Nelson-Aalen Cumulative Hazard

The Nelson-Aalen estimator is a nonparametric estimate of the cumulative hazard function, summing the number of events divided by the number at risk at each observed event time.

넬슨-알렌 추정량은 각 사건 시점의 사건 수를 위험집단 크기로 나눈 값을 더해 누적위험함수를 분포 가정 없이 추정하는 방법입니다.

How does the accumulated risk of the event build up over follow-up time in my censored data?

중도절단이 있는 자료에서 시간이 지나며 사건 위험이 어떻게 누적되는지 보고 싶어요.

The Nelson-Aalen estimator adds up, at each event time, the proportion of subjects at risk who experience the event, giving the cumulative hazard H(t). Its slope shows when risk is high, and exp(-H(t)) gives a survival estimate that closely tracks the Kaplan-Meier curve.

When to use Nelson-Aalen Cumulative Hazard

• You want to see how the hazard accumulates over time without assuming a distribution
• You need to check visually whether the hazard is constant, increasing or decreasing
• You want to check the fit of a parametric survival model against a nonparametric curve

When to use something else

• You need covariate-adjusted effects; use a Cox proportional hazards model
• Several event types compete; use a cumulative incidence (Aalen-Johansen) analysis

Assumptions and requirements

• Censoring is independent of the event process
• Event times are measured on a common time origin
• Subjects are independent

What the analysis reports

• Cumulative hazard at each event time
• Standard error and log-transformed confidence interval
• Number at risk and number of events
• Breslow survival estimate exp(-H)

How to report it

The Nelson-Aalen cumulative hazard at t = [value] was [value] (95% CI [[value], [value]]), based on [value] events among [value] subjects.

Related methods

• Kaplan-Meier Survival Analysis
• Life Table (Actuarial) Analysis
• Cox Proportional Hazards Model

Run Nelson-Aalen Cumulative Hazard on Quorant