Survival estimation using splines.
A nonparametric maximum likelihood procedure is given for estimating the survivor function from right-censored data. It approximates the hazard rate by a simple function such as a spline, with different approximations yielding different estimators. A special case is that proposed by Nelson (1969, Journal of Quality Technology 1, 27-52) and Altshuler (1970, Mathematical Biosciences 6, 1-11). The estimators are uniformly consistent and have the same asymptotic weak convergence properties as the Kaplan-Meier (1958, Journal of the American Statistical Association 53, 457-481) estimator. However, in small and in heavily censored samples, the simplest spline estimators have uniformly smaller mean squared error than do the Kaplan-Meier and Nelson-Altshuler estimators. The procedure is extended to estimate the baseline hazard rate and regression coefficients in the Cox (1972, Journal of the Royal Statistical Society, Series B 34, 187-220) proportional hazards model and is illustrated using experimental carcinogenesis data.
Whittemore
A S
AS
Keller
J B
JB
D000818:Animals; D001699:Biometry; D004285:Dogs; D006801:Humans; D009010:Monte Carlo Method; D009381:Neoplasms, Radiation-Induced / Q000209:etiology; D012516:Osteosarcoma / Q000209:etiology; D011005:Plutonium; D011336:Probability; D012107:Research Design; D013534:Survival
D011005:Plutonium