TABLE OF CONTENTS Where a variable is clearly endogeneous, although we might not wish to include it as an independent variable within our analysis, we might be able to increase the power of our analysis by considering it as informative about the end-point of the trial. For example, some endogeneous biological marker might be used to define an intermediate state of disease progression within what would now be a multi-state survival model. This would have the effect of reducing the number of fully censored observations. Treatment effects on the risk functions to both the intermediate state and the final end state can then be estimated, using the framework of competing risks described in the previous section. Hsieh et al. (1983) and Pocock et al. (1987) consider the analysis of two time-dependent events. However, as our previous discussion of multiple end-points in Chapter 4 made clear, the question of how to combine effects requires assigning some measure of relative importance to them. This has not always proved straight forward.
An alternative is to assume that the importance of the event is reflected in its effect on the final end-point itself. Lagakos (1977) described an approach for using auxiliary information for this purpose within a simple exponential survival framework. Finkelstein and Schoenfeld (1994) present a method that uses the time to the intermediate state as a covariate for subsequent survival. Their simulations suggest that although improvements in precision of the estimates of main interest are possible, losses of efficiency are...
