Invited commentary: influence of incomplete death information on cumulative risk estimates

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;193(9):1281-1290) 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 showed 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 estimation of treatment effects in more varied populations than are typically included in randomized clinical trials. In this commentary, I derive an analytical expression for the bias and provide 2 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 CIs can be created using the first bound on the bias; an algorithm is provided. If the bias is large, obtaining mortality information is important. Barberio et al show that obtaining mortality information can be essential in practice. This article is part of a Special Collection on Pharmacoepidemiology.