Large Sample Theory for Schemper's Measures of Explained Variation in the Cox Regression Model

Autor: Ethan Reiner, Philippe Flandre, John O'Quigley
Rok vydání: 1999
Předmět:
Zdroj: Journal of the Royal Statistical Society: Series D (The Statistician). 48:53-62
ISSN: 1467-9884
0039-0526
DOI: 10.1111/1467-9884.00170
Popis: Two new measures aimed at quantifying the predictive precision of a proportional hazards regression model have recently been introduced by Schemper, who argued that the measures could provide a useful generalization to the notion of the proportion of variation explained for linear models. Other approaches to the problem have a potential advantage over the Schemper measures, that of having a clearly defined population quantity to which their suggested measures converge. The purpose of this paper is to work out population characteristics of the Schemper measures. Large sample comparisons then become possible. On the basis of this population study we conclude that the Schemper measures have some weaknesses that have not previously been observed, e.g. the fact that the population counterparts of the measures depend on the unknown censoring mechanism even for mechanisms that are independent of time, a common working assumption is such contexts. For the balanced exponential model without censoring, studied by Schemper, we derive exact asymptotic properties, enabling us to conclude that the two measures converge to the same population quantity and that they are bounded absolutely by the value 0.5. The population model enables us to see how it would be possible to derive an estimator converging to a quantity that does not depend on an independent censoring mechanism.
Databáze: OpenAIRE
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