# Identification and estimation of treatment effects on long-term outcomes in clinical trials with external observational data

arXiv: https://arxiv.org/abs/2208.10163 · HTML: https://mlsanity.com/paper/2208.10163/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Aug 2022.

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

- [Policy Learning for Balancing Short-Term and Long-Term Rewards](https://mlsanity.com/paper/2405.03329/) (2024)
- [Estimating Long-term Heterogeneous Dose-response Curve: Generalization Bound Leveraging Optimal Transport Weights](https://mlsanity.com/paper/2406.19195/) (2024)
- [Long-Term Individual Causal Effect Estimation via Identifiable Latent Representation Learning](https://mlsanity.com/paper/2505.05192/) (2025)
- [Nonparametric Heterogeneous Long-term Causal Effect Estimation via Data Combination](https://mlsanity.com/paper/2502.18960/) (2025)
- [Long-term Causal Inference via Modeling Sequential Latent Confounding](https://mlsanity.com/paper/2502.18994/) (2025)
- [Pareto-Optimal Estimation and Policy Learning on Short-term and Long-term Treatment Effects](https://mlsanity.com/paper/2403.02624/) (2024)
- [Optimal Policy Adaptation under Covariate Shift](https://mlsanity.com/paper/2501.08067/) (2025)
- [Identification and Estimation of Long-Term Treatment Effects with Monotone Missing](https://mlsanity.com/paper/2504.19527/) (2025)

## Abstract (arXiv)

In biomedical studies, estimating drug effects on chronic diseases requires a long follow-up period, which is difficult to meet in randomized clinical trials (RCTs). The use of a short-term surrogate to replace the long-term outcome for assessing the drug effect relies on stringent assumptions that empirical studies often fail to satisfy. Motivated by a kidney disease study, we investigate the drug effects on long-term outcomes by combining an RCT without observation of long-term outcome and an observational study in which the long-term outcome is observed but unmeasured confounding may exist. Under a mean exchangeability assumption weaker than the previous literature, we identify the average treatment effects in the RCT and derive the associated efficient influence function and semiparametric efficiency bound. Furthermore, we propose a locally efficient doubly robust estimator and an inverse probability weighted (IPW) estimator. The former attains the semiparametric efficiency bound if all the working models are correctly specified. The latter has a simpler form and requires much fewer model specifications. The IPW estimator using estimated propensity scores is more efficient than that using true propensity scores and achieves the semiparametric efficient bound in the case of discrete covariates and surrogates with finite support. Both estimators are shown to be consistent and asymptotically normally distributed. Extensive simulations are conducted to evaluate the finite-sample performance of the proposed estimators. We apply the proposed methods to estimate the efficacy of oral hydroxychloroquine on renal failure in a real-world data analysis.