We consider continuous time to treatment initiation. This can commonly occur in preventive medicine, such as disease screening and vaccination; it can also occur with non-fatal health conditions such as HIV infection without the onset of AIDS. While traditional causal inference focused on `when to treat' and its effects, we consider the incremental causal effect when the intensity of time to treatment initiation is intervened upon. We derive the efficient influence function for this estimand and develop an estimation framework that accommodates flexible machine learning methods while achieving fast convergence rates. Valid confidence bands are obtained leveraging empirical process theory. We illustrate our approach via simulation, and apply it to cervical cancer screening data to study the incremental effect of time to subsequent HPV testing on cervical intraepithelial neoplasia detection.

翻译：我们考虑治疗起始的连续时间。这种情况常见于预防医学，如疾病筛查和疫苗接种；也可出现在非致命性健康状态中，例如未发展为艾滋病的HIV感染。传统因果推断聚焦于“何时治疗”及其效应，而本文则关注当治疗起始时间强度受到干预时的增量因果效应。我们推导了该估计量的高效影响函数，并构建了一个估计框架，该框架兼容灵活机器学习方法的同时实现快速收敛速度。利用经验过程理论，我们获得了有效的置信带。通过模拟研究展示了所提方法的有效性，并将其应用于宫颈癌筛查数据，以研究后续HPV检测时间对宫颈上皮内瘤变检测的增量效应。