Abstract
Estimating treatment effects from time-to-event data in observational studies requires careful adjustment for both confounding and informative censoring. While inverse probability of treatment weighting (IPTW) and inverse probability of censoring weighting (IPCW) have been used to address these sources of bias separately, their combined application remains underexplored, especially in high-dimensional, real-world datasets. In this paper, we benchmark IPTW, IPCW, and their combination to estimate survival curves, restricted mean survival time (RMST), and hazard ratios (HR). Our simulation studies vary strengths of informative censoring and introduce non-proportional hazards, while our real-world study uses a large-scale electronic health record (EHR) dataset (~ 50,000 covariates and >40,000 patients). Our simulations showed that IPCW reduces survival curve estimation error in the presence of informative censoring, but only reduces HR and RMST bias when the strength of informative censoring additionally differs by treatment group. In our real-world study, IPTW alone was typically sufficient for HR estimation, suggesting that when confounding is the primary source of bias and well-addressed through large-scale adjustment, censoring adjustment may yield limited additional benefit. Ultimately, the utility of IPCW likely depends on the underlying data-generating process, the relative magnitude of censoring bias, and the estimand of interest.
Introduction: The Challenge of Informative Censoring
In survival analysis, researchers frequently rely on the assumption of "non-informative censoring." This assumes that the dropout process is independent of the underlying event of interest—essentially, that patients who leave the study are representative of those who remain. However, in real-world clinical data, this assumption is often violated. Patients may drop out due to worsening health (informative censoring) or because a specific treatment causes intolerable side effects (differential censoring).
While Inverse Probability of Treatment Weighting (IPTW) is a standard tool for addressing baseline confounding, the use of Inverse Probability of Censoring Weighting (IPCW) to mitigate censoring bias is less common, particularly in high-dimensional settings. This study investigates whether the added complexity of IPCW provides meaningful improvements in treatment effect estimates across various scenarios.
Defining the Censoring Landscape
To understand when IPCW is necessary, we must distinguish between different types of censoring mechanisms. These can be visualized using Directed Acyclic Graphs (DAGs), where $Z$ represents treatment, $T$ the time-to-event, $C$ the censoring event, and $X$ various covariates.
As shown in the figure above:
- Non-informative censoring (a): The censoring process is independent of treatment and outcome.
- Informative censoring (b): Covariates $X_{TC}$ influence both the time-to-event $T$ and the censoring $C$.
- Differential censoring (c): The treatment $Z$ directly influences the censoring process $C$.
- Differential Informative censoring (d): A combination where both treatment and shared covariates influence dropout.
Methodology
The authors compared four estimation strategies: Unadjusted, IPTW-only, IPCW-only, and a Combined (IPTW + IPCW) estimator. These methods were tested on three primary estimands: Kaplan-Meier survival curves, Restricted Mean Survival Time (RMST), and Cox Proportional Hazard Ratios (HR).
The evaluation used a two-pronged approach:
- Simulations: Controlled environments where the "ground truth" is known, allowing the authors to vary the strength and type of censoring bias.
- Real-World Evidence: A study using Electronic Health Records (EHR) from Columbia University Medical Center, involving 41,996 patients starting either ACE inhibitors or thiazide diuretics, with nearly 50,000 high-dimensional covariates.
Key Findings: When Does IPCW Matter?
Simulation Results
The simulations revealed a critical distinction: IPCW is essential for accurate survival curve estimation whenever censoring is informative. However, for relative effect measures like Hazard Ratios (HR) or RMST differences, IPCW only significantly reduced bias when censoring was differentially informative (Scenario d). If the censoring process is identical across treatment groups, the biases often cancel out when calculating relative risks.
Real-World Evidence
In the EHR study comparing medications for Acute Myocardial Infarction (AMI), the results were telling:
- The Unadjusted HR was 0.46, showing massive bias compared to the 0.84 benchmark from meta-analyses.
- IPTW-only brought the HR to 0.81, very close to the benchmark.
- The Combined (IPTW+IPCW) method yielded an HR of 0.92.
While the combined method moved the estimate, IPTW performed the vast majority of the "heavy lifting." This suggests that in high-dimensional EHR data, the variables predicting treatment (confounders) often overlap with those predicting dropout. Consequently, a robust IPTW model may implicitly adjust for much of the censoring bias.
The Cost of Complexity
Implementing IPCW is not without costs. IPCW weights are time-varying and require frequent refitting of models as the "risk set" changes over time. In the real-world study, the authors had to update weights every 60 days to maintain computational feasibility. This added complexity must be weighed against the potential for marginal gains in accuracy.
Conclusion
The utility of IPCW is highly dependent on the research goal and the underlying data structure. While vital for absolute survival curves, its benefit for relative treatment effects is most pronounced in cases of differential informative censoring. Given the computational burden, researchers should prioritize identifying whether dropout mechanisms differ significantly between treatment arms before committing to IPCW adjustment.