Bandingkan kaedah

	Penganggar Kumulatif Bahaya Nelson-Aalen	Regresi Bahaya Proporsional Cox	Model Frailiti Kongsi untuk Data Survival Terkelompok
Bidang	Analisis Survival	Analisis Survival	Analisis Survival
Keluarga	Survival analysis	Survival analysis	Survival analysis
Tahun asal	1972	1972	1979
Pengasas	Wayne Nelson & Odd Aalen	Cox, D. R.	Vaupel, J.W., Manton, K.G. & Stallard, E.
Jenis	Non-parametric cumulative hazard estimator	Semi-parametric hazard regression model	Random effects survival model
Sumber perintis	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.
Alias	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)
Berkaitan	5	3	3
Ringkasan	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.