OBJECTIVES: A common critic of partitioned survival models is that they model progression free survival (PFS) and overall survival (OS) independent of each other, this becomes especially problematic in the probabailsiitc sensitivity analysis (PSA). Our objective was to resolve this by develop a new framework to jointly model theparametric extrapolations of progression-free survival (PFS) and overall survival (OS) and to assess the joint uncertainty around the associated parameter estimates.

METHODS: We used a copula method to link OS and PFS survivals. A copula is a multivariate distribution with marginals that are uniform over (0,1). The used copula is a bivariate normal distribution. The approach results in a joint density of OS and PFS. The parameters of the joint distribution and the joint covariance matrix include the parameters of the extrapolation function of OS and PFS (e.g. lognormal, Weibull) and a correlation parameter of the bivariate Normal distribution. Extrapolation functions can be different for PFS and OS. The uncertainty around the parameter estimates is assessed by using asymptotic properties of Maximum Likelihood estimates. We compute the total uncertainty around the parameter estimates by means of the Frobenius norm of the variance-covariance matrices.

RESULTS: The total uncertainty associated with the independent modelling of OS and PFS is 0.0064, whereas the uncertainty associated with the joint modelling is 0.0057, approximately 10% less than the standard independent modelling approach. The joint approach can be easily implemented in Excel-based models.

CONCLUSIONS: By using joint modelling we prevent the parametric extrapolations of PFS and OS to cross when running the probabilistic sensitivity analysis. Further, by accounting for the correlation between the two outcomes the total uncertainty around the estimates is reduced. Finally, this approach can be extended to other outcomes like treatment duration and PFS.