Research studies including randomized controlled trials often have a time-to-event outcome as the primary outcome of interest, although competing events can precede the event of interest and thus may prevent the primary outcome from occurring - for example mortality may prevent observing cancer recurrence or may preclude need for reoperation in patients who undergo surgical repair of heart valves. Researchers often use Kaplan-Meier survival curves or the Cox proportional hazards regression model to estimate survival in the presence of censoring. These models can provide biased estimates (usually upward) of the incidence of the primary outcome over time and therefore other models which address competing risks, such as the Fine-Gray subdistribution hazards model, may be more suitable for estimating the absolute incidence of the primary outcome as well as the relative effect of treatment on the cumulative incidence function (CIF). My question is whether the Nelson-Aalen estimator is a reasonable option for estimating the hazard function and the cumulative incidence of the outcome of interest in the scenario of competing risks and if so, why is this a preferred approach over the Kaplan-Meier estimator?
Google search for this title and I hope it helps you. It's in the attachment. Best wishes David Booth
I do not know whether one or the other estimator produces the least biased estimate.
However, If you have measured a variable, that you may reasonably assume (based on subject matter knowledge and supported by the data at hand) to cause both the competing risk and the event of interest you may minimize (or theoretically completely remove) the bias of the estimate by adjusting for this variable in your analysis. If you are not familiar with statistical methods for causal inference and directed acyclic graphs you may benefit from consulting a person who is.
This e-book is an excellent introduction to the topic:
https://www.hsph.harvard.edu/miguel-hernan/causal-inference-book/
I also can suggest to asses the possible span of the bias. This size may be estimated in a sensitivity analysis:
1. Make your estimates using a selected algorithm.
2. Recode all censored individuals to having an event at the time of censoring. Reperform the analysis from 1).
3. Recode all censored individuals to live to the end of the study with no events occurring. Reperform the analysis from 1).
4. Compare the estimates obtained in 1, 2, and 3. If the differences between your estimates are small, the bias due to lack of independent censoring may be minor.
Best regards
Esben
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