Сравнение методов

	Оценка кумулятивной функции риска Нельсона-Аалена	Регрессия пропорциональных рисков Кокса	Модель общего случайного эффекта для кластеризованных данных выживаемости
Область	Анализ выживаемости	Анализ выживаемости	Анализ выживаемости
Семейство	Survival analysis	Survival analysis	Survival analysis
Год появления	1972	1972	1979
Автор метода	Wayne Nelson & Odd Aalen	Cox, D. R.	Vaupel, J.W., Manton, K.G. & Stallard, E.
Тип	Non-parametric cumulative hazard estimator	Semi-parametric hazard regression model	Random effects survival model
Основополагающий источник	Nelson, W. (1972). Theory and applications of hazard plotting for censored failure data. Technometrics, 14(4), 945–966.	Cox, D. R. (1972). Regression Models and Life-Tables. Journal of the Royal Statistical Society: Series B, 34(2), 187–202.	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.
Другие названия	Nelson-Aalen cumulative hazard, Aalen estimator, empirical cumulative hazard, Nelson-Aalen kümülatif hazard tahmincisi	cox ph model, proportional hazards model, cox ph regression, Cox Orantılı Tehlikeler Regresyonu	shared frailty model, random effects survival model, Frailty Modeli (Paylaşılan Kırılganlık)
Связанные	5	3	3
Сводка	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.	Cox proportional hazards regression, introduced by D. R. Cox in 1972, is a semi-parametric model that estimates how one or more covariates affect the hazard — the instantaneous rate of experiencing an event — while leaving the baseline hazard function unspecified. It is the standard multivariable method in survival analysis and produces hazard ratios that quantify the relative risk associated with each predictor.	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.