Centre for Infectious Disease Epidemiology & Research, University of Cape Town, Cape Town, South Africa.
Institute of Public Health, Medical Decision Making and Health Technology Assessment, Department of Public Health, Health Services Research and Health Technology Assessment, UMIT - University for Health Sciences, Medical Informatics and Technology, Hall in Tirol, Austria.
Stat Med. 2019 Oct 30;38(24):4888-4911. doi: 10.1002/sim.8340. Epub 2019 Aug 22.
Longitudinal targeted maximum likelihood estimation (LTMLE) has very rarely been used to estimate dynamic treatment effects in the context of time-dependent confounding affected by prior treatment when faced with long follow-up times, multiple time-varying confounders, and complex associational relationships simultaneously. Reasons for this include the potential computational burden, technical challenges, restricted modeling options for long follow-up times, and limited practical guidance in the literature. However, LTMLE has desirable asymptotic properties, ie, it is doubly robust, and can yield valid inference when used in conjunction with machine learning. It also has the advantage of easy-to-calculate analytic standard errors in contrast to the g-formula, which requires bootstrapping. We use a topical and sophisticated question from HIV treatment research to show that LTMLE can be used successfully in complex realistic settings, and we compare results to competing estimators. Our example illustrates the following practical challenges common to many epidemiological studies: (1) long follow-up time (30 months); (2) gradually declining sample size; (3) limited support for some intervention rules of interest; (4) a high-dimensional set of potential adjustment variables, increasing both the need and the challenge of integrating appropriate machine learning methods; and (5) consideration of collider bias. Our analyses, as well as simulations, shed new light on the application of LTMLE in complex and realistic settings: We show that (1) LTMLE can yield stable and good estimates, even when confronted with small samples and limited modeling options; (2) machine learning utilized with a small set of simple learners (if more complex ones cannot be fitted) can outperform a single, complex model, which is tailored to incorporate prior clinical knowledge; and (3) performance can vary considerably depending on interventions and their support in the data, and therefore critical quality checks should accompany every LTMLE analysis. We provide guidance for the practical application of LTMLE.
纵向靶向极大似然估计（LTMLE）很少用于在存在长期随访、多个时变混杂因素和复杂关联关系的情况下，当受到先前治疗影响的时变混杂因素时，估计动态治疗效果。原因包括潜在的计算负担、技术挑战、对长期随访的受限建模选项以及文献中有限的实用指导。然而，LTMLE 具有理想的渐近性质，即它是双重稳健的，并且在与机器学习结合使用时可以产生有效的推断。它还具有易于计算分析标准误差的优点，与需要引导的 g 公式形成对比。我们使用来自 HIV 治疗研究的一个有针对性和复杂的问题来表明 LTMLE 可以在复杂的现实环境中成功使用，并将结果与竞争估计器进行比较。我们的示例说明了许多流行病学研究中常见的以下实际挑战：（1）随访时间长（30 个月）；（2）样本量逐渐减少；（3）对一些感兴趣的干预规则的支持有限；（4）潜在调整变量的高维集，这增加了整合适当机器学习方法的必要性和挑战；（5）考虑混杂偏倚。我们的分析以及模拟为 LTMLE 在复杂和现实环境中的应用提供了新的视角：我们表明（1）即使面对小样本和有限的建模选项，LTMLE 也可以产生稳定和良好的估计；（2）如果无法拟合更复杂的学习者，则可以利用一组简单的学习者进行机器学习，这可以优于针对纳入先前临床知识量身定制的单个复杂模型；（3）性能可能会根据干预措施及其在数据中的支持而有很大差异，因此每个 LTMLE 分析都应伴随关键的质量检查。我们为 LTMLE 的实际应用提供了指导。
