Matthew J Smith, Rachael V Phillips, Camille Maringe, Miguel Angel Luque-Fernandez
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引用次数: 0
Abstract
Background: Advanced methods for causal inference, such as targeted maximum likelihood estimation (TMLE), require specific convergence rates and the Donsker class condition for valid statistical estimation and inference. In situations where there is no differentiability due to data sparsity or near-positivity violations, the Donsker class condition is violated. In such instances, the bias of the targeted estimand is inflated, and its variance is anti-conservative, leading to poor coverage. Cross-validation of the TMLE algorithm (CVTMLE) is a straightforward, yet effective way to ensure efficiency, especially in settings where the Donsker class condition is violated, such as random or near-positivity violations. We aim to investigate the performance of CVTMLE compared to TMLE in various settings.
Methods: We utilized the data-generating mechanism described in Leger et al. (2022) to run a Monte Carlo experiment under different Donsker class violations. Then, we evaluated the respective statistical performances of TMLE and CVTMLE with different super learner libraries, with and without regression tree methods.
Results: We found that CVTMLE vastly improves confidence interval coverage without adversely affecting bias, particularly in settings with small sample sizes and near-positivity violations. Furthermore, incorporating regression trees using standard TMLE with ensemble super learner-based initial estimates increases bias and reduces variance, leading to invalid statistical inference.
Conclusions: We show through simulations that CVTMLE is much less sensitive to the choice of the super learner library and thereby provides better estimation and inference in cases where the super learner library uses more flexible candidates and is prone to overfitting.
背景:先进的因果推理方法,如目标最大似然估计(TMLE),需要特定的收敛率和Donsker类条件才能进行有效的统计估计和推理。在由于数据稀疏性或近正性违反而没有可微性的情况下,违反了Donsker类条件。在这种情况下,目标估计的偏差被夸大,其方差是反保守的,导致覆盖面差。交叉验证TMLE算法(CVTMLE)是确保效率的一种直接而有效的方法,特别是在违反Donsker类条件的设置中,例如随机或接近正违例。我们的目标是研究CVTMLE与TMLE在不同环境下的性能。方法:我们利用Leger et al.(2022)中描述的数据生成机制,在不同的Donsker类违规情况下运行蒙特卡罗实验。然后,我们评估了不同的超级学习器库在使用和不使用回归树方法的情况下,TMLE和CVTMLE各自的统计性能。结果:我们发现CVTMLE极大地提高了置信区间覆盖率,而不会对偏倚产生不利影响,特别是在小样本量和接近正违规的情况下。此外,将使用标准TMLE的回归树与基于集成超级学习器的初始估计相结合会增加偏差并减少方差,从而导致无效的统计推断。结论:我们通过模拟表明,CVTMLE对超级学习器库的选择不太敏感,因此在超级学习器库使用更灵活的候选对象并且容易过度拟合的情况下,可以提供更好的估计和推断。
期刊介绍:
The journal aims to influence practice in medicine and its associated sciences through the publication of papers on statistical and other quantitative methods. Papers will explain new methods and demonstrate their application, preferably through a substantive, real, motivating example or a comprehensive evaluation based on an illustrative example. Alternatively, papers will report on case-studies where creative use or technical generalizations of established methodology is directed towards a substantive application. Reviews of, and tutorials on, general topics relevant to the application of statistics to medicine will also be published. The main criteria for publication are appropriateness of the statistical methods to a particular medical problem and clarity of exposition. Papers with primarily mathematical content will be excluded. The journal aims to enhance communication between statisticians, clinicians and medical researchers.