In longitudinal observational studies, marginal structural models (MSMs) are a class of causal models used to analyse the 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 the positivity assumption, which ensures that, for any combination of measured confounders among individuals, there is a non-zero probability of receiving each possible treatment strategy. Positivity is crucial for valid causal inference through IPTW-based MSMs, but is often overlooked compared to confounding bias. Positivity violations may also arise due to randomness, in situations where the assignment to a specific treatment is theoretically possible but is either absent or rarely observed in the data, leading to near violations. These situations 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 analysed across various scenarios and weight truncation (WT) strategies. 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.

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