مقایسهٔ روش‌ها

	برآوردگر خطر تجمعی نلسون-آلن	مدل فراژتی مشترک برای داده‌های بقای خوشه‌ای
حوزه	تحلیل بقا	تحلیل بقا
خانواده	Survival analysis	Survival analysis
سال پیدایش	1972	1979
پدیدآور	Wayne Nelson & Odd Aalen	Vaupel, J.W., Manton, K.G. & Stallard, E.
نوع	Non-parametric cumulative hazard estimator	Random effects survival model
منبع بنیادین	Nelson, W. (1972). Theory and applications of hazard plotting for censored failure data. Technometrics, 14(4), 945–966.	Vaupel, J.W., Manton, K.G. & Stallard, E. (1979). The Impact of Heterogeneity in Individual Frailty on the Dynamics of Mortality. Demography, 16(3), 439–454.
نام‌های دیگر	Nelson-Aalen cumulative hazard, Aalen estimator, empirical cumulative hazard, Nelson-Aalen kümülatif hazard tahmincisi	shared frailty model, random effects survival model, Frailty Modeli (Paylaşılan Kırılganlık)
مرتبط	5	3
خلاصه	The Nelson-Aalen estimator is a non-parametric estimator of the cumulative hazard function from right-censored time-to-event data. Developed by Wayne Nelson for reliability hazard plotting in 1972 and placed on a rigorous counting-process foundation by Odd Aalen in 1978, it accumulates the ratio of observed events to the number at risk at each event time, providing the natural hazard-scale companion to the Kaplan-Meier survival curve.	The shared frailty model, introduced by Vaupel, Manton, and Stallard in 1979, extends standard survival regression by incorporating a random effect — the 'frailty' — that captures unobserved heterogeneity among subjects or clusters. When survival outcomes are measured on individuals who share a common environment (patients in the same hospital, members of the same family, animals in the same litter), a frailty term accounts for the within-cluster dependence that ordinary Cox regression ignores.