Marker Processes in Survival Analysis

In the development of many diseases there are often associated variables that continuously measure the progress of an individual towards the final expression of the disease (failure). Such variables are stochastic processes, here called marker processes, and, at a given point in time, they may provide information about the current hazard and subsequently on the remaining time to failure. Here we consider a simple additive model for the relationship between the hazard function at time t and the history of the marker process up until time t. We develop some basic calculations based on the model. Interest is focused on statistical applications for makers related to estimation of the survival distribution of time to failure. Possibilities include (i) the use of markers as surrogate responses for failure with censored data; (ii) the use of markers as predictors of the time elapsed since onset of a survival process in prevalent individuals, and (iii) the use of markers to adjust for onset confounding. Attention is primarily directed to (i) and (ii) and the particular issue of the potential gains in efficiency incurred by using marker process information. Some examples are noted, with some of the results illustrated for the case where the marker process is a Poisson process. Where appropriate, a brief discussion is given regarding motivation for the above issues from such practical problems as estimation of the incubation distribution of AIDS, and estimation of time to tumor distributions in tumorigenicity experiments