  We are concerned with the flexible parametric analysis of bivariate survival
data. Elsewhere, we have extolled the virtues of the "power generalized
Weibull" (PGW) distribution as an attractive vehicle for univariate parametric
survival analysis: it is a tractable, parsimonious, model which interpretably
allows for a wide variety of hazard shapes and, when adapted (to give an
adapted PGW, or APGW, distribution), covers a wide variety of important
special/limiting cases. Here, we additionally observe a frailty relationship
between a PGW distribution with one value of the parameter which controls
distributional choice within the family and a PGW distribution with a smaller
value of the same parameter. We exploit this frailty relationship to propose a
bivariate shared frailty model with PGW marginal distributions: these marginals
turn out to be linked by the so-called BB9 or "power variance function" copula.
This particular choice of copula is, therefore, a natural one in the current
context. We then adapt the bivariate PGW distribution, in turn, to accommodate
APGW marginals. We provide a number of theoretical properties of the bivariate
PGW and APGW models and show the potential of the latter for practical work via
an illustrative example involving a well-known retinopathy dataset, for which
the analysis proves to be straightforward to implement and informative in its
outcomes. The novelty in this article is in the appropriate combination of
specific ingredients into a coherent and successful whole.
