heterogeneous Treatment Effect with Trained Kernels of the Nadaraya-Watson Regression

The efficient treatment for a patient with her/his clinical and other characteristics [1, 2] can be regarded as an important goal of the real personalized medicine. The goal can be achieved by means of the machine learning methods due to the increasing amount of available electronic health records which are a basis for developing accurate models. To estimate the treatment effect, patients are divided into two groups called treatment and control, and then patients from the different groups are compared. One of the popular measures of the efficient treatment used in machine learning models is the average treatment effect (ATE) [3], which is estimated on the basis of observed data about patients as the mean difference between outcomes of patients from the treatment and control groups. Due to the difference between the patients characteristics and the difference between their responses to a particular treatment, the treatment effect is measured by the conditional average treatment effects (CATE) or the heterogeneous treatment effect (HTE) defined as ATE conditional on a patient feature vector [4, 5, 6, 7]. Two main problems can be pointed out when CATE is estimated. The first one is that the control group is usually larger than the treatment group. As a result, we meet the problem of a small training dataset, which does not allow us to apply directly many efficient machine learning methods.