A Consistent Estimator of the Absolute Deviation Between Predicted and Observed Survival Functions

• Activity Number: 360
• Type: Contributed
• Date/Time: Tuesday, August 3, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Matthias Schmid*+
• Companies: University of Erlangen-Nuremberg
• Keywords: survival analysis ; prognostic value ; model misspecification ; prediction error

Abstract

Distance-based measures of prediction error have become a popular tool to assess and compare the prognostic value of survival models. The talk is focused on the properties of an estimator suggested by Schemper and Henderson (Biometrics 2000, "SH estimator"), which quantifies the time-dependent absolute distance between predicted and observed survival functions of the observations in a data set. It is shown that the SH estimator is not robust w.r.t. misspecification of the working model, i.e., the estimator may be biased if the assumptions needed for a consistent estimation of the survival functions are not met. To correct for the misspecification bias, an alternative estimator of the absolute distance between survival functions is suggested. The new estimator, which is based on inverse-probability-of-censoring weights, proves to be consistent for the true mean absolute prediction error.