When using the Cox model to analyze the effect of a time-varying treatment on a survival outcome, treatment is commonly included, using only the current level as a time-dependent covariate. Such a model does not necessarily assume that past treatment is not associated with the outcome (the Markov property), since it is possible to model the hazard conditional on only the current treatment value. However, modeling the hazard conditional on the full treatment history is required in order to interpret the results causally, and such a full model assumes the Markov property when only including current treatment. This is, for example, common in marginal structural Cox models. We demonstrate that relying on the Markov property is problematic, since it only holds in unrealistic settings or if the treatment has no causal effect. This is the case even if there are no confounders and the true causal effect of treatment really only depends on its current level. Further, we provide an example of a scenario where the Markov property is not fulfilled, but the Cox model that includes only current treatment as a covariate is correctly specified. Transforming the result to the survival scale does not give the true intervention-specific survival probabilities, showcasing that it is unclear how to make causal statements from such models.

翻译：在使用Cox模型分析时变处理对生存结局的影响时，通常仅将当前处理水平作为时依协变量纳入模型。此类模型未必假定既往处理与结局无关（马尔可夫性），因为仍可建立仅以当前处理值为条件的风险模型。然而，为对结果进行因果解释，必须建立以完整处理史为条件的风险模型，而仅纳入当前处理的完整模型实际隐含了马尔可夫性假设——这在边际结构Cox模型中尤为常见。本文论证了依赖马尔可夫性的问题：该性质仅在非现实场景或处理无因果效应时成立，即使不存在混杂因素且处理的真实因果效应确实仅取决于当前水平时亦然。此外，我们构建了一个马尔可夫性不满足、但仅含当前处理的Cox模型却正确设定的案例。将结果转换至生存尺度后无法得到真实的干预特异性生存概率，这表明此类模型难以进行因果推断。