# Sequential Double Robustness in Right-Censored Longitudinal Models

arXiv: https://arxiv.org/abs/1705.02459 · HTML: https://mlsanity.com/paper/1705.02459/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 May 2017.

## Built on by (most cited first, 10 of 10)

- [DoubleGen: Debiased Generative Modeling of Counterfactuals](https://mlsanity.com/paper/2509.16842/) (2025)
- [Sequential Kernel Embedding for Mediated and Time-Varying Dose Response Curves](https://mlsanity.com/paper/2111.03950/) (2021)
- [Causal inference through multi-stage learning and doubly robust deep neural networks](https://mlsanity.com/paper/2407.08560/) (2024)
- [General targeted machine learning for modern causal mediation analysis](https://mlsanity.com/paper/2408.14620/) (2024)
- [Causal machine learning for heterogeneous treatment effects in the presence of missing outcome data](https://mlsanity.com/paper/2412.19711/) (2024)
- [Efficient estimation of weighted cumulative treatment effects by double/debiased machine learning](https://mlsanity.com/paper/2305.02373/) (2023)
- [Non-parametric efficient estimation of marginal structural models with multi-valued time-varying treatments](https://mlsanity.com/paper/2409.18782/) (2024)
- [Deep Doubly Debiased Longitudinal Effect Estimation with ICE G-Computation](https://mlsanity.com/paper/2602.12379/) (2026)
- [Targeted learning of heterogeneous treatment effect curves for right censored or left truncated time-to-event data](https://mlsanity.com/paper/2603.26502/) (2026)
- [Orthogonal machine learning for conditional odds and risk ratios](https://mlsanity.com/paper/2604.10412/) (2026)

## Abstract (arXiv)

Consider estimating the G-formula for the counterfactual mean outcome under a given treatment regime in a longitudinal study. Bang and Robins provided an estimator for this quantity that relies on a sequential regression formulation of this parameter. This approach is doubly robust in that it is consistent if either the outcome regressions or the treatment mechanisms are consistently estimated. We define a stronger notion of double robustness, termed sequential double robustness, for estimators of the longitudinal G-formula. The definition emerges naturally from a more general definition of sequential double robustness for the outcome regression estimators. An outcome regression estimator is sequentially doubly robust (SDR) if, at each subsequent time point, either the outcome regression or the treatment mechanism is consistently estimated. This form of robustness is exactly what one would anticipate is attainable by studying the remainder term of a first-order expansion of the G-formula parameter. We show that a particular implementation of an existing procedure is SDR. We also introduce a novel SDR estimator, whose development involves a novel translation of ideas used in targeted minimum loss-based estimation to the infinite-dimensional setting.