Random time changes for multivariate counting processes

If N is a univariate counting process with intensity process A, it is well known that N[ψ−1(.)] is a Poisson process with parameter 1 if ψ is the cumulative intensity process. This paper proves multivariate analogues of this result and points out their usefulness in the statistical analysis of data appearing in disciplines like reliability life testing, medical survival studies, demography and insurance. So far, the full power of existing theory of random time changes has not been utilized, not even in the univariate case. This paper points out how the scope of some existing methods can be extended considerably, and in particular methods based on the total time on test (or aggregate lifetime) statistic. An example from disability insurance and one from the mating of Drosophila are used for illustration.