Markers Models in Survival Analysis and Applications to Issues Associated with AIDS

Jewell and Kalbfleisch (1992) consider the use of marker processes for applications related to estimation of the survival distribution of time to failure. Marker processes were assumed to be stochastic processes that, at a given point in time, provide information about the current hazard and consequently on the remaining time to failure. Particular attention was paid to calculations based on 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. Specific applications to the analysis of AIDS data included the use of markers as surrogate responses for onset of AIDS with censored data and as predictors of the time elapsed since infection in prevalent individuals. Here we review recent work on the use of marker data to tackle these kinds of problems with AIDS data. The Poisson marker process with an additive model, introduced in Jewell and Kalbfleisch (1992) may be a useful "test" example for comparison of various procedures.

Generalizations of Current Status Data With Applications

In estimation of a survival function, current status data arises when the only information available on individuals is their survival status at a single monitoring time. Here we briefly review extensions of this form of data structure in two directions: (i) doubly censored current status data, where there is incomplete information on the origin of the failure time random variable, and (ii) current status information on more complicated stochastic processes. Simple examples of these data forms are presented for motivation.