Abstract: Regression models in survival analysis based on homogeneous and
inhomogeneous phase-type distributions are proposed. The intensity function in
this setting plays the role of the hazard function, having the additional benefit
of being interpreted in terms of a hidden Markov structure. For unidimensional
intensity matrices, we recover the proportional hazard and accelerated failure
time models, among others. However, when considering higher dimensions, the
proposed methods are only asymptotically equivalent to their classical
counterparts and enjoy greater flexibility in the body of the distribution. For
their estimation, the latent path representation of inhomogeneous Markov models
is exploited. Consequently, an adapted EM algorithm is provided for which the
likelihood increases at each iteration. The methodology is universal but is
particularly well-suited for actuarial applications.