Survival estimation using splines

Biometrics. 1986 Sep;42(3):495-506.


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.

Publication types

  • Research Support, Non-U.S. Gov't
  • Research Support, U.S. Gov't, Non-P.H.S.
  • Research Support, U.S. Gov't, P.H.S.

MeSH terms

  • Animals
  • Biometry
  • Dogs
  • Humans
  • Monte Carlo Method
  • Neoplasms, Radiation-Induced / etiology
  • Osteosarcoma / etiology
  • Plutonium
  • Probability
  • Research Design
  • Survival*


  • Plutonium