Linganisha mbinu

	Cox Proportional Hazards kwa Mechi	Uchanganuzi wa Kaplan-Meier
Nyanja	Epidemiolojia	Epidemiolojia
Familia	Process / pipeline	Process / pipeline
Mwaka wa asili	1972 (Cox model); matched extension widely adopted 1970s–1980s	1958
Mwanzilishi	D. R. Cox (Cox model, 1972); stratification extension for matched designs by subsequent methodologists including D. C. Thomas	Edward L. Kaplan and Paul Meier
Aina	Semi-parametric survival regression for matched data	Nonparametric survival estimator
Chanzo asilia	Cox, D. R. (1972). Regression models and life-tables. Journal of the Royal Statistical Society: Series B (Methodological), 34(2), 187–202.	Kaplan, E. L., & Meier, P. (1958). Nonparametric estimation from incomplete observations. Journal of the American Statistical Association, 53(282), 457–481.
Majina mbadala	stratified Cox regression, conditional Cox model, matched survival analysis, Cox model for matched pairs	KM analysis, KM estimator, product-limit estimator, Kaplan-Meier curve
Zinazohusiana	4	5
Muhtasari	Matched Cox proportional hazards is a survival analysis method that extends the Cox regression model to appropriately handle data arising from matched study designs — matched cohorts or matched case-control studies with time-to-event outcomes. By stratifying the partial likelihood by matched set, the method eliminates confounding from matching factors without estimating their baseline hazard, yielding valid hazard ratio estimates that are free from matching-induced bias.	Kaplan-Meier (KM) analysis is a nonparametric method for estimating the survival function from time-to-event data. Introduced by Kaplan and Meier in 1958, it produces the classic step-function survival curve that shows the probability of surviving beyond each observed event time, correctly accounting for censored observations — participants who left the study or had not yet experienced the event by the end of follow-up. It is one of the most widely used techniques in clinical and epidemiological research.