Dynamic path analysis-a new approach to analyzing time-dependent covariates

In this article we introduce a general approach to dynamic path analysis. This is an extension of classical path analysis to the situation where variables may be time-dependent and where the outcome of main interest is a stochastic process. In particular we will focus on the survival and event history analysis setting where the main outcome is a counting process. Our approach will be especially fruitful for analyzing event history data with internal time-dependent covariates, where an ordinary regression analysis may fail. The approach enables us to describe how the effect of a fixed covariate partly is working directly and partly indirectly through internal time-dependent covariates. For the sequence of times of event, we define a sequence of path analysis models. At each time of an event, ordinary linear regression is used to estimate the relation between the covariates, while the additive hazard model is used for the regression of the counting process on the covariates. The methodology is illustrated using data from a randomized trial on survival for patients with liver cirrhosis.