مقایسهٔ روش‌ها

	برآوردگر خطر تجمعی نلسون-آلن	مدل فراژتی مشترک برای داده‌های بقای خوشه‌ای	تخمینگر بقای کاپلان-مایر	آزمون لوک-رنک برای مقایسه منحنی‌های بقا
حوزه	تحلیل بقا	تحلیل بقا	تحلیل بقا	تحلیل بقا
خانواده	Survival analysis	Survival analysis	Survival analysis	Survival analysis
سال پیدایش	1972	1979	1958	1966
پدیدآور	Wayne Nelson & Odd Aalen	Vaupel, J.W., Manton, K.G. & Stallard, E.	Kaplan, E. L. & Meier, P.	Mantel, N.
نوع	Non-parametric cumulative hazard estimator	Random effects survival model	Non-parametric survival estimator	Non-parametric hypothesis test
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.	Kaplan, E. L. & Meier, P. (1958). Nonparametric Estimation from Incomplete Observations. Journal of the American Statistical Association, 53(282), 457–481.	Mantel, N. (1966). Evaluation of Survival Data and Two New Rank Order Statistics Arising in Its Consideration. Cancer Chemotherapy Reports, 50(3), 163–170.
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)	product-limit estimator, km curve, kaplan-meier sağkalım analizi	Mantel log-rank test, Mantel-Cox test, log-rank sağkalım testi, Log-Rank Testi
مرتبط	5	3	2	2
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.	The Kaplan-Meier estimator, introduced by Kaplan and Meier in 1958, is a non-parametric method that estimates the survival curve — the probability of remaining event-free over time — from right-censored time-to-event data. The log-rank test is the companion procedure used to compare survival curves between groups.	The log-rank test, developed by Nathan Mantel in 1966, is a non-parametric hypothesis test that compares the overall survival experience of two or more groups throughout the entire follow-up period. It is the standard companion to Kaplan-Meier curves and determines whether observed differences between curves are statistically meaningful.