Why your limb salvage rate is probably wrong
You are studying limb salvage after revascularization for CLTI. At 2 years, 30 patients had major amputations, 45 patients died (with limbs intact), and 125 are alive and limb-intact. Standard Kaplan-Meier censors the 45 deaths and estimates 2-year limb salvage at 81%.
But those 45 patients who died can never have an amputation. They did not "survive" the amputation risk -- they exited it permanently via a different route. KM treats them as if they might still have an amputation tomorrow. That is biologically wrong.
A competing risk is an event that prevents the outcome of interest from ever occurring. Death is the most common competing risk in surgical outcomes research. Ignoring it inflates your event-free estimates.
Patients start in one state and can transition to one of multiple mutually exclusive outcomes.
Standard KM assumes censored patients have the same future risk as those still being followed. When you censor deaths, you are saying: "These patients might still have an amputation." But they cannot -- they are dead. This assumption inflates the estimated probability of amputation (or equivalently, deflates limb salvage).
The overestimation gets worse as the competing event rate increases. In CLTI populations with high mortality, the bias can be substantial.
Answers: What is the actual probability of the event occurring, accounting for the fact that some patients will die first?
Also called the Aalen-Johansen estimator. Replaces the KM estimate when competing risks exist. The CIF for all competing events must sum to less than or equal to 1 at every time point. This is the correct way to report limb salvage, graft patency, or any endpoint where death is a competing risk.
Answers: Are the cumulative incidence functions different between groups?
The competing risks analogue of the log-rank test. Compares CIFs between groups while properly accounting for competing events. Replaces the log-rank test when competing risks are present.
The choice of model depends on the question you are asking.
Question: What is the actual probability of the event over time, in a world where competing events also happen?
Best for prognosis and clinical prediction. Tells patients: "Given your risk factors, what is the probability you will actually experience this event?" Keeps patients who had a competing event in the risk set (as if they could still have the primary event). Produces subdistribution hazard ratios (sHR). Use this for clinical counseling and prognostic modeling.
Question: Among patients who have not yet had ANY event, what is the rate of the primary event?
Best for understanding etiology and biology. Tells researchers: "What factors affect the rate of this specific event?" Censors patients at competing events (standard Cox). Produces cause-specific hazard ratios (csHR). Use this for understanding causal mechanisms and treatment effects on specific pathways.
| Feature | Fine-Gray (sHR) | Cause-Specific (csHR) |
|---|---|---|
| Best for | Prognosis, prediction | Etiology, biology |
| Competing event patients | Kept in risk set | Censored |
| Interpretation | Effect on actual probability | Effect on event-specific rate |
| Clinical counseling | Yes | No (misleading for prognosis) |
| Treatment effect assessment | Indirect | Direct (mechanism of action) |
Many papers report only cause-specific Cox models for endpoints like limb salvage. This is methodologically incomplete when mortality is high. Both cause-specific and Fine-Gray models should ideally be reported, as they answer complementary questions.
Situations in vascular surgery where ignoring competing risks is particularly dangerous.
CLTI and limb salvage
CLTI patients have 2-year mortality rates of 30-50%. Standard KM censors these deaths and overestimates limb salvage. The sicker the population, the larger the bias. SVS reporting standards now recommend competing risks analysis for limb salvage endpoints.
AAA repair and long-term survival
When comparing open vs EVAR for freedom from reintervention, patients who die are censored in KM. If EVAR patients have higher late mortality (from endoleak complications or other causes), they are differentially removed from the reintervention analysis. This can make EVAR's reintervention rate look better than it actually is.
Elderly patients and any surgical endpoint
In patients over 80, all-cause mortality is a competing risk for virtually every surgical outcome. A study of graft patency in octogenarians that censors death is reporting fantasy numbers. The probability of actually experiencing graft failure (vs dying first) is what matters clinically.
"But the competing risk rate is low in our cohort."
If competing events are rare, KM and CIF estimates will be similar. This is a valid argument. In a young, healthy cohort where mortality is less than 5%, the bias from ignoring competing risks is negligible. The problem is that most vascular surgery cohorts are neither young nor healthy. Always check the competing event rate before deciding.
Rule of thumb: if the competing event rate exceeds 10%, KM estimates for the primary endpoint are noticeably biased. If it exceeds 20%, the bias is usually clinically meaningful.
Decide when and how competing risks apply.
Module 4 - Lesson 5 complete
You have completed Module 4: Survival Analysis for Surgeons. You can now read, critique, and interpret the survival analyses that fill every vascular surgery journal.