Causal nearest neighbor rules for optimal treatment regimes
This work addresses the problem of personalized treatment assignment in precision medicine, offering an incremental improvement by adapting a known method to handle high-dimensional data.
The authors tackled the problem of estimating optimal treatment regimes for precision medicine by proposing a causal k-nearest neighbor method, which is universally consistent with established convergence rates but suffers from the curse of dimensionality, leading to an adaptive version that performs metric and variable selection, illustrated in simulations and a chronic depression trial.
The estimation of optimal treatment regimes is of considerable interest to precision medicine. In this work, we propose a causal $k$-nearest neighbor method to estimate the optimal treatment regime. The method roots in the framework of causal inference, and estimates the causal treatment effects within the nearest neighborhood. Although the method is simple, it possesses nice theoretical properties. We show that the causal $k$-nearest neighbor regime is universally consistent. That is, the causal $k$-nearest neighbor regime will eventually learn the optimal treatment regime as the sample size increases. We also establish its convergence rate. However, the causal $k$-nearest neighbor regime may suffer from the curse of dimensionality, i.e. performance deteriorates as dimensionality increases. To alleviate this problem, we develop an adaptive causal $k$-nearest neighbor method to perform metric selection and variable selection simultaneously. The performance of the proposed methods is illustrated in simulation studies and in an analysis of a chronic depression clinical trial.