Censoring at death is the only feasible option if death is not recorded and individuals who died simply no longer contribute visits, such as in the setting of Barberio et al (Am J Epidemiol. 2024) before they acquired access to mortality information. Censoring at death is known to lead to biased estimates of the probability of the event of interest before time $t$. Barberio et al show through simulations that this bias increases with increasing mortality. However, when analyzing claims data it is often important to not exclude individuals with shorter life expectancies: an important strength of observational studies is that they allow estimating treatment effects in more varied populations than typically included in randomized clinical trials. We derive an analytic expression for the bias, and provide two upper bounds for the bias. The bounds inform the usefulness of obtaining mortality information. If the probability of death before the event is known to be small, wider confidence intervals can be created using the first bound on the bias; we provide an algorithm. If the bias is large, obtaining mortality information is important. Barberio et al show that obtaining mortality information can be essential in practice.
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