On Goodness-of-Fit Tests for Aalen's Additive Risk Model |
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Authors: | AXEL GANDY UWE JENSEN |
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Institution: | Department of Stochastics, University of Ulm;and Institute for Applied Mathematics and Statistics, University of Hohenheim |
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Abstract: | Abstract. In this paper we propose goodness-of-fit tests for Aalen's additive risk model. They are based on test statistics the asymptotic distributions of which are determined under both the null and alternative hypotheses. The results are derived using martingale techniques for counting processes. An important feature of these tests is that they can be adjusted to particular alternatives. One of the alternatives we consider is Cox's multiplicative risk model. It is perhaps remarkable that such a test needs no estimate of the baseline hazard in the Cox model. We present simulation studies which give an impression of the performance of the proposed tests. In addition, the tests are applied to real data sets. |
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Keywords: | Aalen model additive risk model counting process Cox regression goodness-of-fit martingale residuals survival analysis |
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