Goodness of Fit Tests for Multivariate Counting Process Models with Applications

Authors: Sun, Yanqing¹; Tiwari, Ram C.¹; Zalkikar, Jyoti N.²

Source: Scandinavian Journal of Statistics, Volume 28, Number 1, March 2001 , pp. 241-256(16)

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Abstract:

In this paper, we develop some distribution-free tests for checking the adequacy of the parametric forms of the intensity processes of a multivariate counting process model. The proposed tests, based in Khmaladze's transformations, are derived from the transforms of weighted aggregated martingale residual processes. The transformed processes converge weakly to independent Gaussian martingales under the assumed model. The distribution-free tests, such as Kolmogorov-Smirnov and Cramer-von Mises type tests, are appropriately defined to account for deviations in each of the transformed aggregated martingale residual processes. Consistency of the tests are discussed. The tests are applicable to multiplicative intensity models such as a competing risks model as well as to non-multiplicative intensity models such as a constant relative or excess mortality model. A small simulation study is conducted and an illustration to a real data example is provided.

Keywords: cause-specific hazard rate; censored data; Cramer-von Mises type test; Khamaladze's transformation; Kolmogorov-Smirnov type test; parametric family

Document Type: Original article

DOI: http://dx.doi.org/10.1111/1467-9469.00234

Affiliations: 1: The University of North Carolina at Charlotte, 2: Florida International University

Publication date: 2001-03-01