一种基于降维的简约个体化剂量发现模型
A Parsimonious Personalized Dose Finding Model via Dimension Reduction
摘要：
在个体化医疗中，学习个体化剂量规则是一个具有挑战性的统计问题。现有的方法往往遭受灾难的维数，特别是当决策函数估计非参数。为了解决这个问题，我们提出了一个降维框架，有效地减少估计的协变量的一个低维子空间。我们利用的个性化剂量规则可以定义在一个子空间跨越的几个线性组合的协变量，导致一个更简约的模型。由于直接最大化的价值函数，所提出的框架不需要观察性研究下的倾向得分的逆概率。这将我们与结果加权学习框架区分开来，后者也直接解决决策规则。在相同的框架下，我们进一步提出了一个伪直接学习的方法，更侧重于估计的降维子空间的治疗结果。这两种方法中的参数可以有效地估计使用正交约束优化算法的Stiefel流形。在较弱的正则性假设下，分别建立了估计量的渐近正态性结果。在估计的最优剂量准则下，我们还得到了值函数的相合性和收敛速度。我们通过广泛的模拟研究和华法林药物遗传学数据集评估所提出的方法的性能。
英文摘要：
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 a lower-dimensional subspace of the covariates. We exploit that the individualized dose rule can be defined in a subspace spanned by a few linear combinations of the covariates, leading to a more parsimonious model. The proposed framework does not require the inverse probability of the propensity score under observational studies due to a direct maximization of the value function. This distinguishes us from the outcome weighted learning framework, which also solves decision rules directly. Under 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, the results on the asymptotic normality of the proposed estimators are established, respectively. We also derive the consistency and convergence rate for the value function under the estimated optimal dose rule. We evaluate the performance of the proposed approaches through extensive simulation studies and a warfarin pharmacogenetic dataset.
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