In longitudinal observational studies, marginal structural models (MSMs) are a class of causal models used to analyze the effect of an exposure on the (survival) 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 each individual in the population has a non-zero probability of receiving each exposure level within confounder strata. Positivity, along with consistency, conditional exchangeability, and correct specification of the weighting model, is crucial for valid causal inference through IPTW-based MSMs but is often overlooked compared to confounding bias. Positivity violations can arise from subjects having a zero probability of being exposed/unexposed (strict violations) or near-zero probabilities due to sampling variability (near violations). This article discusses the effect of violations in the positivity assumption on the estimates from IPTW-based MSMs. Building on the algorithms for simulating longitudinal survival data from MSMs by Havercroft and Didelez (2012) and Keogh et al. (2021), systematic simulations under strict/near positivity violations are performed. Various scenarios are explored by varying (i) the size of the confounder interval in which positivity violations arise, (ii) the sample size, (iii) the weight truncation strategy, and (iv) the subject's propensity to follow the protocol violation rule. This study underscores the importance of assessing positivity violations in IPTW-based MSMs to ensure robust and reliable causal inference in survival analyses.

翻译：在纵向观察性研究中，边际结构模型是一类因果模型，用于分析暴露对感兴趣（生存）结局的影响，同时考虑受暴露影响的时间依赖性混杂因素。在应用文献中，逆概率治疗加权被广泛用于估计边际结构模型。基于IPTW的边际结构模型的一个基本假设是正值性假设，该假设确保人群中每个个体在混杂层内接受各暴露水平的概率均不为零。正值性假设与一致性、条件可交换性及权重模型的正确设定，共同构成了通过IPTW-MSM进行有效因果推断的关键要素，然而相较于混杂偏倚，该假设常被忽视。正值性违反可源于个体暴露/未暴露概率为零（严格违反），或因抽样变异性导致概率趋近于零（近似违反）。本文讨论了正值性假设违反现象对基于IPTW的边际结构模型估计结果的影响。基于Havercroft与Didelez（2012）及Keogh等（2021）提出的边际结构模型纵向生存数据模拟算法，我们系统开展了严格/近似正值性违反条件下的模拟研究。通过改变（i）正值性违反产生的混杂区间范围、（ii）样本量、（iii）权重截断策略，以及（iv）个体遵循方案违反规则的倾向性，探索了多种场景。本研究强调了在基于IPTW的边际结构模型中评估正值性违反的重要性，以确保生存分析中因果推断的稳健性与可靠性。