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Biometrika Advance Access published online on November 19, 2007
Biometrika, doi:10.1093/biomet/asm062
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© 2007 Biometrika Trust

Articles

A general approach to the predictability issue in survival analysis with applications

Enno Mammen

Department of Economics, University of Mannheim, L7, 3-5, 68131 Mannheim, Germany emammen{at}rumms.uni-mannheim.de

Jens Perch Nielsen

Cass Business School, City University, 106 Bunhill Row, London EC1Y 8TZ, U.K. festinalente{at}nielsen.mail.dk


  Abstract

Very often in survival analysis one has to study martingale integrals where the integrand is not predictable and where the counting process theory of martingales is not directly applicable, as for example in nonparametric and semiparametric applications where the integrand is based on a pilot estimate. We call this the predictability issue in survival analysis. The problem has been resolved by approximations of the integrand by predictable functions which have been justified by ad hoc procedures. We present a general approach to the solution of this problem. The usefulness of the approach is shown in three applications. In particular, we argue that earlier ad hoc procedures do not work in higher-dimensional smoothing problems in survival analysis.

Key Words: Bias-correction • Kernel hazard estimation • Martingale central limit theorem • Nonparametric smoothing • Predictability • Survival analysis


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