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SURVIVAL ESTIMATION USING SPLINES
Citation:
Whittemore, A. SURVIVAL ESTIMATION USING SPLINES. U.S. Environmental Protection Agency, Washington, D.C., EPA/600/J-86/525.
Description:
A non parametric maximum likelihood procedure is given for estimating the survivor function from right-censored data. t approximates the hazard rate by a simple function such as a spline, with different approximations yielding different estimators. pecial case is that proposed by Nelson (1969, Journal of Quality Technology 1,27-52) and Altshuler (1970, Mathematical Biosciences 6, 1-11). he 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. owever, 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. he procedure is extended to estimate the baseline hazard rate and regression of 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.