Table 1.

Comparison of the Total and Controlled Direct Effect of Smoking Cessation on Dementia Diagnosis When Death (a Competing Event for Dementia) Is Present

Feature	Total Effect	Controlled Direct Effect
Estimands for the risk differencea
Exchangeability assumption needed for death (competing events)?b	Not needed	Needed. Requires that at each follow-up time, conditional on the measured past, death is independent of future counterfactual outcomes had everyone followed and death was eliminated.
Positivity assumption needed for death (competing events)?b	Not needed	Needed. Requires that for any possibly observed level of exposure and covariate history among those remaining uncensored (alive) and free of dementia diagnosis through k, some individuals continue to remain alive through k + 1.
Consistency assumption needed for death (competing events)?b	Not needed	Needed. Requires that an intervention that “eliminates death (competing events)” is well-defined.
Interpretation	The effect captures all pathways by which exposure affects dementia, which may include both direct and indirect exposure effects outside and through the exposure’s effect on mortality	Direct effect on dementia not via death, referring to scenario where death has (somehow) been eliminated.

^a denotes counterfactual dementia diagnosis status by k + 1 under exposure level . denotes counterfactual dementia diagnosis status by k + 1 under exposure level and (somehow) eliminating the competing event such that .

^b See Web Appendix 2 for fuller discussion.