Learning an individualized dose rule in personalized medicine is a challenging statistical problem. Existing methods often suffer from the curse of dimensionality, especially when the decision function is estimated nonparametrically. To tackle this problem, we propose a dimension reduction framework that effectively reduces the estimation to an optimization on a lower-dimensional subspace of the covariates. We exploit the fact that the individualized dose rule can be defined in a subspace spanned by a few linear combinations of the covariates to obtain a more parsimonious model. Owing to direct maximization of the value function, the proposed framework does not require the inverse probability of the propensity score under observational studies. This distinguishes our approach from the outcome-weighted learning framework, which also solves decision rules directly. Within the same framework, we further propose a pseudo-direct learning approach that focuses more on estimating the dimensionality-reduced subspace of the treatment outcome. Parameters in both approaches can be estimated efficiently using an orthogonality-constrained optimization algorithm on the Stiefel manifold. Under mild regularity assumptions, results on the asymptotic normality of the proposed estimators are established. We also derive the consistency and convergence rate of the value function under the estimated optimal dose rule. We evaluate the performance of the proposed approaches through extensive simulation studies and analysis of a pharmacogenetic dataset.

中文翻译：

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通过降维的简约个性化剂量寻找模型

在个性化医疗中学习个体化剂量规则是一个具有挑战性的统计问题。现有方法经常遭受维数灾难，特别是当决策函数是非参数估计时。为了解决这个问题，我们提出了一个降维框架，该框架可以有效地将估计减少到对协变量的低维子空间的优化。我们利用这样一个事实，即个体化剂量规则可以在由协变量的一些线性组合跨越的子空间中定义，以获得更简约的模型。由于价值函数的直接最大化，所提出的框架不需要观察研究下倾向得分的逆概率。这将我们的方法与结果加权学习框架区分开来，后者也直接解决决策规则。在同一框架内，我们进一步提出了一种伪直接学习方法，该方法更侧重于估计治疗结果的降维子空间。两种方法中的参数都可以使用 Stiefel 流形上的正交约束优化算法进行有效估计。在温和的规律性假设下，建立了所提出的估计量的渐近正态性结果。我们还推导了估计最佳剂量规则下价值函数的一致性和收敛率。我们通过广泛的模拟研究和药物遗传学数据集分析来评估所提出方法的性能。