A general family of distributions for longitudinal dependence with special reference to event histories

Event histories play an increasingly important role in medical studies. Examples include times between recurrences of tumours, as with bladder cancer, and between repeated infections, as with chronic granulotomous disease. A general method for generating new distributions is proposed by introducing an intensity function into a density. This procedure yields, as special cases, several distributions already proposed in the literature. The families of distributions based on the Pareto distribution are of particular interest for event history analysis because of their relationship to the Laplace transform of a gamma distribution. They can yield multivariate distributions, with longitudinal (serial) dependence by a procedure similar to updating in the Kalman filter and with uniform dependence in a similar way to copulas. For longitudinal dependence, several such updating procedures are proposed.