  We consider a parametric modelling approach for survival data where
covariates are allowed to enter the model through multiple distributional
parameters, i.e., scale and shape. This is in contrast with the standard
convention of having a single covariate-dependent parameter, typically the
scale. Taking what is referred to as a multi-parameter regression (MPR)
approach to modelling has been shown to produce flexible and robust models with
relatively low model complexity cost. However, it is very common to have
clustered data arising from survival analysis studies, and this is something
that is under developed in the MPR context. The purpose of this article is to
extend MPR models to handle multivariate survival data by introducing random
effects in both the scale and the shape regression components. We consider a
variety of possible dependence structures for these random effects
(independent, shared, and correlated), and estimation proceeds using a
h-likelihood approach. The performance of our estimation procedure is
investigated by a way of an extensive simulation study, and the merits of our
modelling approach are illustrated through applications to two real data
examples, a lung cancer dataset and a bladder cancer dataset.
