Illustrating implications of misaligned causal questions and statistics in settings with competing events and interest in treatment mechanisms
In the presence of competing events, many investigators are interested in a direct treatment effect on the event of interest that does not capture treatment effects on competing events. Classical survival analysis methods that treat competing events like censoring events, at best, target a controlled direct effect: the effect of the treatment under a difficult to imagine and typically clinically irrelevant scenario where competing events are somehow eliminated. A separable direct effect, quantifying the effect of a future modified version of the treatment, is an alternative direct effect notion that may better align with an investigator's underlying causal question. In this paper, we provide insights into the implications of naively applying an estimator constructed for a controlled direct effect (i.e., "censoring by competing events") when the actual causal effect of interest is a separable direct effect. We illustrate the degree to which controlled and separable direct effects may take different values, possibly even different signs, and the degree to which these two different effects may be differentially impacted by violation and/or near violation of their respective identifying conditions under a range of data generating scenarios. Finally, we provide an empirical comparison of inverse probability of censoring weighting to an alternative weighted estimator specifically structured for a separable effect using data from a randomized trial of estrogen therapy and prostate cancer mortality.