قارن الطرق

	نموذج البقاء متعدد الحالات	نموذج الهشاشة المشتركة للبيانات البقائية المجمعة
المجال	تحليل البقاء	تحليل البقاء
العائلة	Survival analysis	Survival analysis
سنة النشأة	1978	1979
صاحب الطريقة	Andersen, P.K. & Keiding, N. (foundational framework); popularised by Putter, Fiocco & Geskus (2007)	Vaupel, J.W., Manton, K.G. & Stallard, E.
النوع	Semi-parametric hazard model	Random effects survival model
المصدر التأسيسي	Putter, H., Fiocco, M. & Geskus, R.B. (2007). Tutorial in Biostatistics: Competing Risks and Multi-State Models. Statistics in Medicine, 26(11), 2389–2430.	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.
الأسماء البديلة	illness-death model, multi-state transition model, Çok Durumlu Model (Multi-State / Illness-Death)	shared frailty model, random effects survival model, Frailty Modeli (Paylaşılan Kırılganlık)
ذات صلة	4	3
الملخص	The multi-state model is a generalised survival framework, formalised in the work of Andersen and Keiding and brought to wide biostatistical practice by Putter, Fiocco and Geskus (2007), that models individuals moving through multiple distinct health states — for example, healthy, ill and dead — over time. A separate hazard function is estimated for each possible transition, and transition probabilities are recovered via the product-integral of the cumulative transition intensities.	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.