Stochastic calculus as a tool in survival analysis: a review

摘要

This paper gives a brief survey of the uses of stochastic calculus in survival analysis. The role played by martingale central limit theory in deriving asymptotic distributions of estimators and test statistics is described. The Nelson-Aalen estimator, the Kaplan-Meier estimator, Cox's proportional-hazards model, Aalen's additive-risk model, and a goodness-of-fit test for Cox's model are discussed. Sketches of the proofs of the main results are included.