1Department of Statistics, North Carolina State University, Raleigh, NC, USA.
Stat Methods Med Res. 2013 Oct;22(5):493-504. doi: 10.1177/0962280211428383. Epub 2011 Nov 23.
In decision-making on optimal treatment strategies, it is of great importance to identify variables that are involved in the decision rule, i.e. those interacting with the treatment. Effective variable selection helps to improve the prediction accuracy and enhance the interpretability of the decision rule. We propose a new penalized regression framework which can simultaneously estimate the optimal treatment strategy and identify important variables. The advantages of the new approach include: (i) it does not require the estimation of the baseline mean function of the response, which greatly improves the robustness of the estimator; (ii) the convenient loss-based framework makes it easier to adopt shrinkage methods for variable selection, which greatly facilitates implementation and statistical inferences for the estimator. The new procedure can be easily implemented by existing state-of-art software packages like LARS. Theoretical properties of the new estimator are studied. Its empirical performance is evaluated using simulation studies and further illustrated with an application to an AIDS clinical trial.
在决策最优治疗策略时，确定与治疗相互作用的决策规则中涉及的变量非常重要。有效的变量选择有助于提高预测精度，并增强决策规则的可解释性。我们提出了一种新的惩罚回归框架，该框架可以同时估计最优治疗策略和识别重要变量。新方法的优点包括：（i）它不需要估计响应的基线均值函数，这大大提高了估计量的稳健性；（ii）基于损失的方便框架使得更容易采用收缩方法进行变量选择，这极大地方便了估计量的实现和统计推断。新程序可以通过现有的最先进的软件包（如 LARS）轻松实现。研究了新估计量的理论性质。通过模拟研究评估了其经验性能，并通过 AIDS 临床试验的应用进一步说明了这一点。
