Robust Statistical Learning For Optimizing Individual Treatment Regimes

The significant heterogeneity in clinical treatment outcomes among different patients has emphasized the crucial need for developing individualized treatment regimes based on patient characteristics.Individualized treatment regimes can better address specific patient requirements,improve treatment effectiveness,and reduce the risk of adverse reactions.The aging of global population,rising healthcare costs,and increased access to patient-level data have created an urgent need for high-quality methods of individualized treatment regimes that can be applied to observational data.This is an extremely promising research direction that will bring many new opportunities and challenges to the fields of medicine and statistics.Individualized treatment regimes aim to maximize the overall clinical outcome for patients.Typically,the first step is to estimate the value function,which represents the average outcome under a given treatment regime.Currently,most statistical methods require assumptions of the outcome regression model or propensity score model to estimate the value function.If the model assumptions are inaccurate,then the resulting value function estimates could be inconsistent,making the optimal treatment plan unreliable.Therefore,it is crucial to reduce the reliance on models.Additionally,the current methods for learning the optimal treatment plan are mainly applicable to binary treatment regimes,and relatively few studies have been conducted on the problem of multicategorical treatment regimes commonly found in clinical practice.Furthermore,along with the improved capabilities of data collection,we are often confronted with data from multiple heterogeneous datasets.Therefore,we need to develop new methods to handle the heterogeneity of these datasets.To address the above issues,we propose a series of robust learning methods for the problems of model misspecification,multicategorical treatment regimes,and optimal treatment regimes with heterogeneous data.The main contributions of this paper are divided into three parts:1.To overcome the problem of estimation bias caused by model misspecification,we propose a doubly robust hybrid estimation method.This method defines a contrast value function and proposes a general framework for estimating the contrast value function using a hybrid estimation approach.Furthermore,we use inverse probability weighting and matching methods to further propose a robust covariate-balance(RCB)estimation method,which is shown to have doubly robustness and a convergence rate of n-1/2.2.To address the problem of estimating multicategorical treatment regimes,we propose a doubly robust matched learning called ACML.This method combines matching and regression to estimate the value function.Additionally,we construct a new surrogate loss and use the angle-based optimization method to find the optimal treatment regime.Theoretical results show that the method has doubly robustness and a convergence rate of n-1/2.Furthermore,we prove that the estimation of the treatment rule is Fisher consistent.3.For high-dimensional and heterogeneous datasets,we propose a double-penalized robust learning that eliminates the main effects unrelated to treatment regimes within each subgroup and identifies homogeneity and heterogeneity of coefficient matrix by penalizing pairwise differences of the coefficients of any two subgroups for the same covariate.The double-penalized robust learning not only eliminates the non-ignorable residual confounding caused by the misspecification of the main effects model,but also makes full use of the relationship information between different datasets.We further investigate the oracle property of this estimation.Extensive simulation studies and real data analyses have shown that our method has excellence in constructing optimal treatment regimes.Compared to current popular methods,our method can improve treatment outcomes with better robustness.