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On Goodness‐of‐Fit Tests for Aalen's Additive Risk Model
Author(s) -
GANDY AXEL,
JENSEN UWE
Publication year - 2005
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2005.00457.x
Subject(s) - goodness of fit , mathematics , martingale (probability theory) , multiplicative function , statistics , econometrics , hazard , null hypothesis , proportional hazards model , mathematical analysis , chemistry , organic chemistry
. 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.