Linganisha mbinu

	Rega ya Hatari za Uwiano wa Cox	Kielelezo cha Frailty Kilichoshirikiwa kwa Data za Kuishi zilizopangwa	Kikokotozi cha Kuishi cha Kaplan-Meier
Nyanja	Uchanganuzi wa Uhai	Uchanganuzi wa Uhai	Uchanganuzi wa Uhai
Familia	Survival analysis	Survival analysis	Survival analysis
Mwaka wa asili	1972	1979	1958
Mwanzilishi	Cox, D. R.	Vaupel, J.W., Manton, K.G. & Stallard, E.	Kaplan, E. L. & Meier, P.
Aina	Semi-parametric hazard regression model	Random effects survival model	Non-parametric survival estimator
Chanzo asilia	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.	Kaplan, E. L. & Meier, P. (1958). Nonparametric Estimation from Incomplete Observations. Journal of the American Statistical Association, 53(282), 457–481.
Majina mbadala	cox ph model, proportional hazards model, cox ph regression, Cox Orantılı Tehlikeler Regresyonu	shared frailty model, random effects survival model, Frailty Modeli (Paylaşılan Kırılganlık)	product-limit estimator, km curve, kaplan-meier sağkalım analizi
Zinazohusiana	3	3	2
Muhtasari	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.	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.