# Impact of Near‐Positivity Violations on IPTW‐Estimated Marginal Structural Survival Models With Time‐Dependent Confounding

## TL;DR

This paper explores how near-positivity violations affect causal estimates in survival analysis using inverse probability weighting.

## Contribution

The study introduces simulation algorithms to investigate near-positivity violations in IPTW-based survival models.

## Key findings

- Near-positivity violations can destabilize IPTW estimators, increasing variance and bias.
- Aggressive weight truncation worsens estimator performance in survival analysis.
- The study highlights the importance of the positivity assumption in longitudinal causal inference.

## Abstract

In longitudinal observational studies, marginal structural models (MSMs) are used to analyze the causal effect of an exposure on the (time‐to‐event) outcome of interest, while accounting for exposure‐affected time‐dependent confounding. In the applied literature, inverse probability of treatment weighting (IPTW) has been widely adopted to estimate MSMs. An essential assumption for IPTW‐based MSMs is positivity, which requires that, for any combination of measured confounders among individuals, there is a nonzero probability of receiving each treatment strategy. Positivity is crucial for valid causal inference through IPTW‐based MSMs, but is often overlooked compared to confounding bias. Near‐positivity violations, where certain treatments are theoretically possible but rarely observed due to randomness, are common in practical applications, particularly when the sample size is small, and they pose significant challenges for causal inference. This study investigates the impact of near‐positivity violations on estimates from IPTW‐based MSMs in survival analysis. Two algorithms are proposed for simulating longitudinal data from hazard‐MSMs, accommodating near‐positivity violations, a time‐varying binary exposure, and a time‐to‐event outcome. Cases of near‐positivity violations, where remaining unexposed is rare within certain confounder levels, are analyzed across various scenarios and weight truncation (WT) strategies. Through comprehensive simulations, this study shows that even minor near‐positivity violations in longitudinal survival analyses can substantially destabilize IPTW‐based estimators, inflating variance and bias, especially under aggressive WT. This work aims to serve as a critical warning against overlooking the positivity assumption or naively applying WT in causal studies using longitudinal observational data and IPTW.