مقایسهٔ روش‌ها

	مدل فراژتی مشترک برای داده‌های بقای خوشه‌ای	مدل توأم برای داده‌های طولی و زمان تا رویداد	تخمینگر بقای کاپلان-مایر
حوزه	تحلیل بقا	تحلیل بقا	تحلیل بقا
خانواده	Survival analysis	Survival analysis	Survival analysis
سال پیدایش	1979	2004	1958
پدیدآور	Vaupel, J.W., Manton, K.G. & Stallard, E.	Tsiatis, A.A. & Davidian, M.; Rizopoulos, D.	Kaplan, E. L. & Meier, P.
نوع	Random effects survival model	Semiparametric regression model	Non-parametric survival estimator
منبع بنیادین	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.	Rizopoulos, D. (2012). Joint Models for Longitudinal and Time-to-Event Data. CRC Press.	Kaplan, E. L. & Meier, P. (1958). Nonparametric Estimation from Incomplete Observations. Journal of the American Statistical Association, 53(282), 457–481.
نام‌های دیگر	shared frailty model, random effects survival model, Frailty Modeli (Paylaşılan Kırılganlık)	joint model, shared random effects model, longitudinal-survival joint model, Joint Model (Boylamsal + Sağkalım Birleşik Model)	product-limit estimator, km curve, kaplan-meier sağkalım analizi
مرتبط	3	5	2
خلاصه	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 joint model for longitudinal and time-to-event data, formalised by Tsiatis and Davidian in 2004 and extended comprehensively by Rizopoulos in 2012, simultaneously estimates a mixed-effects model for repeatedly measured biomarkers and a survival model for the time to an event, linking the two processes through shared random effects. It resolves two major problems that simpler approaches cannot handle: informative dropout from longitudinal studies and the endogeneity of time-varying biomarkers used as covariates in a Cox model.	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.