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Updated: Jun 19, 2025
Establishing a Competing Risk Regression Nomogram Model for Survival Data
Published on: October 23, 2020
Invited commentary: influence of incomplete death information on cumulative risk estimates
1Department of Mathematics and Statistics, College of Arts and Sciences, Boston University, Boston, MA 02215,United States.
Insights
Censoring at death can bias estimates in observational studies, especially with high mortality. This study provides analytical bounds to assess bias and guide when mortality data is essential for accurate pharmacoepidemiology research.
Area of Science:
- Pharmacoepidemiology
- Biostatistics
- Observational Study Design
Background:
- Censoring at death is a common method in observational studies when mortality data is unavailable.
- This method can lead to biased estimates of event probabilities, particularly when mortality rates are high.
- Previous simulations by Barberio et al. demonstrated this increasing bias with higher mortality.
Purpose of the Study:
- To derive an analytical expression for the bias introduced by censoring at death.
- To provide upper bounds for this bias to inform the necessity of mortality data.
- To offer guidance on when obtaining mortality information is crucial for accurate pharmacoepidemiology.
Main Methods:
- Derivation of an analytical formula quantifying the bias from censoring at death.
- Development of two upper bounds for the bias.
- Presentation of an algorithm for constructing wider confidence intervals (CIs) when the probability of death is low.
Main Results:
- An analytical expression for bias due to censoring at death was derived.
- Two upper bounds for the bias were established, informing the value of mortality data.
- The results indicate that obtaining mortality information is essential when the bias is substantial.
Conclusions:
- The derived bounds help assess the impact of censoring at death on study estimates.
- Mortality information is critical in pharmacoepidemiology to avoid significant bias in observational studies.
- The findings support the practical importance of incorporating mortality data, as highlighted by Barberio et al.
Abstract:
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.
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