Causal Inference
Causal survival analysis in the presence of unmeasured confounding for a competing event Emma McGee* Emma McGee Mathieu Chalouni Daniela K. Van Santen Sara Lodi Miguel A. Hernán
Prior work characterizing causal effects in the presence of competing events has relied on the assumption of no unmeasured confounding for the competing event. This assumption is often violated in real-world analyses (e.g., if treatment is prioritized based on unmeasured factors to individuals more or less likely to experience a competing event, like death). We examined the magnitude of bias for different estimands in the presence of unmeasured confounding for a competing event via a simulation study.
We simulated 500,000 individuals under a null effect of a binary baseline treatment. We estimated the total effect, controlled direct effect, and separable direct effect for a time-to-event outcome and, for comparison, the total effect for a competing event. We varied the strength of unmeasured confounding for the competing event, risk of the competing event, and strength of an unmeasured common cause of the competing event and outcome. Bias was defined as the difference between the estimated 4-year risk difference and risk ratio vs. the null.
All estimands were biased. Bias increased as the strength of unmeasured confounding for the competing event, risk of the competing event, and strength of the unmeasured common cause of the competing event and outcome increased. For example, when bias for the competing event was -8.4 percentage points [-0.35 on the risk ratio scale], bias for the total, controlled direct, and separable direct effects was 0.6 [0.04], 0.4 [0.03], and 0.2 [0.01], respectively. When bias for the competing event was -15.2 [-0.63], bias for the total, controlled direct, and separable direct effects was 2.4 [0.20], 2.1 [0.18], and 1.6 [0.18].
Unmeasured confounding for a competing event leads to biased estimates for the outcome of interest. The magnitude of bias may be modest unless bias for the competing event is strong. Researchers should consider the potential strength of unmeasured confounding for a competing event and conduct sensitivity analyses.
