Joint lifetime modeling with matrix distributions

Abstract Acyclic phase-type (PH) distributions have been a popular tool in survival analysis, thanks to their natural interpretation terms of aging toward its inevitable absorption. In this article, we consider an extension the bivariate setting for modeling joint lifetimes. contrast previous models literature that were based on separate estimation marginal behavior and dependence structure through copula, propose new time-inhomogeneous version multivariate PH (mIPH) class leads model lifetimes without separation. We study properties mIPH members provide adapted procedure allows right-censoring covariate information. show initial distribution vectors our construction can be tailored reflect random variables use multinomial regression determine influence covariates starting probabilities. Moreover, highlight flexibility parsimony, needed phases, introduced by time inhomogeneity. Numerical illustrations are given data set Frees et al., where 10 phases turn out sufficient reasonable fitting performance. As by-product, proposed approach enables causal association mechanism goes beyond statistical fit.