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Aydemir, Sibel and Aydemir, Ülker and Dirschedl, Peter (1996): Das lineare Regressionsmodell von Aalen zur Analyse von Überlebenszeiten unter Berücksichtigung zeitveränderlicher Kovariablen. Collaborative Research Center 386, Discussion Paper 25
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Abstract

Data from clinical studies often contain time-dependent covariates, e.g. events like transplantation or an adverse drug reaction, or the changing measurements of laboratory data. The common approach uses only the covariate information at time t=0 for regression analyses, but this baseline analysis is not very satisfying. This paper applies the linear counting process by Aalen for failure time analysis, modified to deal with time-dependent covariates. In the main part we describe methods to estimate and visualize the cumulated regression function with respect to time-dependent covariates. After introducing a test for significance of the influence of covariates we display different methods to investigate model validity depending on martingale residuals, or by use of the Arjas plot. Coding and interpretation problems are shortly discussed. Results are illustrated with data from the Stanford Heart Transplantation Study and a study on Oropharynx carcinoma.