# Inference for treatment-specific survival curves using machine learning

arXiv: https://arxiv.org/abs/2106.06602 · HTML: https://mlsanity.com/paper/2106.06602/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jun 2021.

## Built on by (most cited first, 8 of 8)

- [Orthogonal Survival Learners for Estimating Heterogeneous Treatment Effects from Time-to-Event Data](https://mlsanity.com/paper/2505.13072/) (2025)
- [Assessing the robustness of heterogeneous treatment effects in survival analysis under informative censoring](https://mlsanity.com/paper/2510.13397/) (2025)
- [Efficient estimation of weighted cumulative treatment effects by double/debiased machine learning](https://mlsanity.com/paper/2305.02373/) (2023)
- [Causal inference for the expected number of recurrent events in the presence of a terminal event](https://mlsanity.com/paper/2306.16571/) (2023)
- [A Stable and Efficient Covariate-Balancing Estimator for Causal Survival Effects](https://mlsanity.com/paper/2310.02278/) (2023)
- [Efficient and Debiased Learning of Average Hazard Under Non-Proportional Hazards](https://mlsanity.com/paper/2602.13475/) (2026)
- [Nonparametric Regression Discontinuity Designs with Survival Outcomes](https://mlsanity.com/paper/2604.03502/) (2026)
- [Adaptive Experimentation for Censored Survival Outcomes](https://mlsanity.com/paper/2605.18459/) (2026)

## Abstract (arXiv)

In the absence of data from a randomized trial, researchers often aim to use observational data to draw causal inference about the effect of a treatment on a time-to-event outcome. In this context, interest often focuses on the treatment-specific survival curves; that is, the survival curves were the entire population under study to be assigned to receive the treatment or not. Under certain causal conditions, including that all confounders of the treatment-outcome relationship are observed, the treatment-specific survival can be identified with a covariate-adjusted survival function. Several estimators of this function have been proposed, including estimators based on outcome regression, inverse probability weighting, and doubly robust estimators. In this article, we propose a new cross-fitted doubly-robust estimator that incorporates data-adaptive (e.g. machine learning) estimators of the conditional survival functions. We establish conditions on the nuisance estimators under which our estimator is consistent and asymptotically linear, both pointwise and uniformly in time. We also propose a novel ensemble learner for combining multiple candidate estimators of the conditional survival estimators. Notably, our methods and results accommodate events occurring in discrete or continuous time (or both). We investigate the practical performance of our methods using numerical studies and an application to the effect of a surgical treatment to prevent metastases of parotid carcinoma on mortality.