Das lineare Regressionsmodell von Aalen zur Analyse von Überlebenszeiten unter Berücksichtigung zeitveränderlicher Kovariablen

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.