Event History Modeling: Causality and Interdependence

In many fields extensive data are collected repeatedly over time. The advancing computerization of society makes such detailed follow-up data increasingly available. To extract useful information from the data one needs good statistical methods; indeed ne w methods are needed, especially when it comes to complex event history data. An emerging issue in such data is the interdependence which occurs in family data, in infectious disease data etc. In Oslo we have an internationally strong group in survival a nd event history analysis. Pioneering work in the use of counting processes, the present mathematical basis of event history analysis, was made in this group. Counting process theory is internationally used in numerous textbooks and papers in statistics. In spite of the success of counting process theory, a number of issues remain unresolved, especially when it comes to complex data collected over time. A major approach to modeling stochastic processes consists in defining quantities that connect the pas t and the future. These are the intensities of counting processes, the local characteristics of stochastic differential equations etc. This can be termed a dynamic point of view, and is naturally connected to emerging ideas of causal modeling. We develop a time-dependent version of graphical models, called dynamic path analysis, thereby extending the concepts of direct, indirect and total effects. Analysis is carried out by an additive regression model for counting processes. Further connections are drawn to the concept of Granger causality in econometrics. We believe this approach has considerable promise in analysis how observed processes influence one another. We will show how related ideas are also of relevance in infectious disease studies and in th e new field of systems biology. Special issues are the interdependence between individuals which can de modeled through dynamic analysis, and network models which are also defined through dynamic mechanism.