Patient-level health economic data collected alongside clinical trials are an important component of the process of technology appraisal, with a view to informing resource allocation decisions. For end of life treatments, such as cancer treatments, modelling of cost-effectiveness/utility data may involve some form of partitioned survival analysis, where measures of health-related quality of life and survival time for both pre- and post-progression periods are combined to generate some aggregate measure of clinical benefits (e.g. quality-adjusted survival). In addition, resource use data are often collected from health records on different services from which different cost components are obtained (e.g. treatment, hospital or adverse events costs). A critical problem in these analyses is that both effectiveness and cost data present some complexities, including non-normality, spikes, and missingness, that should be addressed using appropriate methods. Bayesian modelling provides a powerful tool which has become more and more popular in the recent health economics and statistical literature to jointly handle these issues in a relatively easy way. This paper presents a general Bayesian framework that takes into account the complex relationships of trial-based partitioned survival cost-utility data, potentially providing a more adequate evidence for policymakers to inform the decision-making process. Our approach is motivated by, and applied to, a working example based on data from a trial assessing the cost-effectiveness of a new treatment for patients with advanced non-small-cell lung cancer.