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Estimating optimal interpretable individualized treatment regimes from a classification perspective using adaptive LASSO

Yunshu Zhang, Shu Yang, Wendy Ye, Ilya Lipkovich, Douglas E. Faries

TL;DR

The paper tackles the challenge of deriving interpretable, sparse individualized treatment regimes from high-dimensional real-world data by recasting the search for an optimal linear ITR as a weighted classification problem. It introduces an adaptive LASSO–regularized framework that learns a sparse linear score $f(X;\eta)=X^T\eta$ with the optimal policy $d_\eta(x)=I(x^T\eta>0)$, using surrogate losses (hinge and smoothed ramp) and an augmented inverse probability weighting (AIPW) estimator for the ITE contrast $\tau(x)$. The optimization combines adaptive LASSO penalties with either a convex hinge loss or a DC-decomposed ramp loss to obtain an interpretable policy, with cross-validation for tuning parameters and a refitting step for stability. Empirical results indicate that adaptive LASSO improves variable selection and sparsity while achieving competitive value versus state-of-the-art methods such as causal forests and R-learning, supporting practical adoption of sparse, interpretable ITRs in real-world decision-making. The approach also accommodates extensions to survival outcomes and is demonstrated on real data (e.g., TRIUMPH migraine) and simulations, highlighting its potential to balance interpretability with predictive performance in high-dimensional causal inference.

Abstract

Real-world data (RWD) gains growing interests to provide a representative sample of the population for selecting the optimal treatment options. However, existing complex black box methods for estimating individualized treatment rules (ITR) from RWD have problems in interpretability and convergence. Providing an interpretable and sparse ITR can be used to overcome the limitation of existing methods. We developed an algorithm using Adaptive LASSO to predict optimal interpretable linear ITR in the RWD. To encourage sparsity, we obtain an ITR by minimizing the risk function with various types of penalties and different methods of contrast estimation. Simulation studies were conducted to select the best configuration and to compare the novel algorithm with the existing state-of-the-art methods. The proposed algorithm was applied to RWD to predict the optimal interpretable ITR. Simulations show that adaptive LASSO had the highest rates of correctly selected variables and augmented inverse probability weighting with Super Learner performed best for estimating treatment contrast. Our method had a better performance than causal forest and R-learning in terms of the value function and variable selection. The proposed algorithm can strike a balance between the interpretability of estimated ITR (by selecting a small set of important variables) and its value.

Estimating optimal interpretable individualized treatment regimes from a classification perspective using adaptive LASSO

TL;DR

The paper tackles the challenge of deriving interpretable, sparse individualized treatment regimes from high-dimensional real-world data by recasting the search for an optimal linear ITR as a weighted classification problem. It introduces an adaptive LASSO–regularized framework that learns a sparse linear score with the optimal policy , using surrogate losses (hinge and smoothed ramp) and an augmented inverse probability weighting (AIPW) estimator for the ITE contrast . The optimization combines adaptive LASSO penalties with either a convex hinge loss or a DC-decomposed ramp loss to obtain an interpretable policy, with cross-validation for tuning parameters and a refitting step for stability. Empirical results indicate that adaptive LASSO improves variable selection and sparsity while achieving competitive value versus state-of-the-art methods such as causal forests and R-learning, supporting practical adoption of sparse, interpretable ITRs in real-world decision-making. The approach also accommodates extensions to survival outcomes and is demonstrated on real data (e.g., TRIUMPH migraine) and simulations, highlighting its potential to balance interpretability with predictive performance in high-dimensional causal inference.

Abstract

Real-world data (RWD) gains growing interests to provide a representative sample of the population for selecting the optimal treatment options. However, existing complex black box methods for estimating individualized treatment rules (ITR) from RWD have problems in interpretability and convergence. Providing an interpretable and sparse ITR can be used to overcome the limitation of existing methods. We developed an algorithm using Adaptive LASSO to predict optimal interpretable linear ITR in the RWD. To encourage sparsity, we obtain an ITR by minimizing the risk function with various types of penalties and different methods of contrast estimation. Simulation studies were conducted to select the best configuration and to compare the novel algorithm with the existing state-of-the-art methods. The proposed algorithm was applied to RWD to predict the optimal interpretable ITR. Simulations show that adaptive LASSO had the highest rates of correctly selected variables and augmented inverse probability weighting with Super Learner performed best for estimating treatment contrast. Our method had a better performance than causal forest and R-learning in terms of the value function and variable selection. The proposed algorithm can strike a balance between the interpretability of estimated ITR (by selecting a small set of important variables) and its value.
Paper Structure (6 sections, 1 theorem, 12 equations, 1 figure, 1 algorithm)

This paper contains 6 sections, 1 theorem, 12 equations, 1 figure, 1 algorithm.

Table of Contents

  1. Introduction
  2. Notation and assumptions
  3. Algorithm
  4. Classification perspective and surrogate functions
  5. Penalize the coefficients via LASSO and adaptive LASSO
  6. Smoothed ramp loss function and d.c. algorithm

Key Result

Lemma 1

zhang2012estimating The coefficient of the optimal ITR $\eta^{opt}$, which maximizes the value function $V\left(d_{\eta}\right)$, is also the minimizer of the risk function where $l_{0-1}\left(u\right)=I\left(u\leq0\right)$ and $\mathcal{F}$ is the domain of the ITR coefficient $\eta$, for example, $\mathbb{R}^{p}$.

Figures (1)

  • Figure 1: Illustrating example comparing direct method and indirect method. The true ITE is a second-degree polynomial function of $x$, but the true optimal ITR is linear. The indirect method is concerned with minimizing the prediction error, while the direct method focuses on the sign and thus approaches the true optimal regime by-passing contrast estimation.

Theorems & Definitions (1)

  • Lemma 1