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Causal Survival Forests with Negative Controls

This paper introduces Negative Control Causal Survival Forests (NC-CSF), a novel nonparametric method that integrates negative controls from proximal causal inference with causal survival forests to accurately estimate heterogeneous treatment effects in observational survival studies despite the presence of unmeasured confounding and censored outcomes.

Original authors: Zijun Gao, Kyounggeui Hong, Leyi Ma, Qianli Wu, Zachary Izzo, Ruishan Liu

Published 2026-08-21

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CC BY 4.0

Original authors: Zijun Gao, Kyounggeui Hong, Leyi Ma, Qianli Wu, Zachary Izzo, Ruishan Liu

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the world of medical research, scientists often look to the past to understand the future. They examine records of patients who received different treatments to see which ones helped them live longer or recover faster. This is a powerful way to learn, but it comes with a hidden trap. In a real-world hospital, doctors do not assign treatments randomly like flipping a coin. Instead, they choose based on what they see: a patient's age, their blood pressure, or the severity of their illness. Sometimes, they also rely on information they cannot see, such as a patient's genetic makeup or their lifestyle habits before they ever walked into the clinic. These invisible factors can skew the results, making a treatment look better or worse than it truly is. When researchers try to figure out how a treatment works for specific groups of people, these hidden influences can lead them to the wrong conclusions, potentially harming future patients.

To solve this, a team of researchers has developed a new method that acts like a detective for these invisible factors. They call their approach Negative Control Causal Survival Forests. The core idea relies on using "negative controls," which are pieces of data that act as clues. Imagine a doctor looking at a patient's medical history. They might find a measurement taken before the treatment started that is linked to the patient's underlying health but was not changed by the treatment itself. By studying how this pre-existing measurement relates to the outcome, the new method can mathematically untangle the hidden influences. This allows the researchers to isolate the true effect of the treatment, even when they cannot directly measure the factors that caused the doctor to choose that treatment in the first place.

The researchers tested this method by simulating thousands of different medical scenarios, ranging from simple cases to complex situations where the hidden influences were very strong and the data was incomplete because some patients dropped out of the study before their outcomes were known. In these computer experiments, the new method consistently outperformed existing tools. It reduced the error in estimating treatment effects by a significant margin, often cutting the mistake rate by nearly half compared to standard approaches. The method proved especially effective when the data was messy or when the hidden factors were difficult to detect, showing that it could find the true signal even in noisy environments.

The team then took their method to real-world medical records to see how it would perform outside the safety of a simulation. They analyzed data from a major HIV clinical trial involving over a thousand patients. In this study, they looked at how a specific drug combination affected survival time across different ages. Previous methods suggested that the drug combination was beneficial for everyone, regardless of age. However, the new method revealed a more nuanced picture. It suggested that for younger patients, the combination offered little to no benefit, and might even be slightly less effective than the standard treatment. For older patients, the benefit was clear and positive. This finding aligns better with existing medical recommendations that suggest tailoring treatment based on age, whereas the older methods had missed this critical difference entirely.

In another test using data from a large study of critically ill adults, the researchers examined the effect of a specific diagnostic procedure on survival. The new method confirmed what other studies had suggested: the procedure was associated with lower survival rates. The results were consistent with findings from other advanced statistical techniques, giving the researchers confidence that their approach was working correctly. They also applied the method to a database of hospital records to study how a specific drug interaction affected kidney health. The method detected a clear harmful effect when the drug was combined with another medication, a result that other standard tools had failed to identify with the same clarity.

The researchers did not stop at just finding the answers; they also built a complete software package that allows other scientists to use this method without needing to be experts in advanced mathematics. They carefully designed the software to handle the practical difficulties of real data, such as missing information or extreme values, ensuring that the results remain stable and reliable. By making the tool accessible, they hope to enable other researchers to apply this rigorous approach to their own studies, leading to more accurate medical insights.

The work suggests that by using these clever statistical clues, we can see through the fog of unmeasured factors that often cloud medical research. It does not claim to be a magic wand that solves every problem, but it offers a robust way to handle the messy reality of observational data. The findings indicate that when we account for these hidden influences, our understanding of who benefits from a treatment and who does not becomes much sharper. This clarity is essential for making better decisions about patient care, ensuring that treatments are given to those who will truly benefit from them.

Technical Summary: Causal Survival Forests with Negative Controls

Problem Formulation
This paper addresses the estimation of heterogeneous treatment effects (HTE) in observational survival studies characterized by two simultaneous challenges: right-censored outcomes and unmeasured confounding. While existing machine learning methods, such as Causal Survival Forests (CSF), offer flexible nonparametric estimation of HTE, they typically rely on the ignorability assumption (no unmeasured confounding). In many biomedical contexts, this assumption is unrealistic; unobserved confounders can induce significant bias in treatment-effect estimates. Furthermore, standard proximal causal inference frameworks, which utilize negative controls to address unmeasured confounding, have primarily been developed for average treatment effects (ATE) under parametric assumptions or for uncensored data. There is a lack of flexible, nonparametric methods capable of estimating HTE in the presence of both censoring and unobserved confounding.

Methodology: Negative Control Causal Survival Forests (NC-CSF)
The authors propose Negative Control Causal Survival Forests (NC-CSF), a nonparametric learner that integrates proximal causal inference with causal survival forests. The method relies on the availability of a negative-control outcome ( $W$ ) and a negative-control treatment ( $Z$ ), which satisfy specific conditional independence assumptions relative to the latent confounder ( $U$ ), the primary treatment ( $A$ ), and the potential outcomes.

The core of the methodology involves constructing a loss function for random forests that incorporates "bridge functions" to adjust for unobserved confounding. The approach proceeds as follows:

Bridge Functions: The method assumes the existence of bridge functions $f_a(w, x)$ and $q(z, x)$ that satisfy specific conditional moment equations. These functions allow the representation of latent conditional outcome and treatment mechanisms using observable variables ( $W, Z, X$ ), effectively bypassing the unobserved $U$ .
Residualization: The authors define bridge-adjusted residuals for both the treatment and the outcome.
- The treatment residual is $A^{res}_i = A_i - \hat{q}(Z_i, X_i)$ .
- The outcome residual, $Y^{res}_i$ , is a censoring-corrected, bridge-adjusted pseudo-outcome. It combines the observed event time, censoring indicators, and bridge estimates to form a score that is orthogonal to nuisance function estimation errors.
Loss Function: The forest is trained to minimize the squared error between the outcome residual and the product of the treatment effect function $\tau(X)$ and the treatment residual:
$\ell_{NC-CSF} = \sum_{i=1}^n (Y^{res}_i - \tau(X_i) A^{res}_i)^2$
Nuisance Estimation and Orthogonality: The method employs Neyman orthogonalization, ensuring that the score function has a zero pathwise derivative with respect to the nuisance functions (propensity scores, bridge functions, censoring hazards, etc.) at the truth. This provides robustness against estimation errors in these nuisance components. The authors utilize cross-fitting to prevent overfitting during the nuisance estimation stage.
Target Estimand: The method targets a weighted heterogeneous treatment effect, $\tau^w(x)$ , which equals the standard conditional average treatment effect (CATE) when the latent confounder does not modify the treatment effect beyond the observed covariates, or when the weighting function is uncorrelated with the treatment effect.

Key Contributions

Methodological Innovation: The paper introduces a flexible, nonparametric framework for HTE estimation in censored survival data that explicitly adjusts for unmeasured confounding using negative controls. It extends the CSF loss function to incorporate bridge functions derived from proximal causal inference.
Theoretical Justification: The authors provide theoretical proofs demonstrating that the proposed loss function mitigates bias from unobserved confounding. They establish the Neyman orthogonality of the score, showing that the estimator is only second-order sensitive to nuisance estimation errors. Furthermore, they prove asymptotic normality and consistency for the cross-fitted estimator under standard boundedness and overlap conditions.
Empirical Performance: Through extensive simulations spanning 264 configurations (varying confounding strength, proxy relevance, censoring mechanisms, and dimensionality), NC-CSF demonstrates substantial reductions in bias and estimation error compared to existing baselines, including standard Causal Survival Forests (CSF), Random Survival Forests (RSF), and BART.
Practical Implementation: The authors provide a ready-to-use Python package that handles practical implementation details such as nuisance estimation, variable clipping, and cross-fitting to ensure stable finite-sample performance.

Results

Simulations: In censored settings, NC-CSF reduced the Root Mean Squared Error (RMSE) for Restricted Mean Survival Time (RMST) by 40.2% and for survival probability by 22.2% relative to a matched censored baseline (which lacks the negative control bridge). It also outperformed external learners like the grf R-CSF implementation. The method remained robust across varying levels of confounding and proxy quality, though performance degraded slightly when proxies were non-injective or coarsened.
Real Data Applications:
- ACTG175 (HIV Trial): Applied to a subset comparing ddI monotherapy vs. ZDV+ddI, NC-CSF revealed an age-dependent treatment effect: the benefit of ZDV+ddI was negative for younger individuals and positive for older individuals. This contrasts with standard R-CSF, which yielded uniformly positive estimates across all ages, aligning better with existing individualized treatment rule literature.
- SUPPORT (Right Heart Catheterization): The method estimated a negative average treatment effect for 30-day survival, consistent with previous literature suggesting harm from RHC in observational settings.
- MIMIC-IV (Pharmacologic Study): Analyzing the interaction between tacrolimus and CYP3A inhibitors, NC-CSF detected a significant increase in the risk of acute kidney injury (AKI) in the positive-control group, while finding no effect in the inert-control group, demonstrating the method's ability to detect specific interactions without generating false signals.

Significance and Claims
The paper claims that NC-CSF offers a practical solution for survival analysis where unobserved confounding is a concern, a scenario where standard causal inference methods often fail. By leveraging negative controls within a flexible machine learning framework, the method enables the discovery of interpretable patterns of treatment-effect heterogeneity that might otherwise be obscured by bias. The authors emphasize that while the method improves upon existing baselines significantly, the validity of the negative control assumptions remains application-specific and cannot be verified solely from observed data. They also note that the target estimand is a weighted average, which may differ from the conventional CATE if latent treatment-effect heterogeneity covaries with the bridge-adjusted treatment variation. The work is presented as a step toward more robust causal inference in complex observational survival studies, supported by open-source software to facilitate adoption.

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