Causal Inference in Survival Analysis: Emerging Methods for Complex Data Challenges

In randomized trials and observational studies, it is often necessary to evaluate how an exposure affects a time-to-event outcome, which is only partially observed due to right censoring. For instance, in infectious disease studies, it is of interest to characterize the relationship between the time until diagnosis of pathogen infection and a preceding measurement of a biomarker quantifying an immune response against that pathogen. Such analyses are commonly conducted within the counterfactual outcomes framework, seeking inferences about the counterfactual probability of survival through a given time point, at any given biomarker/exposure level. To determine whether a causal effect is present, one can test whether this quantity differs by exposure level. When the exposure is continuous, hypothesis testing and estimation in a nonparametric model is challenging. Recent theoretical developments made important strides for tackling this problem by considering either continuous exposures with uncensored outcomes or binary exposures with time-to-event outcomes. However, the existing work does not accommodate the simultaneous presence of continuous exposures and time-to-event outcomes. To fill this gap, we develop a new method for assessing whether the counterfactual survival probabilities remain constant across the range of a continuous exposure. We apply our methods to data from a pair of HIV monoclonal antibody prevention efficacy trials, and to data from a COVID-19 vaccine trial. 

The hazard ratio from the Cox proportional hazards model is a ubiquitous summary of treatment effect. However, when hazards are non-proportional, the hazard ratio can lose a stable causal interpretation and become study-dependent because it effectively averages time-varying effects with weights determined by follow-up and censoring. We consider the average hazard (AH) as an alternative causal estimand: a population-level person-time event rate that remains well-defined and interpretable without assuming proportional hazards. Although AH can be estimated nonparametrically and regression-style adjustments have been proposed, existing approaches do not provide a general framework for flexible, high-dimensional nuisance estimation with valid $\sqrt{n}$ inference. We address this gap by developing a semiparametric, doubly robust framework for covariate-adjusted AH. We establish pathwise differentiability of AH in the nonparametric model, derive its efficient influence function, and construct cross-fitted, debiased estimators that leverage machine learning for nuisance estimation while retaining asymptotically normal, $\sqrt{n}$-consistent inference under mild product-rate conditions. Simulations demonstrate that the proposed estimator achieves small bias and near-nominal confidence-interval coverage across proportional and non-proportional hazards settings, including crossing-hazards regimes where Cox-based summaries can be unstable. We illustrate practical utility in comparative effectiveness research by comparing immunotherapy regimens for advanced melanoma using SEER-Medicare linked data. 

Existing conformal prediction methods for time-to-event outcomes leverage only baseline covariates, producing prediction intervals that are insufficiently informative to facilitate decision making. We propose History-Aware Prediction Sets (HAPS), a conformal framework that constructs prediction sets for individual event times using covariate histories observed up to a decision time, targeting coverage among individuals who have survived to this time. HAPS handles right censoring adjusted for time-varying confounders via inverse probability of censoring weighting. When the censoring weights are consistently estimated, it achieves PAAC (probably asymptotically approximately correct) coverage among survivors. We further propose two doubly robust extensions of HAPS to weaken reliance on consistent estimation of the censoring distribution. In simulations, HAPS and its extensions reduce median prediction interval length by up to 75\% relative to baseline comparators while maintaining close to nominal coverage. On two public benchmark data sets, HAPS reduces the median interval length by up to 60\% for predictions at year 5, compared to the baseline comparators. 

In many epidemiological study designs, time-to-event outcomes may be subject to current status sampling: rather than observing the outcome itself, the investigator observes each study participant at a single monitoring time, recording a binary indicator of whether the event has occurred by that time. Such study design results in an extreme form of interval censoring. Existing nonparametric methods for current status data typically require independence between the monitoring time and the event time, which may be unrealistic in practice. We propose an approach to estimating the survival curve of a time-to-event outcome under current status sampling using tools from semiparametric efficiency theory and shape-constrained estimation. This approach is closely related to existing methods for estimating a causal dose-response curve under an assumption of monotonicity. Our proposed method allows for monitoring processes that are informed by measured covariates and employs machine learning tools to flexibly estimate nuisance parameters. We devise a sensitivity analysis approach investigating the degree to which the resulting estimates change under deviations from conditionally uninformative monitoring. We use the proposed methods to estimate the duration of COVID-19 symptoms in a university population.  

The Antibody Mediated Prevention (AMP) trials opened a new scientific frontier by demonstrating that passively administered monoclonal broadly neutralizing antibodies (bnAbs) could prevent HIV-1 acquisition. Conducted across multiple geographic regions, including the United States, Brazil, Peru, Switzerland, and sub-Saharan Africa, the AMP trials revealed substantial regional heterogeneity in treatment efficacy. These differences, together with privacy and regulatory limits on central data pooling, call for methods that appropriately borrow strength across regions without sharing individual-level data. To estimate region- and treatment–specific survival curves under distributional heterogeneity, we develop a federated learning approach that reweights site-specific estimators via an L1-regularized loss that penalizes data sources not aligned with the target. We showcase our method for a general class of causal contrasts, including the risk difference (RD), survival ratio (SR), and restricted mean survival time (RMST) difference. We conduct extensive simulations and analyze the AMP trials for different target populations, demonstrating that our approach yields region-adaptive and privacy-preserving inference with improved precision.