Variate generation for a nonhomogeneous poisson process with time dependent covariates

Abstract

Algorithms are developed for generating a sequence of event times from a nonhomogeneous Poisson process that is influenced by the values of covariates that vary with time. Closed form expressions for random variate generation are shown for several baseline intensity and link functions. Two specific models linking the baseline process to the general model are considered: the accelerated time model and the proportional intensity model. In the accelerated time model, the cumulative intensity function of a nonhomogeneous Poisson process under covariate effects is , where z is a covariate vector, ⋀0(t) is the baseline cumulative intensity function and ψ(z) is the link function. In the proportional intensity model, the cumulative intensity function of a nonhomogeneous Poisson process under covariate effects is , where λ0(t) is the baseline intensity function.