Journal of Statistical Planning and Inference 136 (2006) 1669 – 1686 www.elsevier.com/locate/jspi Testing dependence between the failure time and failure modes: An application of enlarged filtration Dario Gasbarra a , ∗ , S.B. Kulathinal b , Isha Dewan c , Aulikki Nissinen b a Rolf Nevanlinna Institute, University of Helsinki, P.L. 4, 00014 Helsinki, Finland b Department of Epidemiology and Health Promotion, National Public Health Institute, Mannerheimintie 166, 00300 Helsinki, Finland c Indian Statistical Institute, New Delhi, India Received 5 October 2003; received in revised form 10 May 2004; accepted 4 June 2004 Available online 24 August 2005 Abstract The model of independent competing risks provides no information for the assessment of competing failure modes if the failure mechanisms underlying these modes are coupled. Models for dependent competing risks in the literature can be distinguished on the basis of the functional behaviour of the conditional probability of failure due to a particular failure mode given that the failure time exceeds a fixed time, as a function of time. There is an interesting link between monotonicity of such conditional probability and dependence between failure time and failure mode, via crude hazard rates. In this paper, we propose tests for testing the dependence between failure time and failure mode using the crude hazards and using the conditional probabilities mentioned above. We establish the equivalence between the two approaches and provide an asymptotically efficient weight function under a sequence of local alternatives. The tests are applied to simulated data and to mortality follow-up data. © 2005 Elsevier B.V.All rights reserved. Keywords: Competing risks; Conditional probability; Crude hazards; Enlarged filtration; Functional delta method; Kolmogorov–Smirnov-type tests 1. Introduction In a follow-up study of mortality, it is observed that the contribution of death due to causes cardiovascular diseases, cancer, accident and suicide combined to total death decreases with ∗ Corresponding author. Tel.: +358 9 191 22765; fax: +358 9 191 22779. E-mail address: dag@rni.helsinki.fi (D. Gasbarra). 0378-3758/$ - see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jspi.2005.07.002