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.

翻译：在纵向观察性研究中，边际结构模型（MSMs）是一类用于分析暴露对（时间至事件）结局影响的因果模型，同时考虑受暴露影响的时间依赖性混杂。在应用文献中，逆概率处理加权（IPTW）已被广泛用于估计MSMs。基于IPTW的MSMs的一个基本假设是正向性假设，该假设确保对于个体中任何已测量混杂因子的组合，接受每种可能处理策略的概率均非零。正向性对于通过基于IPTW的MSMs进行有效因果推断至关重要，但与混杂偏倚相比常被忽视。正向性违背也可能因随机性而产生，即理论上可能分配到特定处理但在数据中缺失或极少观察到的情况，导致近似违背。这些情况在实际应用中很常见，尤其是在样本量较小时，对因果推断构成重大挑战。本研究探讨了生存分析中近似正向性违背对基于IPTW的MSMs估计值的影响。提出了两种从风险MSMs模拟纵向数据的算法，可容纳近似正向性违背、时变二元暴露以及时间至事件结局。分析了近似正向性违背的情况（即在某些混杂因子水平下保持未暴露状态较为罕见），涵盖了多种场景和权重截断（WT）策略。本研究旨在作为一个重要警示，提醒在使用纵向观察性数据和IPTW的因果研究中，不应忽视正向性假设或轻率地应用WT。