Doubly-robust causal inference for multi-valued treatment regimes with recurrent neural networks

Abstract

We propose a doubly-robust method to estimate the causal effects of multi-valued treatment regimes on patient outcomes. A multi-valued treatment regime assigns personalized treatments from a set of competing options based on a patient's history. Existing methods for optimal treatment regimes are largely limited to binary or continuous treatments. We extend the longitudinal targeted minimum loss-based estimator (LTMLE) to accommodate multi-valued treatments by modeling treatment assignments with a multinomial model. We further integrate recurrent neural networks (RNNs) into the LTMLE framework as learners for the outcome, treatment, and censoring models, and compare this approach to ensemble machine learning. Simulation studies show that LTMLE with either ensemble machine learning or RNNs is approximately unbiased, with close to nominal coverage, whereas sequential g-computation with ensemble machine learning is substantially biased under a dynamic rule. A multinomial treatment model performs similarly to a series of binomial regressions with ensemble machine learning, but yields more stable inference when the treatment model is an RNN.