Vertaile menetelmiä

	Yhteismalli pitkittäisille tiedoille ja tapahtuma-aika-tiedolle	Kaplan-Meierin selviytymisestimaattori	Nelson-Aalen-estimaattori
Tieteenala	Elinaika-analyysi	Elinaika-analyysi	Elinaika-analyysi
Menetelmäperhe	Survival analysis	Survival analysis	Survival analysis
Syntyvuosi	2004	1958	1972
Kehittäjä	Tsiatis, A.A. & Davidian, M.; Rizopoulos, D.	Kaplan, E. L. & Meier, P.	Wayne Nelson & Odd Aalen
Tyyppi	Semiparametric regression model	Non-parametric survival estimator	Non-parametric cumulative hazard estimator
Alkuperäislähde	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.	Nelson, W. (1972). Theory and applications of hazard plotting for censored failure data. Technometrics, 14(4), 945–966.
Rinnakkaisnimet	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	Nelson-Aalen cumulative hazard, Aalen estimator, empirical cumulative hazard, Nelson-Aalen kümülatif hazard tahmincisi
Liittyvät	5	2	5
Tiivistelmä	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.	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.