title: Dynamic path analysis for event time data: large sample properties and inference.
abstract: We consider the situation with a survival or more generally a counting process endpoint for which we wish to investigate the effect of an initial treatment. Besides the treatment indicator we also have information about a time-varying covariate that may be of importance for the survival endpoint. The treatment may possibly influence both the endpoint and the time-varying covariate, and the concern is whether or not one should correct for the effect of the dynamic covariate. Recently Fosen et al. (Biometrical J 48:381-398, 2006a) investigated this situation using the notion of dynamic path analysis and showed under the Aalen additive hazards model that the total effect of the treatment indicator can be decomposed as a sum of what they termed a direct and an indirect effect. In this paper, we give large sample properties of the estimator of the cumulative indirect effect that may be used to draw inferences. Small sample properties are investigated by Monte Carlo simulation and two applications are provided for illustration. We also consider the Cox model in the situation with recurrent events data and show that a similar decomposition of the total effect into a sum of direct and indirect effects holds under certain assumptions.
authors.affiliation: Department of Biostatistics, University of Southern Denmark, J.B. Winslows Vej 9B, 5000 Odense C, Denmark. tmartinussen@health.sdu.dk
authors.forename: T
authors.initials: T
authors.lastname: Martinussen
mesh_terms: D003198:Computer Simulation; D005260:Female; D006801:Humans; D008136:Longevity; D008297:Male; D015233:Models, Statistical; D009010:Monte Carlo Method; D013269:Stochastic Processes; D016019:Survival Analysis; D016896:Treatment Outcome
references.citation: Stat Med. 1989 Aug;8(8):907-25
references.pmid: 2678347
references.citation: Hepatology. 1983 Nov-Dec;3(6):889-95
references.pmid: 6354903
references.citation: Stat Med. 1997 Jan 15-Feb 15;16(1-3):273-83
references.pmid: 9004397
references.citation: Lifetime Data Anal. 2006 Jun;12(2):143-67
references.pmid: 16817006
references.citation: Int J Epidemiol. 2002 Feb;31(1):163-5
references.pmid: 11914314
references.citation: Epidemiology. 1992 Mar;3(2):143-55
references.pmid: 1576220
references.citation: Lifetime Data Anal. 2002 Sep;8(3):247-62
references.pmid: 12182121
references.citation: Biom J. 2006 Jun;48(3):381-98
references.pmid: 16845903
references.citation: Stat Med. 1993 Sep 15;12(17):1569-88
references.pmid: 8235179
references.citation: Proc Natl Acad Sci U S A. 2008 Sep 9;105(36):13274-9
references.pmid: 18711139