  In this paper, we derive the joint distribution of progression-free and
overall survival as a function of transition probabilities in a multistate
model. No assumptions on copulae or latent event times are needed and the model
is allowed to be non-Markov. From the joint distribution, statistics of
interest can then be computed. As an example, we provide closed formulas and
statistical inference for Pearson's correlation coefficient between
progression-free and overall survival in a parametric framework. The example is
inspired by recent approaches to quantify the dependence between
progression-free survival, a common primary outcome in phase III trials in
oncology, and overall survival. We complement these approaches by providing
methods of statistical inference while at the same time working within a much
more parsimonious modelling framework. Our approach is completely general and
can be applied to other measures of dependence. We also discuss extensions to
nonparametric inference. Our analytical results are illustrated using a large
randomized clinical trial in breast cancer.
